Sound Waves Of Finite Amplitude Research Articles

Nonlinear supersonic flutter of a composite panel backed by an acoustic cavity with finite-amplitude sound waves

In this paper, an implicit partitioned fluid-structure-acoustic interaction method is presented for predicting nonlinear aeroelastic response of an elastic composite laminated panel backed by an acoustic cavity and subject to a supersonic flow. The method is formulated in an arbitrary Lagrangian-Eulerian framework based on the unsteady Navier-Stokes equations for the supersonic flow, a geometrical nonlinear dynamics model for the composite laminated panel, and the nonlinear Westervelt equation for the finite-amplitude sound waves in cavity. A theoretical fluid-structure-acoustic model of the supersonic panel is proposed for validating the present numerical method, in which the nonlinear structural model of the panel, the first-order piston aerodynamics model of the supersonic flow and the nonlinear sound wave model of the cavity are coupled in a monolithic manner. It is found that cavity acoustic resonance can appear in the case a vibration mode of the panel coalescing with an acoustic mode of the cavity. Several new physical features of nonlinear acoustic resonance have been discovered, such as the presence of shock wave with high pressure gradients travelling along the resonant cavity in axial direction and the presence of higher-order harmonic wave components, which emphasize a nonlinear acoustic wave model of the cavity must be used to fully characterize these phenomena. In addition, the nonlinearity of the standing wave is quantitatively related to the acoustic modes by means of a proper orthogonal decomposition analysis.

Bridging shock: Blackstock’s general solution for propagation of finite-amplitude sound waves

Reflections are offered on D. T. Blackstock [“Connection between the Fay and Fubini solutions for plane sound waves of finite amplitude,” J. Acoust. Soc. Am. 39, 1019–1026 (1966)]. This work treats the propagation of planar finite-amplitude sound waves. It nominally links the Fourier-series-based solution of Fubini for the pre-shock condition, and the distant, post-shock solution of Fay. However, addressing the transition region between these two required solving the entire problem, which Blackstock did with aplomb. This additionally enabled specification of undetermined factors in the Fay solution, statement of an explicit bound on the applicability of the solution, and generalization to cylindrical and spherical waves. Hallmarks of Blackstock’s work are evident: scholarly mindfulness of historical precedent, meticulous analysis that inevitably advanced understanding of nonlinear acoustic phenomena, and elegance in presentation, which was, moreover, pedagogically convincing.

Acoustics of noise, vibration, and harshness

In this paper, we will go to a more fundamental level of treating acoustics. We introduced the gauge invariance into the acoustic wave equation of motion in 2007. This is an important milestone in the history of gauge invariance. The earliest gauge invariance is shown by Maxwell’s electromagnetic wave equations. The root of acoustics originated from fluid mechanics. We show that the usual form of acoustic wave equation for fluids is in fact the linearized form of the Navier Stokes equations. Hence there is in fact, no need to use acoustic analogy to derive the formula for the jet noise which was done by James Lighthill. In this paper we also treat finite amplitude sound wave and finite amplitude vibration using the deductive approach. This is a generalization of the linear theory to the nonlinear theory using relativistic and curvilinear spacetime treatment. This produces the linear case as a special case of the nonlinear case. The usual method is the reverse which starts from the linear theory and extend to the nonlinear theory. This will miss out some useful information. The treatment of vibration will need to incorporate the theory of elasticity. This paper is also the first introduction of singularities into vibration. Singularities is mathematically more sophisticated than resonance.

Nonlinear Distortion Characteristic Analysis for the Finite Amplitude Sound Pressures in the Pistonphone

The wide concern on absolute calibration of microphones at high pressure levels prompts the development of the pistonphone technique. However, as the sound pressure level goes higher, the linear hypothesis, which is applicable for the small amplitude sound wave, will no longer be valid. The nonlinear characteristics of the finite amplitude sound wave will produce high order harmonic components and also some other complex frequency components, which eventually result in the distortion of the sound pressure in the pistonphone, and should be quantitatively calculated to assess the accuracy of absolute sound pressure calibration of microphones at high sound pressure levels using pistonphones. In this paper, the linearized wave equations were built based on the perturbation method and the Euler system. Then, the distributed parameter expressions for the finite amplitude sound pressure both neglecting and considering the intermodulation characteristic have been explicitly derived. Nonlinear distortion characteristics of the sound pressure in the pistonphone have been studied, and the effects of the intermodulation on the sound pressure distortion have been evaluated. Computations reveal that the nonlinear distortion characteristics of the sound pressure produced by pistonphones should be quantitatively considered when the sound pressure level reaches 148[Formula: see text]dB, and the intermodulation characteristic can be neglected when the sound pressure level is lower than 174[Formula: see text]dB.

On the appearance of a system of ring vortices in the mixing layer of axially symmetric turbulent jets under acoustic action

The shadow visualization method is applied to study the process of loss of stability of the mixing layer of a subsonic axially symmetric turbulent jet under longitudinal internal action of saw-tooth sound waves of finite amplitude. Such action leads to the formation of a system of ring vortices in the mixing layer at the frequency of its intrinsic instability. The interaction of the vortices can be accompanied by sound emission. A similar phenomenon is also observed in turbulent jets for small supercritical pressure fluctuations on a nozzle.

Sound radiation produced by vortex/shock interaction in supersonic jets

The results of direct observations on shadowgraphs of the radiation of sound and the broadband component of the shock noise produced by the interaction of compact vortices formed in jets subject to the internal longitudinal and external transverse finite-amplitude sound waves with shocks in supersonic off-design jets are presented.

Bubble nonlinear oscillation in sound field

The complicated mechanism of gas bubble oscillation in sound field is quite fascinating. One simplified case is a single bubble motivated by specific finite-amplitude sound waves. Based on the modified Keller-Miksis model, a theoretical and numerical investigation of the regular and nonlinear radial oscillations of a gas bubble driven by different given finite-amplitude waves is presented. Some crucial control parameters of the bubble radial oscillations, including radius of gas bubble, acoustic frequency and acoustic pressure, are studied with multiple numerical analysis methods. Parameter regions which are benefit for power spectrum variation of the excitation forces are given, which can provide the foundation for potential engineering applications.

A Two-Dimensional Study of Finite Amplitude Sound Waves in a Trumpet Using the Discontinuous Galerkin Method

A model for nonlinear sound wave propagation for the trumpet is proposed. Experiments have been carried out to measure the sound pressure waveforms of the [Formula: see text] and [Formula: see text] notes played forte. We use these pressure measurements at the mouthpiece as an input for the proposed model. The compressible Euler equations are used to incorporate nonlinear wave propagation and compressibility effects. The equations of motion are solved using the discontinuous Galerkin method (DGM) and the suitability of this method is assessed. The third spatial dimension is neglected and the consequences for such an assumption are examined. The numerical experiments demonstrate the validity of this approach. We obtain a good match between experimental and numerical data after the dimensionality of the problem is taken into account.

The Effects of Side Branches on Compression Waves Propagating in High-Speed Railway Tunnels

According to the theory of finite amplitude sound waves, a one-dimensional compressible unsteady non-homentropic flow model, and the method of characteristics based on the average parameter method are applied to calculate the propagation of entry compression waves in a tunnel, in which the strength of the entry compression wave mainly affects the magnitude of the micro-pressure wave. In addition, acoustical principles are used to simulate the effect of side branches in the tunnel on the sound wave to elucidate the distortion of the waveform of the compression wave. A real-world comparison shows that the programs presented correctly reveal the distortion of the compression wave in the tunnel. After validation, the effects of the number, location, and depth of the side branches are studied in detail. The results show that any change in the parameters of a single side branch has almost no effect on the distortion of the waveform of the compression wave. An increase in the number of side branches, however, does make their effect more significant. This is due to an increase in streaming and reflections which substantially reduce the pressure gradient of the compression wave arriving at the exit portal of the tunnel.

The numerical simulation of propagation of intensive acoustic noise

The propagation of intensive acoustic noise is of fundamental interest in nonlinear acoustics. Some of the simplest models describing such phenomena are generalized Burgers’ equations for finite amplitude sound waves. An important problem in this field is to find the wave’s behavior far from the emitting source for stochastic initial waveforms. The method of numerical solution of generalized Burgers equation proposed is step-by-step calculation supported on using Fast Fourier Transform of the considered signal. The general idea is to keep only Fourier image of concerned signal and update it recursively (in space). For simulating the wave evolution we used 4096 (212) point realizations and took averaging over 1000 realizations. Also the object of the present study is a numerical analysis of the spectral and bispectral functions of the intense random signals propagating in nondispersive nonlinear media. The possibility of recovering the input spectrum from the measured spectrum and bispectrum at the output of the nonlinear medium is discusses. The analytical estimations are supported by numerical simulation. For two different types of primary spectrum evolution of jet noise were numerically simulates at a short distance and assayed bispectrum and a spectrum analysis of the signals.

Acoustical shock formation in highly nonlinear fluids.

Weak shock formation is investigated for plane sound waves of finite amplitude in fluids with high‐acoustical nonlinearity. The shock formation length is related to the sound speed of the fluid c and its nonlinear parameter B/A. The use of fluids with low‐sound speed and high parameter of nonlinearity has the advantage that the shock formation can be achieved at much lower pressures. Also, the experiments can be done on a smaller scale because the shock formation length is relatively small. The experiments are performed using short pulsed sound beams produced by a planar transducer with a resonance frequency of 0.5–1 MHz. The propagation medium consists of either different types of fluorocarbon or methanol. Direct pressure measurements of the acoustic waves in the fluid were obtained using a high‐frequency calibrated hydrophone. For comparison, a relatively smaller acoustical nonlinear material like water is also investigated. Experimental results related to second and higher harmonics generated in the fluid and their evolution in time along the propagation axis are compared with theoretical time‐domain predictions of the Khokhlov–Zabolotskaya–Kuznetsov equation.

Phase-coded multi-pulse technique for ultrasonic high-order harmonic imaging of biological tissues in vitro

Second or higher order harmonic imaging shows significant improvement in image clarity but is degraded by low signal–noise ratio (SNR) compared with fundamental imaging. This paper presents a phase-coded multi-pulse technique to provide the enhancement of SNR for the desired high-order harmonic ultrasonic imaging. In this technique, with N phase-coded pulses excitation, the received Nth harmonic signal is enhanced by 20 log10N dB compared with that in the single-pulse mode, whereas the fundamental and other order harmonic components are efficiently suppressed to reduce image confusion. The principle of this technique is theoretically discussed based on the theory of the finite amplitude sound waves, and examined by measurements of the axial and lateral beam profiles as well as the phase shift of the harmonics. In the experimental imaging for two biological tissue specimens, a plane piston source at 2 MHz is used to transmit a sequence of multiple pulses with equidistant phase shift. The second to fifth harmonic images are obtained using this technique with N = 2 to 5, and compared with the images obtained at the fundamental frequency. Results demonstrate that this technique of relying on higher order harmonics seems to provide a better resolution and contrast of ultrasonic images.

The transmission of finite amplitude sound beam in multi-layered biological media

Abstract Based on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, a model in the frequency domain is given to describe the transmission of finite amplitude sound beam in multi-layered biological media. Favorable agreement between the theoretical analyses and the measured results shows this approach could effectively describe the transmission of finite amplitude sound wave in multi-layered biological media.

Improvement of tissue harmonic imaging using the pulse-inversion technique

Harmonic imaging has brought about significant improvements in image quality by taking advantage of the second harmonic component, but it still has one shortcoming, namely, a low signal-to-noise ratio. In this paper, a pulse-inversion technique is used in second harmonic imaging for biologic tissues to increase the signal-to-noise ratio. Enhancement of the second harmonic component is theoretically analyzed based on the theory of the finite amplitude sound wave and confirmed by the measurement. Second harmonic imaging for biologic tissues is constructed with the pulse-inversion technique and compared with the traditional fundamental frequency and also with second harmonic imaging before the use of this technique. Results demonstrate that this technique yields a dramatically cleaner and sharper contrast between the different structures of biologic tissues in ultrasonic images. (E-mail: dzhang@nju.edu.cn)

Propagation of a finite-amplitude sound wave in the atmosphere

Propagation of a finite-amplitude sound wave in the atmosphere

Acoustical nonlinearities in compression chambers and horns of horn drivers

A horn driver is an essential part of sound reinforcement systems. Principles of horn driver operation are associated with generation of acoustical nonlinear distortion. Distortion is generated in a compression chamber by nonlinear compression, and by modulation of air stiffness, mass, and viscous losses, and a nonlinear relationship between particle velocity and sound pressure. Distortion is also generated in the phasing plug and horn by propagation of high amplitude waves. The effect of compression chamber air mass and viscous losses modulation and nonlinearity has not been researched previously. The analysis of modulation and nonlinear effects in the compression chamber is based on analysis of variation of the compression chamber’s air moving mass, viscous losses, and compliance as a function of the diaphragm’s instantaneous position and level of acoustical pressure. The pressure and diaphragm position-dependent parameters are incorporated into the system of nonlinear differential equations governing movement of the diaphragm and oscillation of air in compression chamber. Analysis of nonlinear propagation effects in the phasing plug and horn is based on numerical solution of an implicit nonlinear equation for propagation of finite amplitude sound waves. The work results in the methodology of simulation dynamic performance of horn drivers and provides comparative analysis of different acoustical nonlinear and parametric mechanisms.

A new method to predict the evolution of the power spectral density for a finite-amplitude sound wave.

A method to predict the effect of nonlinearity on the power spectral density of a plane wave traveling in a thermoviscous fluid is presented. As opposed to time-domain methods, the method presented here is based directly on the power spectral density of the signal, not the signal itself. The Burgers equation is employed for the mathematical description of the combined effects of nonlinearity and dissipation. The Burgers equation is transformed into an infinite set of linear equations that describe the evolution of the joint moments of the signal. A method for solving this system of equations is presented. Only a finite number of equations is appropriately selected and solved by numerical means. For the method to be applied all appropriate joint moments must be known at the source. If the source condition has Gaussian characteristics (it is a Gaussian noise signal or a Gaussian stationary and ergodic stochastic process), then all the joint moments can be computed from the power spectral density of the signal at the source. Numerical results from the presented method are shown to be in good agreement with known analytical solutions in the preshock region for two benchmark cases: (i) sinusoidal source signal and (ii) a Gaussian stochastic process as the source condition.

Occurrence and Development of Vortices in Turbulent Jets under the Effect of Sawtooth Sound Waves of Finite Amplitude

Consideration is given to the formation of vortices in turbulent jets under the effect of sawtooth sound waves of finite amplitude in the case of internal longitudinal acoustic action. The convection velocity and the rate of rise of the disturbances are determined. It is shown that the transverse dimensions of the disturbances increase linearly on the initial portion of the flow.

Modified lattice Boltzmann method for compressible fluid simulations.

A modified lattice Boltzmann algorithm is shown to have much better stability to growing temperature perturbations, when compared with the standard lattice Boltzmann algorithm. The damping rates of long-wavelength waves, which determine stability, are derived using a collisional equilibrium distribution function which has the property that the Euler equations are obtained exactly in the limit of zero time step. Using this equilibrium distribution function, we show that our algorithm has inherent positive hyperviscosity and hyperdiffusivity, for very small values of viscosity and thermal diffusivity, which are lacking in the standard algorithm. Short-wavelength modes are shown to be stable for temperatures greater than a lower limit. Results from a computer code are used to compare these algorithms, and to confirm the damping rate predictions made analytically. Finite amplitude sound waves in the simulated fluid steepen, as expected from gas dynamic theory.

Nonlinear effects of the finite amplitude ultrasound wave in biological tissues

Nonlinear effects will occur during the transmission of the finite amplitude wave in biological tissues. The theoretical prediction and experimental demonstration of the nonlinear effects on the propagation of the finite amplitude wave at the range of biomedical ultrasound frequency and intensity are studied. Results show that the efficiency factor and effective propagation distance will decrease while the attenuation coefficient increases due to the existence of nonlinear effects. The experimental results coincided quite well with the theory. This shows that the effective propagation distance and efficiency factor can be used to describe quantitatively the influence of nonlinear effects on the propagation of the finite amplitude sound wave in biological tissues.