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.
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.
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.
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.
Properties of the Nonlinear Standing Waves Generated by a Vibrating Boundary
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 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.
Novel approximate solution of the inhomogeneous Burgers equation in stationary state regime is
shown in this work.
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.
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.
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.
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.