In this study, a rectangular cross-section sonic black hole (SBH) is explored and a one-dimensional model equation for the acoustic field inside it is presented. The model equation's applicability is verified through a comparison with the corresponding two-dimensional Helmholtz equation. A general analytical solution, which takes into account the SBH's quadratically varying internal cross-section, is derived using linearly independent confluent Heun functions. To investigate the acoustic wave behavior in the SBH, the wave splitting method is utilized to obtain forward and backward acoustic pressure waves, and the reflection coefficient is calculated. To confirm the validity of the analytical solution, a comparison is made with numerical results obtained from the Riccati equation. Within the context of this study, a detailed discussion is provided regarding the applicability of the analytical solution.
This paper presents a new Gradient Refractive Index (GRIN) structure, which utilizes a series of thin plates made of functionally graded material separated by narrow gaps, to control elastic P-wave fields. The proposed technique is demonstrated through two basic examples of wave manipulation: focusing and deflecting, but has the potential for a wide range of applications. To verify the theoretical calculations, COMSOL Multiphysics simulation software was utilized to solve the full Navier–Lamé equations. Overall, the results of this study demonstrate the effectiveness of the proposed GRIN structure in manipulating elastic P-wave fields.
Exact analytical solution for shear horizontal wave propagation through locally periodic structures realized by viscoelastic functionally graded materials
The paper presents a novel comprehensive exact analytical solution for modeling linear shear-horizontal
(SH) wave propagation in an isotropic inhomogeneous layer made of functionally graded material, using
local Heun functions. The layer is a composite of two materials with varying properties represented by
spatial variations following the square of the sine function. The Voigt–Kelvin model is used to account for
material losses. The study focuses on SH waves incident at a specific angle and employs the wave splitting
technique to analyze forward and backward waves, facilitating the computation of reflection and transmission
coefficients at any point in the inhomogeneous structure. The proposed solution utilizes the periodic nature
of material functions and employs the Floquet–Bloch theory to derive an exact analytical solution. This
approach is particularly suited for cases where SH waves encounter locally periodic functionally graded
material. A Riccati equation-based verification is conducted to compare the frequency-dependent modulus of
the reflection coefficient obtained from the analytical solution with numerically solved results. The presented
work provides a comprehensive and versatile analytical solution for studying linear SH wave propagation in
locally inhomogeneous isotropic layers, contributing to the theoretical understanding of elastic wave fields and
Fast design of non-uniform acoustic waveguides with prescribed eigenfrequencies
In this article we address the issue of finding acoustic and elastic resonator shapes corresponding to given eigenfrequencies. This problem has a wide range of applications spanning from ultrasonics through the music acoustics to metamaterials. We employ the previously published solution to the Webster horn equation and use it to train an artificial neural network to solve the inverse eigenvalue problem. Subsequently, it is shown how the isospectrality and scalability properties might provide a whole class of fast designed resonator shapes.
Novel design for acoustic silencers for ducts with flow based on the bound states in the continuum
The concept of bound states in the continuum and leaky resonances is utilized in the design of a reactive silencer that can effectively suppress significant spectral lines while maintaining a low-pressure drop within the flow duct and does not require additional installation space. By adjusting the geometrical parameters of thin plates that are embedded in a waveguide, quasi-bound states (or leaky resonances) can be achieved. An optimization algorithm is employed to fine-tune these parameters, and this process is illustrated through two specific examples. The resulting design is validated through numerical simulations that account for the effects of low Mach number flow. The investigations showed that it is possible to design a spectral silencer with low-pressure drop based on the chosen approach. By combining several leaky resonances, stopbands were created with a transmission loss of up to 17 dB in a frequency range of 10 Hz.
Numerical study of the behavior of rectangular acoustic black holes for sound absorption in air
In this work, the behavior of acoustic black holes (ABHs) serving as an anechoic termination of air-filled waveguides with a rectangular cross-section is numerically studied. These ABHs consist of a set of rigid ribs separated by narrow slits, whose height smoothly varies along the structure and whose aim is to slow-down the impinging acoustic wave and cause its absorption. For the purpose of this study, a 2D mathematical model based on linearized Navier–Stokes equations and employing the finite element method has been proposed, which allows for an accurate capturing the thermoviscous losses in the acoustic boundary layer adjacent to the solid–fluid interfaces, as well as the effects connected with geometrical details of the ABHs’ inner structure. The numerical results show that in rectangular ABHs with a fine internal structure, the acoustic wave slow-down plays a significant role and that absorption properties are strongly dependent on their inner structure details. Simplified 1D mathematical models of rectangular ABHs based on the Riccati equation or transfer matrix method have also been proposed. These simplified models are computationally highly efficient, as it has been demonstrated, they provide accurate results, especially in the case of ABHs with a fine internal structure, which feature superior acoustic energy absorbing properties.
Willis couplings in continuously varying cross-sectional area duct
Acoustic wave propagation in a one-dimensional periodic and asymmetric duct is studied theoretically and numerically to derive the effective properties. Closed form expressions for these effective properties, including the asymmetric Willis coupling, are derived through truncation of the Peano–Baker series expansion of the matricant (which links the state vectors at the two sides of the unit-cell) and Padé's approximation of the matrix exponential. The results of the first-order and second-order homogenization (with Willis coupling) procedures are compared with the numerical results. The second-order homogenization procedure provides scattering coefficients that are valid over a much larger frequency range than the usual first-order procedure. The frequency well below which the effective description is valid is compared with the lower bound of the first Bragg bandgap when the profile is approximated by a two-step function of identical indicator function, i.e., two different cross-sectional areas over the same length. This validity limit is then questioned, particularly with a focus on impedance modeling. This article attempts to facilitate the engineering use of Willis materials.
A new class of approximate analytical solutions of the Pridmore-Brown equation
There is only a limited amount of known analytical solutions to the Pridmore-Brown equation, mostly employing asymptotic behavior for a certain frequency limit and specifically chosen flow profiles. In this paper, we show the possibility of transformation of the Pridmore-Brown equation into the Schrödinger-like equation for the case of two-dimensional homentropic mean flow without critical layers. The corresponding potential that depends on the mean flow profile can then be approximated by a quartic polynomial, leading to a triconfluent Heun equation whose solution based on the triconfluent Heun functions is generally known. The quality of this approximation procedure is presented for the case of symmetric polynomial flow profiles for various values of polynomial order and the Mach number. A more detailed example is then shown for a quadratic mean flow profile, where the solution is accurate up to the third order of the Mach number.
An algebraic correction for the Westervelt equation to account for the local nonlinear effects in parametric acoustic array
This work presents a simple computational approach for the calculation of parametrically generated low-frequency sound fields. The Westervelt wave equation is employed as a model equation that accounts for the wave diffraction, attenuation, and nonlinearity. As it is known that the Westervelt equation captures the cumulative nonlinear effects correctly and not the local ones, an algebraic correction is proposed, which includes the local nonlinear effects in the solution of the Westervelt equation. This way, existing computational approaches for the Westervelt equation can be used even in situations where the generated acoustic field differs significantly from the plane progressive waves, such as in the near-field, and where the local effects manifest themselves strongly. The proposed approach is demonstrated and validated on an example of the parametric radiation from a baffled circular piston.
On the role of resonance and thermoviscous losses in an implementation of “acoustic black hole” for sound absorption in air
In this work, we propose a mathematical model of a sound-absorbing structure for anechoic duct termination, commonly called the acoustic black hole. The structure consists of a set of rigid rings separated by narrow fluid-filled cavities. There are holes in the centers of the rings, whose radii smoothly vary along the structure. According to the previously published works, wave speed in this structure can theoretically decrease to zero value, which results in the reduction of the reflection coefficient. The proposed model is based on the linearized Navier–Stokes equations formulated in 2D axisymmetric cylindrical coordinates, which are solved numerically in the frequency domain employing the finite element method. This way, thermoviscous losses in the acoustic boundary layer adjacent to the fluid–solid interfaces, especially in the narrow cavities, are accounted for properly. The numerical results show that the absorption of acoustic energy in this structure is connected with resonances taking place in the cavities forming annular resonators, rather than with the acoustic wave slow-down. This effect has not been captured in the previously published models. It is shown that the geometrical details of the structure strongly influence its behavior, indicating the possibility of its optimization to serve as an efficient absorber of acoustic energy in a relatively wide frequency range.
On the acoustic effects of sonic crystals in heat exchanger arrangements
Heat exchangers can be found in a large number of technical systems and installations. They are usually operated in combination with other machines, such as axial fans, in order to remove or supply heat to a system. The heat exchanger can influence the existing flow field and thus lead to increased noise emission from fans located downstream of the heat exchanger. This can be observed, for example, in air conditioning units in which axial fans operate in combination with heat exchangers. Even though this mechanism is known, it is not yet understood how the heat exchanger affects the sound propagation of the sound produced by the downstream machine. For example, the heat exchanger may lead to a change in directional characteristics or specific frequencies may be attenuated. In order to better understand the interaction of the heat exchanger with the sound field, sound power measurements were carried out on various heat exchangers and the sound propagation was simulated numerically. It was shown that the sound attenuation due to the interaction with the periodic tube array is detectable in heat exchangers and that this leads to a sound reduction at the Bragg frequency. Based on its filling factor, the heat exchanger can reduce the sound propagation in certain frequency bands by up to 10 dB if the geometrirical properties are selected suitably. The simulations of a single unit cell confirm in very good agreement with the experimental results. This allows the conclusion that the approach presented in this paper is a cost-effective way to model acoustic effects of heat exchangers. Furthermore, sound attenuation effects by the heat exchanger were caused by thermoviscous effects on the cooling fins and dimensions of the heat exchanger housing.
Parametric acoustic array lensed by a gradient-index phononic crystal
This work presents a theoretical study of a parametric transmitter employing a small ultrasonic transducer and an acoustic lens for the collimation of the non-directional primary ultrasonic waves into a highly-directional beam. The acoustic lens is represented by a gradient-index phononic crystal (GRIN PC) composed of an array of toroidal scatterers. Parameters of the GRIN PC lens are determined employing an optimization procedure that maximizes the minimum value of the primary-wave amplitude over a wide frequency range at a distant point in front of the transducer-lens system. The Westervelt equation is used as a wave equation taking into account diffraction, nonlinearity, and thermoviscous attenuation. The wave equation is solved numerically in the quasi-linear approximation in the frequency domain employing the finite element method. The numerical results show that employing a simple GRIN PC lens, a highly-directional low-frequency beam can be parametrically radiated from a small ultrasonic transducer.
Surface Love-type waves propagating through viscoelastic functionally graded media
This paper deals with the solution of the model equations, which describes the propagation of the surface Love-type waves in a waveguide structure consisting of a lossy isotropic inhomogeneous layer placed on a viscoelastic homogeneous substrate. The paper points to the possibility of using the triconfluent Heun differential equation to solve the model equation. The exact analytical solution within the inhomogeneous layer is expressed by the triconfluent Heun functions. The exact solutions are general in the sense that only the internal parameters of the triconfluent Heun functions can change the spatial dependencies of the material parameters in the inhomogeneous layer's thickness direction. Based on the comparison, the limits of the WKB method applicability are discussed. It is further demonstrated that substrate losses affect the dispersion characteristics only to a small extent. Using examples in which the surface layer is represented by functionally graded materials, it was shown that the distance between the modes can be influenced through those materials.
The influence of periodic structires on sound propagation through heat exchangers
The study deals with a possibility to formulate the complex fluid–structure interaction problem of noise generation due to the unsteady flow in corrugated pipes by phenomenological formulation. Although the details of fluid dynamics are not accessible this way, the computational framework is much less demanding and the key features are still present. The van der Pol-like equations serve as a model of self-sustained sources coupled to the acoustic resonances of the tube. The effects of the sound field convection are discussed. A closer case-study investigation using linear stability analysis and a semi-analytical solution is presented. Numerical analysis investigating the flow velocity sweeps and fitting the model to the experimental data follows. The proposed system exhibits the key features known from experiments such as mode-locking and hysteresis and is capable of capturing the experimental data correctly.
A wide class of analytical solutions of the Webster equation
This paper aims at presenting closed-form general analytical solutions of the Webster equation describing plane elastic or acoustic waves. The considered radius functions of nonuniform cross-sectioned rods or ducts are based on the triconfluent Heun functions and contain some optional parameters enabling us to set various profiles of the radius functions in a relatively wide range, while it is possible to employ the presented exact general analytical solution of the Webster equation for all selected profiles. If the radius functions are predetermined, then the derived general analytical solution can also be employed for their triconfluent Heun approximations, including certain polynomial ones. The applicability and correctness of the derived analytical solutions are demonstrated by calculations of natural frequencies and mode shapes for representative radius functions while the results based on approximate analytical solutions are verified numerically. (C) 2019 Elsevier Ltd. All rights reserved.
Electromagnetic waves in graded-index planar waveguides
The propagation of guided TE and TM modes through graded-index planar waveguides is reported in this paper. Both a real-valued and complex-valued position-dependent refractive index are supposed for a film layer. It is possible to set various refractive index profiles based on five distribution parameters. For the position-dependent refractive index, the governing equations are transformed to Heun's differential equation, an exact local solution expressed in terms of local Heun functions. The general nature of these functions is demonstrated based on four degenerate cases of Heun's equation. The calculation of guided modes requires evaluation of the general solution in the interval containing two regular singular points. For this purpose, the generalized Heun function is introduced and employed in general solutions to the governing equations. The applicability of the generalized solutions is demonstrated by the calculation of guided modes for both the real-valued and complex-valued refractive index.
Optimized compact wideband reactive silencers with annular resonators
This paper presents a theoretical examination of wave propagation in a cylindrical duct loaded with an array of closely spaced flush-mounted annular resonators forming a simple reactive silencer. A semi-analytical mathematical model is proposed considering higher evanescent modes in the duct and plane-wave- and first transverse mode in annular resonators. Viscothermal losses in annular resonators are considered by employing the equivalent-fluid model. A heuristic optimization algorithm based on the proposed mathematical model is used to maximize the minimum transmission loss in a given frequency range. The numerical results show that multiple resonances of the individual resonators can be effectively utilized to design compact (thin) silencers with a wide frequency range and a relatively small number of resonators. The numerical results are validated by comparison with finite element simulations.
A versatile computational approach for the numerical modelling of parametric acoustic array
This work presents a versatile computational approach for the numerical modeling of a parametrically generated low-frequency sound. The proposed method is based on the quasi-linear approximation, and it does not employ the paraxial approximation. The primary acoustic field is calculated by the Rayleigh integral or the boundary element method; the secondary difference-frequency field is calculated by the finite element method. As governing wave equations, a general second-order wave equation for acoustic pressure, the Westervelt equation, and Kuznetsov equation are tested, and the corresponding numerical results are compared. The proposed approach allows studying the near-field, far-field, as well as the off-axis field of the difference-frequency wave parametrically radiated from complex emitters. As numerical examples, parametric radiation from a baffled piston and a piston combined with a horn are examined.
Analytical solutions for elastic SH-waves propagating through an isotropic inhomogeneous layer
Plane time-harmonic elastic SH-wave propagation through an isotropic inhomogeneous layer surrounded by two homogeneous half-spaces is studied in this article. The material properties of the inhomogeneous layer are assumed to be non-uniform along the thickness direction according to a distribution law described by the triconfluent Heun functions or their polynomial forms that contain a number of optional parameters. The general analytical solution of the governing equation for elastic SH-waves in the layer is presented. Employing optional parameters, the material-property profiles can be varied to a relatively large extent without the need to seek new solutions of the governing equation for a chosen material-property profile. If the wave speed is constant in the inhomogeneous layer, the derived analytical solution is exact; otherwise the analytical solution is approximate. As a part of this article, the method enabling to find an approximate analytical solution of the governing equation for predetermined material functions is also presented. The applicability of the analytical solutions are tested and discussed based on the representative examples, and at the same time, the analytical results are compared with numerical ones to demonstrate their validity.
Method of estimation of frequency spectrum and power of the sound generated by an unsteady flow through a sonic crystal
Although the importance of sonic crystals serving as sound barriers is growing, only a little interest was given to the sound emission from a sonic crystal due to windy weather conditions. The Curle’s aeroacoustic analogy is reviewed in brief to obtain a suitable formulation for the low Mach number flow and rigid crystal structure. The radiation from the crystal has the dipolar characteristic and the dominating frequency corresponds to the Strouhal number 0.3. The values slightly exceeding 50 dB[A] were found for the radiation maxima at 20 m distance. It follows from the method design that it provides maximum estimate of the radiated power.
On the modelling of reactive silencers with narrow side-branch tubes
This work represents a theoretical study of the sound propagation in a waveguide loaded by an array of flush-mounted narrow side-branch tubes, forming a simple low-frequency reactive silencer. The individual tube-lengths and the distances between the adjacent tubes may vary in order to optimize the transmission loss in a given frequency range. The transmission properties of the silencer are calculated using the transfer matrix method, and the finite element method. A~simple heuristic evolutionary algorithm, together with an analytical mathematical model (the transfer matrix method) is employed for the determination of the optimal silencer parameters. The numerical results are validated against the finite element simulation.
Optimized reactive silencers composed of closely-spaced elongated side-branch resonators
This paper reports a theoretical study of the sound propagation in a rectangular waveguide loaded by closely-spaced elongated side-branch resonators forming a simple low-frequency broadband reactive silencer. Semi-analytical calculations account for the evanescent modes both in the main waveguide and side-branch resonators and for the viscothermal losses in the silencer elements. Reasonable accuracy is maintained in the evaluation of transmission, reflection, and absorption coefficients, while the calculation time is reduced by a few hundred times in comparison with the finite element method. Therefore, the proposed method is particularly suitable for optimization procedure. The lengths of the individual equally spaced side-branch resonators are optimized by a heuristic evolutionary algorithm that maximizes the minimum transmission loss (TL) over a pre-defined frequency range. Numerical results indicate that the minimum TL of the optimized silencers is reduced due to the destructive effect of the evanescent coupling from the resonators of the nearest side-branches. In the opposite, the TL increases linearly with the number of the side-branch
Weakly nonlinear oscillations of gas column driven by self-sustained sources
Self-sustained sources coupled to some sort of resonator have drawn attention recently as a subject of nonlinear dynamics with many practical applications as well as interesting mathematical problems from the chaos theory and the theory of synchronizations. In order to mimic the self-sustainability arising from physical background the van der Pol equation is commonly used as a model (e.g. vortex induced noise, flowstructure interactions, vocal folds motion etc.). In many cases the sound field inside the resonator is strong enough for weakly nonlinear formulation based on the Kuznetsov model equation to be employed. An array of sources governed by the inhomogeneous van der Pol equation coupled to the nonlinear acoustic wave equation is studied. The one dimensional constant cross-section open resonator with zero radiation impedance is assumed. The focus is on the main features such as mode-locking, harmonics generation and build-up from infinitesimal fluctuations.
Description of waves in inhomogeneous domains using Heun's equation
There are a number of model equations describing electromagnetic, acoustic or quantum waves in inhomogeneous domains and some of them are of the same type from the mathematical point of view. This isomorphism enables us to use a unified approach to solving the corresponding equations. In this paper, the inhomogeneity is represented by a trigonometric spatial distribution of a parameter determining the properties of an inhomogeneous domain. From the point of view of modeling, this trigonometric parameter function can be smoothly connected to neighboring constant-parameter regions. For this type of distribution, exact local solutions of the model equations are represented by the local Heun functions. As the interval for which the solution is sought includes two regular singular points. For this reason, a method is proposed which resolves this problem only based on the local Heun functions. Further, the transfer matrix for the considered inhomogeneous domain is determined by means of the proposed method. As an example of the applicability of the presented solutions the transmission coefficient is calculated for the locally periodic structure which is given by an array of asymmetric barriers.
Direct numerical simulation of sound absorption in porous media
Numerical simulation of absorption of sound in porous media is an important part of the design of the treatments for the environmental noise reduction. In the porous media, the mechanical energy carried by sound is dissipated by thermo-viscous interactions with the solid surface of the media frame, which usually has complicated geometry at the microscopic (sub-millimetre) scale. In order to be able to absorb the acoustic energy at the low frequencies of interest, a layer of porous material must be rather thick (at the order of centimetres). This is why direct numerical simulation (DNS) of the sound absorption in porous media is a rather computationally challenging task because small geometrical details must be properly resolved in a large computational domain. In order to avoid these difficulties, simplified semi-phenomenological models introducing so called effective fluid have been proposed. For example, the Johnson-Champoux-Allard-Pride-Lafarge (JCAPL) model is based on eight parameters which can be measured or calculated based on the media micro-structural geometry. Within this work, we compare the numerical results obtained by the 3D DNS with the prediction of the JCAPL model in case of several porous media represented by closely-packed spheres. The DNS calculations are performed using the linearised Navier-Stokes equations for layers of spheres of different thicknesses, the parameters for the JCAPL model are calculated subsequently using Laplace, Poisson, and Stokes-flow analyses on a representative volume element of the media. Very good agreement between the results has been found.
Numerical study of the influence of the convective heat transport on acoustic streaming in a standing wave
Within this work, acoustic streaming in an air-filled cylindrical resonator with walls supporting a temperature gradient is studied by means of numerical simulations. A set of equations based on successive approximations is derived from the Navier-Stokes equations. The equations take into account the acoustic-streaming-driven convective heat transport; as time-averaged secondary-field quantities are directly calculated, the equations are much easier to integrate than the original fluid-dynamics equations. The model equations are implemented and integrated employing commercial software COMSOL Multiphysics. Numerical calculations are conducted for the case of a resonator with a wall-temperature gradient corresponding to the action of a thermoacoustic effect. It is shown that due to the convective heat transport, the streaming profile is considerably distorted even in the case of weak wall-temperature gradients.
One-dimensional propagation of longitudinal elastic waves through functionally graded materials
The one-dimensional propagation of longitudinal elastic waves along the thickness of a plate made of functionally graded materials excited by a harmonic force is reported in this article. The material properties of the plate are assumed to be graded along the thickness direction according to a trigonometric law distribution. This distribution smoothly connects the material properties of the upper and lower homogeneous materials that bounds the plate. The corresponding propagation equation is Ince-type equation that can be transformed to Heun's equation a local exact solution of which is expressed in terms of local Heun functions. The general nature of these functions is demonstrated based on four degenerate cases of Heun's equation. The transfer matrix method is used to study the elastic waves propagating in the inhomogeneous domain. The calculation of the transfer matrices requires the evaluation of the general solution in the interval containing two regular singular points. For this purpose, the modified Heun function is introduced. Based on the transfer matrices, the influence of both the asymmetry of the unit cell and various constituent materials on the transmission coefficient spectrum is studied. The transmission coefficient is also calculated for the locally periodic structures with the help of the Chebyshev polynomials. (C) 2018 Elsevier Ltd. All rights reserved.
Optimized reactive silencers with narrow side-branch tubes
This paper presents a theoretical study of the sound propagation in a waveguide loaded by an array of flush-mounted narrow side-branch tubes, forming a simple low-frequency reactive silencer. The individual tube-lengths and the distances between the adjacent tubes are optimized in order to maximize the minimum transmission loss over a given frequency range. The transmission properties of the silencer are calculated using the transfer matrix method, heuristic evolutionary approach is employed for the determination of the optimal parameters. The numerical results are validated against the finite element method simulation. A comprehensive parametric study is performed to demonstrate the optimized silencer performance as a function of the number of side-branch tubes, and the frequency range. It is shown that for the given frequency range, the minimum transmission loss of the optimized silencer increases linearly with the number of the side-branch tubes.
Propagation of electromagnetic waves through non-uniform dielectric layers
The propagation of TE- and TM-polarized electromagnetic (EM) waves through a dielectric layer with spatial variation of the refractive index is reported in this paper. The relative permittivity of the layer is assumed to be graded along the thickness direction, and its spatial variation is described by a quartic polynomial. The corresponding mode equations are Helmholtz equations with variable coefficients that can be transformed to a triconfluent Heun equation, a local exact solution of which is expressed in terms of tri-confluent Heun functions. The solutions cover many particular cases owing to a variability of four optional parameters (coefficients) of the quartic polynomial. The general local solution for a TE-polarized EM wave is employed for the calculation of transmission properties of a periodic one-dimensional photonic crystal using the Floquet theory. (C) 2018 Optical Society of America
Acoustic streaming in resonators with heated walls
Acoustic streaming in fluid-filled resonators with the spatial distribution of walls’ temperature is studied within this work. The method of successive approximations is employed to derive linear
equations for the calculation of ambient, primary acoustic, and time-averaged secondary fields including the mass transport velocity. The model equations have a standard form which allows their numerical integration using COMSOL Multiphysics. The numerical results are validated for the case of a resonator with spatially-constant ambient temperature by comparison with previously published analytical results; an excellent agreement is found. Examples of acoustic streaming structures in resonators with heated walls are given showing a strong influence on the walls’ temperature distribution and the resonator cavity dimensions.
Description and analysis of elastic waves in functionally graded materials
Functionally graded materials (FGMs) belong to a class of advanced materials characterized by variation in properties as the dimension varies. Propagation of elastic waves through FGMs is an issue of scientific and practical interest because the effective use of elastic waves in the industries relies on a good understanding of wave propagation in FGMs. The propagation of one-dimensional elastic waves in a plate made of FGMs excited by a harmonic force is described and studied in this work. The corresponding model equation is solved analytically and its solution is based on the local Heun functions. The elastic waves are investigated by means of the transmission coefficient, which can be utilized in study of transmission properties of locally periodic structures.
Effect of inhomogeneous temperature fields on acoustic streaming structures in resonators
Acoustic streaming in 2D rectangular resonant channels filled with a fluid with a spatial temperature distribution is studied within this work. An inertial force is assumed for driving the acoustic field; the temperature inhomogeneity is introduced by resonator walls with prescribed temperature distribution. The method of successive approximations is employed to derive linear equations for calculation of primary acoustic and time-averaged secondary fields including the streaming velocity. The model equations have a standard form which allows their numerical integration using a universal solver; in this case, COMSOL Multiphysics was employed. The numerical results show that fluid temperature variations in the direction perpendicular to the resonator axis influence strongly the streaming field if the ratio of the channel width and the viscous boundary layer thickness is big enough; the streaming in the Rayleigh vortices can be supported as well as opposed, which can ultimately lead to the appearance of additional vortices.
Fenomenologický model generování zvuku ve vroubkovaných trubicích a jeho modální řešení
Na základě motivace ze základních aeroakustických vlnových rovnic je navržen fenomenologický model generování zvuku ve vroubkovaných trubicích. Numerické simulace velmi dobře korespondují s kvalitativním chováním známým z experimentů (zejména se jedná o efekty nelineární synchronizace a hystereze).
The exact solution of the Schrodinger equation with a polynomially spatially varying mass
The Schrodinger equation with a position-dependent mass (SEPDM) is employed in many areas of quantum physics. Exact solutions for the SEPDM lie at the center of interest of the professional public because it helps us to understand the behavior of quantum particles in the cases in which their mass varies spatially. For this purpose, we used the mass function represented by a quartic polynomial and a quadratic potential function, which extends the current class of exact solutions of the SEPDM. The exact analytical solution of the problem is expressed as a linear combination of local Heun functions. Heun's equation contains many parameters, resulting in its general nature. We studied how limit changes in some of these parameters will affect the solution of the SEPDM. The obtained solutions are particularly suitable for the transfer matrix method and solutions of scattering problems; this is demonstrated by the calculation of bound states.
This work deals with acoustic bandpass filters realized by shaped waveguide-elements inserted between two parts of an acoustic transmission line with generally different characteristic impedance. It is shown that the formation of a wide passband is connected with the eigenfrequency spectrum of the filter element which acts as an acoustic resonator and that the required filter shape substantially depends on whether the filter characteristic impedance is higher or lower than the characteristic impedance of the waveguide. It is further shown that this class of filters can be realized even without the need of different characteristic impedance. A heuristic technique is proposed to design filter shapes with required transmission properties; it is employed for optimization of low-frequency bandpass filters as well as for design of bandpass filters with wide pass band surrounded by wide stopbands as it is typical for phononic crystals, however, in this case the arrangement is much simpler as it consists of only one simple-shaped homogeneous element.
Acoustic streaming in fluid-filled resonators with variable cross-section is studied within this work. An inertial force is assumed for driving the acoustic field. The method of successive approximations is employed to derive linear equations for calculation of primary acoustic and time-averaged secondary fields including the mass transport velocity. The model equations have a standard form which allows their numerical integration using universal solver COMSOL Multiphysics. The numerical results are validated for the case of a resonator with constant cross-section by comparison with previously published analytical results; an excellent agreement is found. Example of acoustic streaming in a shaped resonator is given to demonstrate a strong dependence of the acoustic streaming structure on the resonator shape.
Behavior of plane waves propagating through a temperature-inhomogeneous region
Description and analysis of acoustic waves in ducts with a region containing temperature-inhomogeneous fluid represent a significant problem of scientific and practical interest. This interest is induced by the need of understanding how temperature fields affect acoustic processes which would lead to a more efficient design and control of systems involving thermoacoustic interactions. Most of the works addressing these problems limit themselves to the assumption of weak temperature profile gradients or to temperature profiles which do not connect neighboring temperature-homogeneous regions smoothly. In our work we investigate the behavior of plane acoustic waves that enter a region with an arbitrary temperature gradient. A polynomial character of the used temperature profile ensures smooth connection with constant-temperature regions. The one-dimensional wave equation for ducts with an axial mean temperature gradient is solved analytically. The derived solutions based on Heun functions extend the class of published exact analytical solutions of model wave equations taking into account the medium temperature gradient. Due to the property that our proposed polynomial temperature function has derivatives equal to zero at points which are connected with the surrounding temperature-homogeneous regions we can form more complex smooth temperature profiles for which it is possible to use the transfer matrix method.
Variety of acoustic streaming in 2D resonant channels
Acoustic streaming in 2D resonant channels with uniform or non-uniform cross-sections is studied within this work. An inertial force as well as a vibrating boundary are assumed for driving the acoustic field.
The method of successive approximations is employed to derive linear equations for calculation of primary acoustic and time-averaged secondary fields including the radiation pressure and the mass transport velocity. The model equations have a standard form which allows their numerical integration using a universal solver; in this case, COMSOL Multiphysics was employed. As this software is based on the finite element method, it is simple and straightforward to perform the calculations with moderate computational costs even for complex geometries, which makes the proposed approach an operative tool for study of acoustic streaming.
The numerical results are validated for the case of a rectangular channel by comparison with previously published analytical results; an excellent agreement is found. The numerical results show that the acoustic streaming can be quite complex even in rectangular channels and its structure depends on the manner of driving. Examples of acoustic streaming in wedged and elliptical channels are given to demonstrate a strong dependence of the acoustic streaming structure on the resonator shape.
A simple device consisting of a waveguide and two loudspeakers is proposed for generation of low-frequency standing acoustic field with high amplitude of acoustic velocity and particle displacement, which is primarily intended to be used for stabilization of electric discharges in acoustic field. A~coupled model of loudspeakers and nonlinear wave equation including waveguide radius variability, thermoviscous attenuation in boundary layer and minor losses is developed. The results of the conducted experiments validate the model revealing that the minor losses and acoustically generated turbulence in the boundary layer represent an important means of acoustic energy dissipation in this and similar applications.
Calculation of an axial temperature distribution using the reflection coefficient of an acoustic wave
This work verifies the idea that in principle, it is possible to reconstruct axial temperature distribution of fluid employing reflection or transmission of acoustic waves. It is assumed that the fluid is dissipationless and its density and speed of sound vary along the wave propagation direction because of the fluid temperature distribution. A numerical algorithm is proposed allowing for calculation of the temperature distribution on the basis of known frequency characteristics of reflection coefficient modulus. Functionality of the algorithm is illustrated on a few examples, its properties are discussed.
Description and analysis of plane waves in a temperature-inhomogeneous region
Both from a scientific and practical point of view behavior of acoustic waves within a temperature-inhomogeneous region represents an interesting issue. However, there is a limited class of temper-ature functions for which we know exact analytical solutions of corresponding model equations. Our work extends this class by a temperature function with an arbitrary temperature gradient, and unlike previously published works, the temperature function is smoothly connected with a temperature of surrounding temperature-homogeneous regions. For the chosen temperature function the model equation represents Heun?s equation that can be solved exactly using the Heun functions, which facilitates study of the behavior of acoustic waves. The only software package currently able to work with the Heun functions is MAPLE. Alternative ways for evaluations of those functions do not exist. However, the calculation of the Heun functions in MAPLE has some limitations that can be overcome with the help of F-homotopic transformations, which is shown in this paper.
Finite amplitude standing waves in resonators terminated by a general impedance
A general inhomogeneous Burgers equation describing finite-amplitude standing waves in resonators terminated by a general impedance is derived. This model equation can be used for modeling of nonlinear acoustic processes connected with some methods for enhancement of Q -factor of acoustic resonators. One of them is the method based on using a second-harmonics absorber. For better understanding of this method, it is convenient to know at least an approximate analytical solution of the model equation. This work presents some approximate solutions, which improve and extend the solutions that have been published previously. The solutions are compared with results obtained by numerical integration of the corresponding equations.
On the propagation of acoustic waves through temperature inhomogenities in fluide
The work deals with the transmission and reflection of plane acoustic waves propagating in temperature-inhomogeneous fluids. It is assumed that the temperature gradient is collinear with the direction of the wave propagation and that the inhomogeneity is localized in space, i.e., it forms a “temperature barrier”. An efficient numerical algorithm employing the Riccati equation is proposed for calculation of the frequency-dependencies of the coefficients of transmission or reflection for arbitrary temperature distributions, based on which, their general properties are studied. Further, an inverse problem is studied; it is shown that the distribution of the temperature in a barrier can be calculated from the frequency characteristics of the reflection (transmission) coefficient, an algorithm for which is described.
On the structure of multi-Gaussian beam expansion coefficients
This work deals with the structure and properties of multi-Gaussian beam expansion coefficients.
An alternative formulation of an objective function is proposed for heuristic calculation of the coefficients together with a procedure for reducing the dimensionality of the corresponding optimization problem to a quarter of its original size. The proposed objective function enables us to avoid numerical integration within the process of its evaluation in some practically important cases, which greatly speeds up the calculations. An evolutionary algorithm is employed for global minimization of the objective function resulting in determination of the multi-Gaussian beam expansion coefficients enabling us high-accuracy analytical calculation of acoustic (ultrasonic) fields radiated by planar sources. The calculated expansion coefficients are provided for the case of an axi-symmetric uniform piston, a simply supported or clamped disc and a thin membrane. A simple relation delimiting validity of the approximation is found.}
Acoustic plane waves in a gas-filled duct with an axial temperature gradient
Description and analysis of acoustic waves in ducts with a temperature gradient represents a signifi-
cant problem of science and practical interest. This problem is induced by the need of understanding
how temperature fields affect acoustic processes which leads to a better possibility to design and con-
trol systems in which interactions between the acoustic and temperature fields occur. This includes for
instance thermo-acoustic devices and engines, combustors, automotive mufflers, measuring methods
of impedances of high temperature systems, investigation of thermo-acoustic and combustion instabil-
ities etc. Most of the works dealing with these problems requires either the weak temperature gradient
or temperature gradients, which are not fully consistent with the imposed physical conditions. In our
work we deal with investigating of the behavior of plane acoustic waves that enter a region with
arbitrarily spatially varying temperature gradient. This temperature region smoothly verges into the
remaining regions in which the temperature gradient is constant. The one-dimensional wave equa-
tion for ducts with an axial mean temperature gradient is solved analytically. The derived solutions
extend the class of published analytical solutions of model wave equations taking into account the
temperature gradient of medium by solutions that assume a smooth temperature distribution.
An acoustical resonator for stabilization of electrical discharge
This work deals with study of a device for an efficient generation of standing acoustic field with
high amplitude of acoustic particle displacement. The device is intended to be used for acoustic sta-
bilization of electrical discharges for enhancement of plasma-chemical reactions in ecological applica-
tions. It consists of two out-of-phase-driven loudspeakers interconnected with a symmetrically shaped
waveguide forming together a low-frequency electro-mechano-acoustical resonant system. A theoret-
ical model based on lumped-element circuits is proposed for description of the device, its tuning
capabilities and optimization. An analysis of the model is performed resulting in an experimental
sample realization. Acoustic measurements based on two-microphone method are conducted to prove
functionality of the device even in case of high-amplitude acoustic fields.
Equations for description of nonlinear standing waves in constant-cross-sectioned resonators
This work is focused on investigation of applicability of two widelyused
model equations for description of nonlinear standing waves in
constant-cross-sectioned resonators. The investigation is based on comparison
of numerical solutions of these model equation with solutions
of more accurate model equation whose validity has been verified experimentally
in a number of published papers.
Optimal shaping of acoustic resonators for the generation of high-amplitude standing waves
Within this paper, optimal shaping of acoustic resonators for the generation of high-amplitude standing waves through the use of evolutionary algorithms is discussed.
The resonator shapes are described using sets of control points interconnected with cubic-splines. Positions of the control points are calculated by means of an evolutionary algorithm in order to maximize acoustic pressure amplitude at a given point of the resonator cavity. As an objective function for the optimization procedure, numerical solution of
one-dimensional linear wave equation taking into account boundary-layer dissipation is used. Resonator shapes maximizing acoustic pressure amplitude are found in case of a piston, shaker or loudspeaker driving. It is shown that the optimum resonator shapes depend on the method of driving.
In all the cases, acoustic field attains higher amplitude in the optimized resonators than in simple-shaped non-optimized resonators of similar dimensions.
Theoretical results are compared with experimental data in the case of a loudspeaker driving, good agreement of which is achieved.
Finite-amplitude standing waves in optimized acoustic resonators
he paper deals with optimization of the shape of an axisymme
tric acoustic resonator in order
that acoustic pressure were maximized at one of its ends. In c
omparison to the previously pub-
lished studies, the resonator shape description is not rest
ricted to an elementary function, it is
rather described using a set of control points interconnect
ed with splines allowing a wide vari-
ety of possible shapes. In the first approximation, acoustic
field in a shaped cavity is described
using the quasi-one-dimensional Webster’s equation suppl
emented with a term accounting for
thermoviscous attenuation. A heuristic algorithm based on
Evolution strategies is proposed
for determination of the control points positions resultin
g in maximum acoustic pressure in
the case of a piston or shaker driving of the resonator cavity
. Numerical simulations show that
the optimum shapes differ for individual methods of driving
, they are rather simple, differ from
the previously proposed shapes and possess non-equidistan
t eigenfrequencies. The simplicity
of the optimum resonator shapes allows their subsequent des
cription using simpler mathemat-
ical form. Behavior of the finite-amplitude waves in the opti
mized resonator cavities is further
assessed with use of a nonlinear wave equation.
Non-paraxial model for a parametric acoustic array
This study is concerned with parametric radiation from an arbitrary axisymmetric planar source with a special focus on low-frequency difference-frequency fields. As a model equation accounting for nonlinearity, diffraction and dissipation, the Westervelt equation is used. The difference-frequency-field patterns are calculated in the quasi-linear approximation by the method of successive approximations.
A multi-layer integral for calculation of the acoustic field is reduced to a three-dimensional one by employing an approximate analytical description of the primary field with the use of a multi-Gaussian beam expansion. This integral is subsequently reduced in the paraxial approximation to a one-dimensional form which has previously been published in literature and which represents a means for fast calculations of secondary acoustic fields.
The three-dimensional integral is calculated numerically and
the numerical results predict nonzero amplitude of the low-frequency field in the vicinity of the source which is an effect that cannot be correctly encompassed in the paraxial approximation.
Nonlinear acoustic fields in two mechanically coupled resonators
The paper deals with a description of nonlinear standing waves in cylindrical resonators which are separated by an elastically mounted wall. The wall represents a quasi-harmonically driven oscillator which connects
nonlinear acoustic fields in the resonators. For the description of the nonlinear acoustic fields were derived model equations. The model equations are represented by the inhomogenenous Burgers equations. These
two model equations are supplemented by an oscillator motion equation. The assumed resonant system contains many optional parameters which enable to investigate a number of interesting configurations of parametrically excited nonlinear acoustic fields. The system of model equation was numerically solved both the time and frequency domain. Some of the assumed configurations were solved analytically for the case of steady acoustic fields. Thanks to many optional parameters the investigated resonant system is relatively
complex and enables to study a number of interesting configurations. The resulting acoustic fields for some of the chosen configurations are included in this paper.
On the Optimization of an Acoustic Resonator Shape with Respect to Acoustic Pressure Amplitude
This paper deals with the optimization of an acoustic resonator shape in order to maximize acoustic pressure amplitude. The resonator shape is described using the cubic splines which interconnect a set of control points whose positions are determined using an evolutionary algorithm. As an objective function, numerical solution of modified Webster's equation is used. Numerical results show that the optimized resonators are rather simple-shaped, they differ for a piston- or shaker-driving and the fundamental resonance frequencies are lower than in the case of a constant-cross-section resonator. A nonlinear theory is used for assessment of finite-amplitude fields in the optimized resonators.
Analysis of nonlinear standing waves in two coupled acoustic resonators
The paper deals with description of nonlinear standing waves in acoustic resonators that are coupled mechanically by means of an elastically mounted wall which is implemented between the resonators. The coupling represents a linear oscillators. For the purpose of the behavior description of the nonlinear acoustic fields, the system of three model equations were derived. Two of them are the modified inhomogeneous Burgers equations and the third model equation is the oscillator's equation of motion. The investigated resonant system is excited by the harmonically vibrating pistons. The system of model equations was solved numerically in the frequency domain. The whole system obtains many parameters which can be changed. With help of these parameters we can adjust various configurations of the resonant system. The configurations, which offer interesting results, were studied. One of the configurations ensures that the resonant system behaves as a frequency convertor. Other selected configuration causes suppression of higher harmonic components in the one of the resonators.
Interaction between two nonlinear acoustic resonators
This work is dedicated to problems connected with an interaction between two nonlinear acoustic cylindrical
resonators. The resonators are closed and interact due to an elastically mounted wall which is placed between
them. This wall represents a one-degree-of-freedom mechanical oscillator that is described by the linear
equation of motion. Acoustic fields inside the resonators are generated by vibrating pistons which are located
at their ends. The pistons are capable to excite nonlinear standing waves. For description of the waves
model equations were derived, which represent the modified inhomogeneous Burgers equations. Nonlinear
acoustic fields are coupled linearly by the elastically mounted wall. This resonant system enables to set
a lot of configurations which is due to many optional parameters, e.g. frequency and amplitude of the
vibrating pistons, detuning, characteristic frequency of the mechanical oscillator and its damping. This paper
contains interesting analysis of chosen configurations and demonstrates possibility of using of the coupled
inhomogeneous Burgers equations for these purposes.
This paper is concerned with study of low-frequency sound beams generated as difference-frequency secondary field in parametric array. As model equations for theoretical investigation, KZK equation and Higher-order parabolic equation (HOPE) [Kamakura, T., Masahiko, A., Kenicii, A, Acoust. Sci. & Tech. 25, 2, (2004)] were used. Efficient numerical algorithm capable of massive parallelization was proposed for numerical integration of the model equations. Numerical results obtained using KZK equation and HOPE show that the KZK equation overestimates amplitude of the difference-frequency secondary wave in the near-field of the primary wave at the axis of symmetry. Both the equations provide the same results in the far-field and at the off-axis for both low- and high-frequency secondary fields.
Self-demodulation effects in nonlinear focused beams
In this work, spatial distributions of acoustic pressure of the nonlinear focused sound beams are presented. Focused acoustic beams of periodic waves with an initially Gaussian amplitude distribution are considered. The numerical algorithm is based on the numerical solution of the nonlinear parabolic Khokhlov-Zabololotskaya-Kuznetsov (KZK) equation. The presented model enables to study the process of nonlinear generation of a low-frequency signal by the amplitude modulated high-frequency carrier wave.
Analýza nelineárních stojatých vln ve dvou vázaných akustických rezonátorech
Práce se zabývá popisem nelineárních stojatých vln v akustických rezonátorech, které jsou mechanicky vázány prostřednictvím pružně uložené stěny, která je modelována jako lineární oscilátor. Pro popis systému byly odvozeny tři modelové rovnice, dvě z nich jsou reprezentovány zobecněnými nehomogenními Burgersovými rovnicemi a jedna pohybovou rovnicí oscilátoru. Rezonanční systém je buzen kmitajícím pístem. Soustava modelových rovnic je řešena numericky v kmitočtové oblasti. Výsledný systém vykazuje různé druhy chování v závislosti na volbě příslušných parametrů. Mezi zajímavé výsledky patří jeho schopnost násobit kmitočet či potlačovat vyšší harmonické generované nelineárními procesy.
Comparison of various strategies for colorectal cancer screening tests
Introduction: Colorectal cancer (CRC) is one of the most serious health problems worldwide and thus it is important to assess health and economic impacts of preventative CRC screening strategies.
Methods: For this reason, a theoretical model based on Markov chains is proposed to compare these strategies: fecal occult blood test, capsule endoscopy, once-life and twice-life colonoscopy, and no screening. The model predicts the health state of a population of individuals aged from 50 to 75 years.
Results: The numerical results show that the optimal timing for a once-lifetime colonoscopy screening method is before the age of 50 and that the twice-lifetime colonoscopy is the best screening strategy with respect to CRC incidence. In contrast, it is the most expensive one if the CRC treatment costs are not included. The model predicts that there is a minimal CRC incidence in the population when the second colonoscopy is appropriately timed. By using specific data, this age was found to be 59 years.
Conclusion: The screening strategies probably save expenses on the treatment of the population and at the same time decreases mortality. Optimized twice-lifetime colonoscopy seems to be the most efficient strategy with respect to mortality and overall costs including subsequent treatment.
Práce se zabývá studiem nízkofrekvenčních zvukových svazků generovaných pomocí parametrického pole jako rozdílová složka. Jako modelová rovnice pro teoretický popis byla použita jednak KZK rovnice a dále rovnice odvozená s vyšším stupněm přesnosti v parabolické aproximaci (HOPE) [Kamakura, T., Masahiko, A., Kenicii, A, Acoust. Sci. & Tech. 25, 2, (2004)]. Pro numerickou integraci modelových rovnic byl navržen masivně paralelní numerický algoritmus. Numerické výsledky ukazují, že KZK rovnice (oproti přesnější HOPE) nadhodnocuje amplitudy nízkofrekvenčních složek v blízkém poli primární vlny. Obě rovnice poskytují stejné hodnoty v poli vzdáleném a mimo osu symetrie.
Approximate Description of Finite-Amplitude Acoustical Waves in the Air-Filled Resonator
The main goal of this paper is the description of the properties of the nonlinear standing
waves generated by a vibrating boundary in the air-filled acoustical resonator. The nonlinear
oscillations of gas in the hard-walled resonator having one closed end and the other
periodically oscillating are analysed in this work. All phenomena leading to a progressive
distortion of the wave are supposed to be weak. The analytic approach to finite-amplitude
standing waves in a resonator of a constant diameter is used, based on the inhomogeneous
Burgers equation with a discrepancy. In this paper we present the method of approximate
solution of this equation in the stationary state.
Control of Nonlinear Standing Waves in Acoustic Resonators
Though there are a number of methods which enable to control acoustic fields in resonators,
this paper is focused on possibilities that offer the use of amplitude-modulated primary
waves. This method makes possible to control energy transfer among harmonics and thus to
form the acoustic field inside resonators. Better efficiency is achieved by a combination of the
standard methods of influencing acoustic fields such as the method of acoustic resonance
macrosonic synthesis, induced dispersion, selected absorption etc. The presented method of
acoustic field control enables to suppress the generation of higher harmonics and thus
suppress the nonlinear saturation effect. At the same time it offers new possibilities for
excitation of nonlinear standing acoustic waves which are based on piezoelectric
High-Amplitude Standing Waves Between Collateral Discs
The paper is concerned with study of behaviour of high-amplitude standing acoustic waves
between two collateral discs whose dimensions are comparable with the wavelength. The
work is motivated by research of possibilities of acousto-optical imaging in gases. Firstly, the
system was numerically modeled in linear approximation using the Finite Elements Method in
order to assess its Q-factor and resonant frequencies for different discs' radius-wavelength
ratios. An approximate formula was found for calculation of resonance frequency for given
geometry. Secondly, high-amplitude waveforms and generation of higher harmonics was
studied using time-domain numerical integration of Navier-Stokes equations. It was observed
that typical shock-wave does not develop in spite of considerable amplitudes of acoustic
pressure that is caused by irregular distribution of resonant frequencies for individual modes.
Nonlinear acoustical waves in the air-filled resonator
The main objective of this paper is the description
of the properties of the nonlinear standing waves generated by
a vibrating boundary in the acoustical resonator. The nonlinear
oscillations of gas in the hard-walled air-filled resonator having
one closed end and the other periodically oscillating are analyzed
in this work.
Numerical simulation of parametric field patterns of ultrasonic transducer arrays
The paper is concerned with numerical modeling of planar 2D ultrasonic transducer arrays for highly directional transmission of audio-frequency sound in air. The influences of the transducers arrangement in array is studied with respect to primary and secondary acoustic field patterns.
Parametric excitation of nonlinear standing waves in acoustic resonator
The paper deals with parametric excitation of nonlinear standing waves in acoustic resonators. The used method is based on a parametric acoustic piston source which radiates an amplitude modulated ultrasonic waves. When a frequency of the demodulated wave is equal to some lower eigen-frequency of the resonator it is possible to excite nonlinear standing waves with its help. On the basis of theoretical investigation it was found that the presented method for generation of intensive acoustic fields inside the resonators is applicable.
Propagation of nonlinear acoustic plane waves in an elastic gas-filled tube
This paper deals with modeling of nonlinear plane acoustic waves propagating through an elastic tube filled with viscous gas. A description of the interactions between gas and an elastic tube wall is carried out by the continuity equation of a wall velocity. Simplification on the basis of the local reaction assumption enables to model an acoustic treatment on the tube wall by using a wall impedance. A special form of the Burgers equation was derived as a model equation that takes into account nonlinear, dissipative, and dispersion effects which compete each other. Characteristic lengths of the supposed effects and numerical results with respect to the source frequency were used for a qualitative analysis of the model equation. Applicability of this model equation was demonstrated by series of measurements. By application of the long-wave approximation the Korteweg-de Vries-Burgers and Kuramoto-Sivashinsky equations were derived from the modified Burgers equation.
Adaptive algorithm for active control of high-amplitude acoustic field in resonator
This work is concerned with suppression of nonlinear effects in piston-driven acoustic resonators by means of two-frequency driving technique. An iterative adaptive algorithm is proposed to calculate parameters of the driving signal in order that amplitude of the second harmonics of the acoustic pressure is minimized. Functionality of the algorithm is verified firstly by means of numerical model and secondly, it is used in real computer-controlled experiment. The numerical and experimental results show that the proposed algorithm can be successfully used for generation of high-amplitude shock-free acoustic field in resonators.
Analysis of nonlinear wave processes in an elastic resonator
The paper deals with investigation of nonlinear wave processes in elastic tube resonators which are excited by a vibrating piston. For this purpose we derived the modified inhomogeneous Burgers. equation which enables to model nonlinear standing waves in the supposed resonators. The influence of the dispersion and selective absorption, which are induced by the elastic wall, was investigated on the basis of the derived model equation. It was shown how the choice of the source frequency and amplitude can control an evolution of finite amplitude standing waves. Due to existence of dispersion we studied possibilities of subharmonic generation in the elastic resonator.
Finite amplitude standing waves in the cavity of the acoustical resonator
This paper deals with the description of the forced vibrations of air in an acoustic resonator having one closed end and the other periodically oscillating. Acoustic field in the cavity of the acoustical resonator is described as a sum of counter propagating waves with no cross-interaction. Effects of nonlinearity, absorption and detuning are taken into account. The distortions of traveling waves within the resonator length are assumed to be small, the Mach number for the moving boundary and the difference between one of the resonant frequencies and the fundamental frequency of the driving motion of the piston are also assumed to be small. The novel approximate steady state solution of the model equation using matching in the case of small dissipation is presented in this paper. The nonlinear frequency response of the resonator is calculated here for steady state oscillations for both inviscid and dissipative media. These calculations are based on the presented approximate solution.
High-amplitude acoustic field in a disc-shaped resonator
The work is concerned with study of high-amplitude acoustic fields in thin cylindrical discs, where the transversal mode is driven using a vibrating piston. Due to the fact that higher eigenfrequencies are not integer multiples of the eigenfrequency fundamental, excitation of shock-wave is avoided and nonlinear dissipation is supressed. The problem is described using a set of modified Navier-Stokes equations that are integrated numerically.
Článek se zabývá základními modelovými rovnicemi nelineární akustiky, pomocí nichž lze popisovat chování zvukových vln vysokých amplitud s ohledem na nelineární jevy, disipaci akustické energie a difrakci. Jako příklad je uvedena problematika nelineárních stojatých vln v akustických rezonátorech. K analýze problému je použita Kuzněcovova rovnice, v článku jsou dále nastíněny některé aspekty její numerické integrace.
Description of Plane Progressive Nonlinear Waves in Elastic Tubes
This paper deals with description of progressive plane nonlinear waves in tubes with an elastic wall. For description of the waves it is possible to use the modified Burgers equation. This equation takes into account nonlinear effects, boundary layer effects, volume heat-viscous losses and vibrations of a tube wall which cause both dissipation and dispersion of acoustic waves. It was supposed that the tube wall yield locally to the inner pressure. The Korteweg-de Vries-Burgers (KdVB) equation and the modified KdVB (Benney) equation can be derived from the modified Burgers equation when some relations are satisfied. Comparison of results of the mentioned model equations is presented in this work. Further, it is made comprehensive investigation of limits of the used model equations with respect to a source frequency, resonant character of wall losses and a distance from the source.
The work deals with numerical simulation of intensive acoustic fields in rectangular resonators allowing excitation of transversal modes. Central semi-discrete difference scheme is proposed for integration of Kuznetsov's equation, conditions for excitation of complex modes are studied.
Nonlinear acoustic threewave interactions in elastic waveguides and resonators
The paper is focused on the problems concerning threewave nonlinear acoustic interactions in elastic resonators or tubes. Study of nonlinear threewave interactions enables to understand an influence of elastic wall dispersion on generation of higher harmonics.
This work deals with problems regarding nonlinear standing waves which are confined in an elastic tube resonator. Elastic walls of the supposed resonator interact with nonlinear standing waves and induce relatively strong dispersion which causes that nonlinear acoustic interactions are less effective than in the case of hard-walled resonators. Wall attenuation of the resonators ihas elective character. In the parer a new model equation is derived which is used for dissipation and dispesion effects on nonlinear acoustic interactions.
Nonlinear oscillations of gas in acoustical resonator
The main objective of this paper is the theoretical description of the suppression of the nonlinear attenuation and thus increasing of the quality factor of the given resonator. The decribed method
is based on the active suppression of the second harmonic component of the sound. The resonator is driven by a piston whose motions is characterized by two superposed sinusoidal motions.
The frequency of the first motion f is equal to the resonator eigenfrequency and
the frequency of the second one is 2f and its the phase shift is 180 degrees.
Nonlinear standing waves in 2-D acoustic resonators
The article deals with numerical simulation of high-amplitude acoustic fields in rectangular resonators with dimensions allowing excitation of transverse modes. Set of modified Navier-Stokes equations is used as model equations.
Srovnání různých screeningových programů kolorektálního karcinomu v české populaci Markovovým počítačovým modelem
Článek se zabývá srovnáním dopadu několika typů screeningových metod pro odhalení kolorektálního karcinomu. Dopad těchto metod je zkoumán numerickou simulací s využitím metod Monte Carlo a Markovových řetězců.
Výzkum na katedře fyziky elektrotechnické fakulty ČVUT
The study is concerned with numerical simulation of high-amplitude acoustic fields in variable-cross-section acoustic resonators. Set of two model equations issuing from the Navier-Stokes equations is derived. Central semi-discrete difference scheme is used for integration of model equations.
Nelineární zvukové vlny v kapalinách obsahujících bubliny plynu
Práce se zabývá modelovými rovnicemi nelineární akustiky pro popis šíření zvukových vln v kapalinách obsahujících bubliny plynu. Ve druhém přiblížení je odvozena Kuzněcovova a Kortewegova-de Vriesova-Burgersova vlnová rovnice.
Podmínky vzniku příčných rázů v akustických rezonátorech
Práce je věnována problematice třívlnných nelineárních akustických interakcí v elastických rezonátorech nebo vlnovodech. Elastické stěny způsobují disperzi vln, jejichž vliv na generování vyšších harmonických je studován pomocí třívlnných interakcí.
Active Harmonic Suppression in the Nonlinear Acoustical Resonator
The work is concerned with study of high-amplitude acoustic resonance in field of spherical and cylindrical waves. Numerical results show excitation of high-amplitude shock-free acoustic fields and resonance-frequency shifts depending on amplitude of the field.
Nelineární stojaté vlny v elastických rezonátorech