Ing. Antonín Krpenský

The phenomenon of bound states in the continuum and leaky resonances is employed to design a reactive silencer. It is targeted to prevent a significant spectral line from propagating in a flow-duct while maintaining low pressure drop and installation space (without any lateral extensions). The quasi bound states are achieved by tuning the geometrical parameters of thin plates embedded in a waveguide with dimensions and flow velocities typical for ventilation systems. In general, the procedure works for waveguides with plane wave propagation in the low Mach number regime. An optimization by evolution strategies used for this purpose is described and illustrated on two specific examples.

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.

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 practical applications.

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.

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.

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.

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.