Propagation of sound from a monopole source above an impedance-backed porous layer

In this article, the propagation of sound from a monopole source above an impedance-backed porous layer is examined. The sound fields can be expressed in an integral form that is amenable to further analysis. A standard method of steepest descents is applied to evaluate the integral where the method of pole subtraction is needed to obtain a uniform asymptotic solution for the sound field above the plane surface. To obtain a numerical solution, the location of the pole was determined numerically by means of the Newton-Raphson method. Based on the pole location, the sound fields can then be calculated numerically. It has been demonstrated that the use of a plane wave reflection coefficient to calculate the sound fields is a special case of the asymptotic formula when the pole is located further away from the saddle point.     

The exact response of a two-dimensional flat-layered medium to a probing pulse: An application to a layer stripping reconstruction procedure

Abstract

We consider a simple model problem that can be found in many fields of application such as, for example, reflection seismology. That is we consider an initial boundary value problem on a half-plane for a class of two-dimensional wave equations with a piecewise-constant coefficient. This coefficient describes the flat layered medium under consideration. An initial pulse located on the boundary of the half-plane is used to probe the medium. An integral representation of the solution of this problem is obtained by studying the spectral measures of some differential operators in one variable. This integral representation is exploited to obtain an ‘explicit’ formula for the solution of the problem considered evaluated at the location of the probing pulse. This ‘explicit’ formula is exploited to reconstruct the structure of the medium from its response to a probing pulse via a layer stripping procedure. Some numerical results obtained with this procedure on test problems are shown. The ‘explicit’ formula obtained can be used in several other contexts such as, for example, the study of perturbed flat layered media or the study of random flat layered media.     

Fast asymptotic solutions for sound fields above and below a rigid porous ground

The current study simultaneously addresses the problem of reflection and refraction of sound from a rigid porous ground surface. A more rigorous approach is used to derive more accurate asymptotic solutions that can be cast in a convenient form for ease of numerical implementations. The solutions provide means for rapid computations of the sound fields above and below the rigid porous ground. The improved asymptotic formulas for both situations agree well with numerical results obtained by other numerical schemes, which are more accurate but computationally more intensive. More importantly, the asymptotic solutions can be written in the well-known form of the Weyl-van der Pol formula, which provides a direct correlation between the reflected wave term for the sound field above the porous ground and the transmitted (refracted) wave term for the sound field below.     

Investigation on electromagnetic scattering from rough soil surface of layered medium using the small perturbation method

Electromagnetic scattering from a rough surface of layered medium is investigated, and the formulae of the scattering coefficients for different polarizations are derived using the small perturbation method. A rough surface with exponential correlation function is presented for describing a rough soil surface of layered medium, the formula of its scattering coefficient is derived by considering the spectrum of the rough surface with exponential correlation function; the curves of the bistatic scattering coefficient of HH polarization with variation of the scattering angle are obtained by numerical calculation. The influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the roughness surface parameters and the frequency of the incident wave on the blstatic scattering coefficient is discussed. Numerical results show that the influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the rms and the correlation length of the rough surface, and the frequency of the incident wave on the bistatic scattering coefficient is very complex.     

Sound propagation above a porous road surface with extended reaction by boundary element method

Acoustic impedance of an absorbing interface is easily introduced in boundary element codes provided that a local reaction is assumed. But this assumption is not valid in the case of porous road surface. A two-domain approach was developed for the prediction of sound propagation above a porous layer that takes into account the sound propagation inside the porous material. The porous material is modeled by a homogeneous dissipative fluid medium. An alternative to this time consuming two-domain approach is proposed by using the grazing incidence approximate impedance in the traditional single-domain boundary element method (BEM). It can be checked that this value is numerically consistent with the surface impedance calculated at the interface from the pressure and surface velocity solutions of the two-domain approach. The single-domain BEM introducing this grazing incidence impedance is compared in terms of sound attenuation with analytical solutions and two-domain BEM. The comparison is also performed with the single-domain BEM using the normal incidence impedance, and reveals a much better accuracy for the prediction of sound propagation above a porous interface.     

Surface impedance design with ground corrugation for mitigation of large-calibre gun blast noise

The surface impedance design approach is proposed for mitigating large-calibre gun blast noise. Surrounding the blast noise, we employ a group of concentric trenches with critical depths to dampen the propagation of the acoustic wave. These trenches behave like quarter-wavelength resonators and produce acoustic soft surfaces at their openings. The sound pressure is then mitigated over these soft surfaces by destructive interference and the wave attenuates rapidly along the ground surface. To evaluate the overall acoustic performance of such a design, we develop an efficient numerical solver by treating the geometry as a body of revolution (BOR). The symmetry of the structure in the revolution direction allows the 3D boundary integral equation (BIE) for acoustic wave scattering to be reduced to a 2D integral equation by the use of Fourier series expansions. Numerical experiments show that this model can effectively suppress the acoustic wave propagation horizontally and the reduction can reach about 15 dB for large-calibre gun noise with very low-frequency components.     

Acoustical estimation of parameters of porous road pavement

In the simplest case, porous road pavement of a known thickness is described by such parameters as porosity, tortuosity, and flow resistance. The problem of estimating these parameters is investigated in this paper. An acoustic signal reflected by the pavement is used for this. It is shown that this problem can be solved by an experiment conducted in the time domain (i.e., the pulse response of the media is recorded). The incident sound wave is thrown at a grazing angle to the surface between the pavement and the air to improve penetration into the porous medium. The procedure of computing of the pulse response using the Morse-Ingard model is described in detail.     

Surface response of a viscoelastic medium to subsurface acoustic sources with application to medical diagnosis

The response at the surface of an isotropic viscoelastic medium to buried fundamental acoustic sources is studied theoretically, computationally and experimentally. Finite and infinitesimal monopole and dipole sources within the low audible frequency range (40-400 Hz) are considered. Analytical and numerical integral solutions that account for compression, shear and surface wave response to the buried sources are formulated and compared with numerical finite element simulations and experimental studies on finite dimension phantom models. It is found that at low audible frequencies, compression and shear wave propagation from point sources can both be significant, with shear wave effects becoming less significant as frequency increases. Additionally, it is shown that simple closed-form analytical approximations based on an infinite medium model agree well with numerically obtained "exact" half-space solutions for the frequency range and material of interest in this study. The focus here is on developing a better understanding of how biological soft tissue affects the transmission of vibro-acoustic energy from biological acoustic sources below the skin surface, whose typical spectral content is in the low audible frequency range. Examples include sound radiated from pulmonary, gastro-intestinal and cardiovascular system functions, such as breath sounds, bowel sounds and vascular bruits, respectively.     

多孔弹性介质三层夹心板的隔声性能研究

应用Biot关于流体饱和多孔弹性介质的声传播理论,采用传递矩阵的分析方法,就复合多孔弹性材料夹心三层板在不同结构情况下的隔声性能进行了理论研究和实验分析,并与同等条件下双层夹心板的隔声性能进行了比较。数值计算和实验结果均表明,与双层夹心板相比,三层夹心板在中高频段隔声性能有明显优势,但低频段隔声性能有一定程度上的下降。研究还表明不同结构的复合三层夹心板在隔声效果上也各有特色。     

A finite difference method for a coupled model of wave propagation in poroelastic materials

A computational method for time-domain multi-physics simulation of wave propagation in a poroelastic medium is presented. The medium is composed of an elastic matrix saturated with a Newtonian fluid, and the method operates on a digital representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is presented which can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers.     

含空气层与多孔材料的复合结构隔声特性研究

基于高速列车减振降噪需求,本文应用Biot提出的多孔弹性介质声传播理论,采用传递矩阵法理论推导了典型分层结构的隔声量计算公式,给出了空气层与多孔材料对分层复合结构隔声特性的影响。将传递矩阵与遗传算法相结合,对特定中低频段内的复合结构隔声特性进行了优化。研究结果表明:空气层和多孔材料有助于分层复合结构隔声量的提高,特别是空气层对低频隔声有很好的促进作用,另外空气层与多孔材料的分配情况也影响着隔声效果。含有空气层的复合结构在提高隔声量的同时降低了结构的总体重量,实现了高速列车隔声材料低能耗和轻量化的设计目标。     

分层吸声结构的声学设计与性能分析

本文给出了声波在多层介质中的传播方程，通过数值计算，分析了各层参数对分层吸声结构声学性能的影响规律。用参数匹配方法，对多层吸声结构各层材料的参数进行设计。结果表明，通过合理分布各层材料，多层吸声结构可以在较宽频段上达到满意的吸声性能。     

Theory of sound propagation in superfluid-filled porous media

The theory of sound propagation in macroscopically isotropic and homogeneous porous media saturated with superfluid ⁴He has been developed neglecting all damping processes. The case when the normal fluid component is locked inside a porous medium by viscous forces is investigated in detail. It is shown that in this case one shear wave and two longitudinal, fast and slow, waves exist. Fast wave as well as slow wave is accompanied with temperature oscillations. The velocities of these waves are obtained.     

Numerical simulation of nonlinear propagation of sound waves in a finite horn

Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied.A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solve the governing equation.Because of the nonlinear wave distortion and reflected sound waves at the mouth,broadband time-domain impedance boundary conditions are employed.The impedance approximation can be optimized to identify the complex-conjugate pole-residue pairs of the impedance functions,which can be calculated by fast and efficient recursive convolution.The numerical results agree very well with experimental data in the situations of weak nonlinear wave propagation in an exponential horn,it is shown that the model can describe the broadband characteristics caused by nonlinear distortion.Moreover,finite-amplitude acoustic propagation in types of horns is simulated,including hyperbolic,conical,exponential and sinusoidal horns.It is found that sound pressure levels at the horn mouth are strongly affected by the horn profiles,the driving velocity and frequency of the piston.The paper also discusses the influence of the horn geometry on nonlinear waveform distortion.     

An effective quiescent medium for sound propagating through an inhomogeneous,moving fluid

The idea of similarity between acoustic fields in a moving fluid and in a certain "effective" quiescent medium, first put forward by Lord Rayleigh, proved very helpful in understanding and modeling sound propagation in an atmosphere with winds and in an ocean with currents, as well as in other applications involving flows with small velocity compared to sound speed. Known as effective sound speed approximation, the idea is routinely utilized in the contexts of the ray theory, normal mode representation of the sound field, and the parabolic approximation. Despite the wide use of the concept of effective sound speed in acoustics of moving media, no theoretical justification of Rayleigh's idea was published that would be independent of the chosen representation of the sound field and uniformly apply to distinct propagation regimes. In this paper, we present such a justification by reducing boundary conditions and a wave equation governing sound fields in the inhomogeneous moving fluid with a slow flow to boundary conditions and a wave equation in a quiescent fluid with effective sound speed and density. The derivation provides insight into validity conditions of the concept of effective quiescent fluid. Introduction of effective density in conjunction with effective sound speed is essential to ensure accurate reproduction of acoustic pressure amplitude in the effective medium. Effective parameters depend on sound speed, flow velocity, and density of the moving fluid as well as on sound propagation direction. Conditions are discussed under which the dependence on the propagation direction can be avoided or relaxed.     

高斯分层介质粗糙面光波透射问题的微扰法研究

运用微扰法研究平面波入射分层介质粗糙面的光波透射问题,推出了不同极化状态的透射光波散射系数公式。采用高斯粗糙面来模拟实际的分层介质粗糙面,结合高斯粗糙面的功率谱导出了平面波入射高斯分层介质粗糙面的透射系数计算公式。通过数值计算得到HH极化透射系数随透射光波散射角变化的曲线,讨论底层介质介电常数、中间介质介电常数和厚度、粗糙面参数及入射光波长对透射系数的影响。数值计算结果表明：底层介质介电常数、中间介质介电常数和厚度、粗糙面参数及入射光波长对透射系数的影响是非常复杂的。     

Propagation of sound waves through a spatially homogeneous but smoothly time-dependent medium

The propagation of sound through a spatially homogeneous but non-stationary medium is investigated within the framework of fluid dynamics. For a non-vortical fluid, especially, a generalized wave equation is derived for the (scalar) potential of the fluid velocity distribution in dependence of the equilibrium mass density of the fluid and the sound wave velocity. A solution of this equation for a finite   transition period τ$\tau$ is determined in terms of the hypergeometric function for a phenomenologically realistic, sigmoidal change of the mass density and sound wave velocity. Using this solution, it is shown that the energy flux of the sound wave is not conserved but increases always   for the propagation through a non-stationary medium, independent of whether the equilibrium mass density is increased or decreased. It is found, moreover, that this amplification of the transmitted wave arises from an energy exchange with the medium and that its flux is equal to the (total) flux of the incident and the reflected wave. An interpretation of the reflected wave as a propagation of sound backward in time is given in close analogy to Feynman and Stueckelberg for the propagation of anti-particles. The reflection and transmission coefficients of sound propagating through a non-stationary medium is analyzed in more detail for hypersonic waves with transition periods τ$\tau$ between 15 and 200 ps as well as the transformation of infrasound waves in non-stationary oceans.     

Computing the far field scattered or radiated by objects inside layered fluid media using approximate Green's functions

A numerically efficient technique is presented for computing the field radiated or scattered from three-dimensional objects embedded within layered acoustic media. The distance between the receivers and the object of interest is supposed to be large compared to the acoustic wavelength. The method requires the pressure and normal particle displacement on the surface of the object or on an arbitrary circumscribing surface, as an input, together with a knowledge of the layered medium Green's functions. The numerical integration of the full wave number spectral representation of the Green's functions is avoided by employing approximate formulas which are available in terms of elementary functions. The pressure and normal particle displacement on the surface of the object of interest, on the other hand, may be known by analytical or numerical means or from experiments. No restrictions are placed on the location of the object, which may lie above, below, or across the interface between the fluid media. The proposed technique is verified through numerical examples, for which the near field pressure and the particle displacement are computed via a finite-element method. The results are compared to validated reference models, which are based on the full wave number spectral integral Green's function.     

Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green's function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed.