Evolution of acoustic waves in microinhomogeneous media with quadratic elastic nonlinearity and relaxation

A nonlinear wave equation for the velocity “relaxator” is derived in the framework of the rheological model and the corresponding equation of state of a microinhomogeneous medium containing viscoelastic defects with quadratic nonlinear elasticity. The equation is qualitatively analyzed, and numerical solutions to it are presented for a stationary symmetric shock wave and the evolution of initially harmonic waves.     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

Implementation of a constrained Ritz series modeling technique for acoustic cavity-structural systems

A prior study [Ginsberg, J. H. (2010b). J. Acoust. Soc. Am. 127, 2749-2758] used Ritz series in conjunction with Hamilton's principle to derive general equations describing the time domain response of an acoustic cavity bounded by an elastic structure. The equations of motion are supplemented by constraint equations that explicitly enforce velocity continuity at the cavity's surface. These constraints are imposed by the surface traction, which is represented by unknown coefficients of Ritz-type series. The resulting set of equations are differential-algebraic type. Three methods are presented to convert the governing equations to forms that are familiar to structural acoustics, including one that transforms them from differential-algebraic type to the standard ordinary differential equations associated with linear multi-degree-of-freedom vibratory systems. In cases where only the structure is excited, the formulation offers options as to how displacement/velocity boundary conditions on the nonstructural boundary are enforced, as well as whether zero pressure boundary conditions are enforced at all. An example of a one-dimensional waveguide that is closed at one end by an oscillator is used to explore the quality of solutions obtained from each of these options. Results for natural frequencies and mode functions are examined for accuracy and convergence.     

Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices

We present an algorithm for polarized radiative transfer in a vertically stratified system consisting of two plane-parallel media with different refractive indices. It is based on the discrete ordinate method and includes multiple elastic scattering, thermal radiation, Fresnel reflection and transmission, incident parallel-beam or isotropic radiation at the top of the upper medium and bidirectional reflection at the bottom of the lower medium. Comparisons with results from Monte Carlo simulations show that the discrete-ordinate code provides accurate results for all four elements of the Stokes vector (I, Q, U, and V) at a speed that is orders of magnitude faster.     

Variable step-size based method for acoustic feedback modeling and neutralization in active noise control systems

This paper investigates the issue of the acoustic feedback during online operation of active noise control (ANC) systems. In the existing approach, two FIR filters are used for this task: adaptive for feedback path modeling (FBPM) and fixed for feedback neutralization (FBN). Previously, a simplified method is proposed where these two tasks of modeling and neutralization have been combined into one feedback path modeling and neutralization (FBPMN) adaptive filter. Here we introduce an intuition based variable step size (VSS) parameter, for LMS equation of FBPMN filter. This VSS is motivated from the fact that the error signal of FBPMN filter contains a disturbance-component that is decreasing in nature. The computer simulations are carried out for single-channel and multichannel ANC systems. It is demonstrated that the proposed method achieves better performance than the existing methods.     

Modelling of linear wave propagation in spatial fluid filled pipe systems consisting of elastic curved and straight elements

This paper is concerned with the theoretical analysis of time harmonic dynamics of compound elastic pipes with and without internal fluid loading. Compound pipes are assembled as a sequence of segments, each of which has a constant curvature. As a prerequisite for the wave propagation analysis, dispersion equations are solved, Green’s matrices are formulated and Somigliana’s identities are derived for an isolated curved segment. The governing equations of wave motion of a compound pipe are obtained as an ensemble of the boundary integral equations for individual segments and the continuity conditions at their interfaces. The proposed methodology is validated in several benchmark problems and then applied for analysis of the periodicity effects. The results obtained for piping systems with a variable number of identical curved segments are put into the context of the classical Floquet theory. Brief parametric studies suggest that the curved inserts can be employed as a tool for the passive control of wave propagation in fluid-filled pipes, and their stop band characteristics may be tailored to reach desirable attenuation levels in prescribed frequency ranges.     

Masterequation,H-theorem and stationary solution for coupled quantum systems

We extend the Zwanzig projector formalism to coupled systems taking into account the mutual interactions of the reduced density matrices of both systems. In the Born- and Markoff-approximation we end up with a bilinear masterequation for occupation probabilities, in contrast to the usually studied linear equations. We derive theH-theorem for this equation and show that the stationary solution is the canonical or more generally a grand canonical density matrix.     

Theory and calculation for acoustic radiation mode of weak coupled enclosure

Active structural acoustic control(ASAC)is an efficient method in acoustic radiation control of coupled enclosure.In the past research of ASAC,the concept of acoustic radiation mode(ARM)of coupled enclosurewas proposed,which was a set of basis functions of structural mode amplitude.However,there was an incompatibility with the ARM definition in free space radiation case which was a set of basic functions of normal velocity or pressure on the vibrating surface.Also,there was severe inconvenience for application as structural modes were required while accurate and useful structural modes were difficult to be extracted in practice.To overcome these problems,by analogy to ARM theory of free space,the acoustic potential energy was expressed in quadratic form of normal velocity on coupling surface and ARM of coupled enclosure was redefined.Furthermore,theoretic derivation showed that ARM of coupled enclosure could be replaced simply by corresponding acoustic mode projection of enclosure when the coupling surface was discretized into equal size elements.Therefore,the ARM theory of coupled enclosure which was consistent with that of free space and convenient for application was formed.Finally,numerical calculation was performed and the results proved that the presented theory was very efficient in ARM calculation of coupled enclosure and ASAC.     

Finite element model for waves guided along solid systems of arbitrary section coupled to infinite solid media

The Semi-Analytical Finite Element (SAFE) method is becoming established as a convenient method to calculate the properties of waves which may propagate in a waveguide which has arbitrary cross-sectional shape but which is invariant in the propagation direction. A number of researchers have reported work relating to lossless elastic waves, and recently the solutions for nonpropagating waves in elastic guides and for complex waves in viscoelastic guides have been presented. This paper presents a further development, addressing the problem of attenuating waves in which the attenuation is caused by leakage from the waveguide into a surrounding material. This has broad relevance to many practical problems in which a waveguide is immersed in a fluid or embedded in a solid. The paper presents the principles of a procedure and then validates and illustrates its use on some examples. The procedure makes use of absorbing regions of material at the exterior bounds of the discretized domain.     

Processing of acoustic signals and computer modeling instrumental and programming measuring complex for acoustic navigation investigations

This paper describes the main systems and results of testing a mobile instrumental programming complex developed for experiments on investigation of the influence of hydrophysical processes in the marine environment on the quality of solving the navigation problems using stationary acoustic beacons.     

对声波和弹性波传播模拟的Hamilton系统方法

建立了离散化网格上的准粒子体系，引入此体系的Hamilton系统描述，用来模拟声波和弹性波的传播.介绍了准粒子间相互作用的九点模型并给出互作用系数.证明了Hamilton系统方法 和声波、弹性波方程的关系，并给出两个方法中所使用物理量的关系.使用辛算法对给定的 介质模型进行数值模拟. 关键词： Hamilton系统方法 九点互作用模型 声波方程 弹性波方程 辛算法     

Specific propagation directions of acoustic waves for piezoelectric and nonpiezoelectric media

I reanalyze the problem of the existence of longitudinal normals inside the symmetry planes of piezoelectric crystals belonging to the symmetry class mm2. The equations determining components of longitudinal normals situated outside the symmetry planes for media of this symmetry are discussed. It is proven that nonpiezoelectric media of rhombic symmetry could have 4 or 8 distinct acoustic axes. Examples of nonpiezoelectric elastic media of monoclinic symmetry without acoustic axes are given. The method of determination of the components of acoustic axes for piezoelectric media of arbitrary symmetry is presented. With the help of this method, I discuss the problem of acoustic axes for piezoelectric media of the symmetry class mm2. The text was submitted by the author in English.     

Measurement and modeling of the acoustic field near an underwater vehicle and implications for acoustic source localization

The performance of traditional techniques of passive localization in ocean acoustics such as time-of-arrival (phase differences) and amplitude ratios measured by multiple receivers may be degraded when the receivers are placed on an underwater vehicle due to effects of scattering. However, knowledge of the interference pattern caused by scattering provides a potential enhancement to traditional source localization techniques. Results based on a study using data from a multi-element receiving array mounted on the inner shroud of an autonomous underwater vehicle show that scattering causes the localization ambiguities (side lobes) to decrease in overall level and to move closer to the true source location, thereby improving localization performance, for signals in the frequency band 2-8 kHz. These measurements are compared with numerical modeling results from a two-dimensional time domain finite difference scheme for scattering from two fluid-loaded cylindrical shells. Measured and numerically modeled results are presented for multiple source aspect angles and frequencies. Matched field processing techniques quantify the source localization capabilities for both measurements and numerical modeling output.     

Resonant frequency method for the measurement and uncertainty analysis of acoustic and elastic properties

A resonant frequency method is proposed to determine the bar speed and the Poisson's ratio of a rod several meters long of the kind often used for manufacturing power sonic transducers and mechanical horns in mass production. This method is shown to be robust in a field test and with high resolution for estimation of the bar speed. The uncertainty (standard deviation/average) for the bar speed and the Poisson's ratio can be reduced by appropriately selecting the mode number pairs and increasing the mode number. In this study, the uncertainties of the bar speed and Poisson's ratio are less than 0.043% and 2.9%, respectively. The resonant frequency method is verified by comparing the dilatational wave speeds calculated by elastic theory with those from experiments, the difference between them being less than 0.17%.     

The stabilities, electronic structures and elastic properties of Rb-As systems

The structural, electronic and elastic properties of Rb–As systems (RbAs in NaP, LiAs and AuCu structures, RbAs2 in the MgCu2 structure, Rb3 As in Na3As, Cu3 P and Li3Bi structures, and Rb5 As4 in the A5B4 structure) are investigated with the generalized gradient approximation in the frame of density functional theory. The lattice parameters, cohesive energies, formation energies, bulk moduli and the first derivatives of the bulk moduli (to fit Murnaghan’s equation of state) of the considered structures are calculated and reasonable agreement is obtained. In addition, the phase transition pressures are also predicted. The electronic band structures, the partial densities of states corresponding to the band structures and the charge density distributions are presented and analysed. The second-order elastic constants based on the stress-strain method and other related quantities such as Young’s modulus, the shear modulus, Poisson’s ratio, sound velocities, the Debye temperature and shear anisotropy factors are also estimated.