Acoustic Field Equations Research Articles

On the acoustic wave attenuation in a turbulent medium

Abstract The equation for the mean acoustic field has been obtained for a random turbulent medium using the Green function approach. The correlation function was described by the Karman distribution with the index n=2 approximately≃11/6. Applying Bourret's approximation, the exact expression for the mass operator has been calculated analytically. The frequency dependence of the scattering coefficient of the mean field has been derived. Conditions of Cherenkov radiation are discussed.

Brillouin-induced four-wave mixing using beams with gaussian temporal and spatial profiles

Numerical solutions are obtained to the coupled acoustic and optical field equations for the case where the signal beam is anti-Stokes shifted relative to the pump beam. It is shown that when gaussian temporal pulse profiles are used, the theoretically pre-dicted reflectivity and efficiency are greatly modified owing to the strong dependence of conjugate build up time on signal and pump beam intensity. The effect of varying pulse length, phonon lifetime, and signal-pump timing is studied. Finally the effect of gaussian spatial profiles is considered.

Electromagnetic perturbation on acoustic shear waves generated by magnetostriction

The problem of coupling between mechanical shear waves and electromagnetic waves propagating in magnetostrictive materials has been stressed. The system of the acoustic field equations and the Maxwell ones has been combined with the piezomagnetic constitutive relations to obtain z-propagating x-polarized transversal standing wave characterized both by particle displacement, Ux(z,t), and magnetic field, Hx(z,t). Attention has been paid on the separation of the purely acoustic wave from the hybrid one to the scope to evaluate their difference in velocity D. Generally, the latter is very small (1/105) but it cannot be neglected in new technological materials exhibiting low magnetoelastic coupling coefficients. The difference D has been theoretically obtained for magnetoelastic waves generated in transversally isotropic samples versus the permeability and the magnetoelastic coupling coefficient. Moreover, it has been possible to check the electromagnetic disturbance behavior as a function of the bias field by using our experimental results.

Infrasonic ambient noise in the ocean due to atmospheric pressure fluctuations on the surface

The theory of infrasonic ambient noise in a semiinfinite, isotropic ocean due to random wind-pressure fluctuations acting on the sea surface is reexamined. The surface pressure field is modeled as a Poisson distribution of point forces. This provides a boundary condition that must be satisfied by the solution of the homogeneous Helmholtz equation for the resultant acoustic field in the ocean. Using this solution the spatial coherence function of the ambient noise is constructed, from which the directionality in the vertical is derived and shown to be the same as that for the noise field produced by a random distribution of vertical dipoles on the surface. The power spectrum of the noise scales with the point spectrum of the wind-pressure fluctuations, which is determined empirically from published measurements of wind-pressure spectra taken over water, and with the square of the Helmholtz number for the turbulent sources. Since the Helmholtz number is very much less than unity, it is concluded that wind turbulence is an inefficient mechanism for producing sound in the ocean. A comparison of the final result for the ambient noise power spectrum with measured noise spectra, taken by several investigators in various parts of the world, indicates that wind turbulence generally makes an insignificant contribution to the infrasonic ambient noise in the ocean.

Finite element modeling of acoustic singularities with application to propeller noise

Numerical formulations and results that expand on recent developments in finite element modeling of acoustic volume sources and acoustic dipoles are presented. It is shown that with a suitable structuring of the acoustic field equations it is possible to include monopoles and dipoles within the same analysis framework as has been extensively used for interior duct acoustic and duct inlet radiation problems. This allows the extension of the finite element modeling method to include the noise sources in such applications as propellers enclosed in a duct or in free space with mean flows. The necessary structuring of the acoustic field equations is shown, and example calculations are given for the case of one-dimension al sources and body forces in the presence of mean flow, two-dimensional sources, axial body forces, and transverse body forces in the presence of uniform mean flow. Three-dimensional sources and dipoles are modeled as the Fourier sum of axially symmetric solutions without the necessity of introducing singular elements. It is further demonstrated that distributions of singularities can be readily modeled, and an example is given of the computation of the near- and far-field radiation of a propeller. Comparison of the far-field radiation directivity is made with the Gutin theory.

Deterministic geoacoustic model for a randomly layered ocean bottom

A deterministic wave equation for the mean acoustic field in a randomly layered medium is derived. The wave equation is used to define a “smooth” deterministic geoacoustic model which is acoustically equivalent at low frequencies to a randomly layered model. The wave equation derivation starts with fundamental relations (Newton's law and Hooke's law) and leads to deterministic expressions for effective sound speed, density, and absorption which are similar to those obtained for periodic medium. In particular, the effective sound speed of the deterministic model depends on the grazing angle, being higher for propagation parallel to the layering than for propagation perpendicular to it. When the angular dependence of the effective sound speed is included, the low-frequency (f < 100 –200 Hz) reflection coefficients for the deterministic model are in good agreement with the ensemble averaged coefficients for the associated randomly layered model. Without the angular dependence, the agreement is marginal.

Noise transmission into semicylindrical enclosures through discretely stiffened curved panels

An analytical study of sound transmission into semicylindrical enclosures through discretely stiffened curved elastic panels is presented. The transmitted sound is estimated by solving the acoustic wave equation for the interior acoustic field, a Galerkin-like method being used. This solution is then coupled to the vibration of the stiffened panels. The response characteristics of these panels are determined by using a modal analysis where the modes are obtained by the finite element-strip method. Numerical results include spectra of the interior sound pressure due to white noise, turbulent boundary layer and propeller noise inputs.

Thermoviscous effects on acoustic scattering by thermoelastic solid cylinders and spheres

This paper presents analytic solutions and numerical results of the scattering of plane sound waves from a thermoelastic circular cylinder and from a thermoelastic sphere in an infinite, thermoviscous fluid medium. The thermoelastic properties of the cylinder and the sphere and the viscosity and thermal conductivity of the surrounding fluid are taken into consideration in the solutions of the acoustic-scattering problems. We started with examining the acoustic field equations in thermoviscous fluids and in thermoelastic solids from the standpoints of continuum mechanics and thermodynamics, and then presented the normal-mode solutions to, and numerical examples of, the acoustic scattering by a single cylinder and a sphere. The acoustic parameters of interest are the farfield scattering pattern, the acoustic-radiation force, and the absorption and scattering cross sections. These parameters were first derived in closed forms and then evaluated numerically for a given set of material properties.

Classroom exercise programs for numerically predicting and graphically displaying propagation characteristics of sound

Several computer programs will be described which were developed for an introductory graduate course in underwater acoustics that was offered at a government laboratory (DTNSRDC) where Tektronix or H.P. graphics computers were available to most of the students. One program numerically solves the acoustic field equations in one dimension by a finite difference method. This program has been used to illustrate the reflection of sound at boundaries and effects of transmission into a second (or third) medium where the acoustic impedance and sound speed might differ. A second program numerically solves the acoustic field equations in two spatial dimensions. A ray tracing program will be described which illustrates the major features of sound propagation in inhomogeneous media and a program which plots beam patterns for an array with an arbitrary number of elements spaced at arbitrary distances apart will also be presented. The programs are written in BASIC and include interactive features which allow the studen...

Dynamics of a Submerged Ring-Stiffened Spherical Shell

The transient response of a ring-stiffened spherical shell to a sudden pressure increase in the surrounding acoustic medium is investigated. A modal expansion approach is used to analyze the shell, while the acoustic field equation is solved by invoking the Helmholtz integral. Coupling of the two fields occurs through the enforcement of continuity of the velocity components at the shell-fluid interface. Two solutions to the same problem are obtained by using plane and cylindrical wave approximations of the acoustic field. These approximate solutions fail to predict the transient behavior for the shell configuration analyzed. The result of this study indicates that a large dynamic factor must be assumed in the design of submerged, stiffened, spherical shell structures, if explosive loads are likely to be encountered.

Perturbation Theory for Electromagnetic Coupling to Elastic Surface Waves on Piezoelectric Substrates

Starting from the fundamental acoustic and electromagnetic field equations an approximate expression is obtained for the perturbation in propagation wavenumber of a surface acoustic wave in a piezoelectric crystal. The source of perturbation is taken to be a surface spaced an air-gap distance h above the piezoelectric and is described in terms of an electrical impedance. The resulting perturbation is found in terms of the perturbing electrical impedance, an effective dielectric constant for the piezoelectric, the air-gap spacing h, and a perturbation coupling constant defined in terms of the unperturbed electric potential at the piezoelectric surface and the average acoustic power flow per unit frequency. The theory is applied to the case of a short-circuit perturbing surface and found to be in excellent agreement with certain numerical results for Y-cut Z-propagating LiNbO3 and several cuts of Bi12 GeO20. In the general case of a complex perturbing impedance, such as that exhibited by a semiconductor, the theory indicates that attenuation or gain and dispersion may be introduced by the perturbation, in close agreement with experimental observations.

Application of Microwave Concepts to the Theory of Acoustic Fields and Waves in Solids

During the past 20 years the value of the microwave approach to electromagnetic field problems has been amply demonstrated. The purpose of this paper is to show the basic similarity of acoustic and electromagnetic field equations and to exploit this fact in applying microwave methods to acoustic resonator and waveguide problems. This is accomplished most directly and efficiently by using symbolic notation, rather than tensor subscripts, for the acoustic fields. The usefulness of this notation is illustrated by the problems of plane wave propagation and piezoelectric stiffening in an anisotropic medium, and by derivations of Poynting's and reciprocity theorems for a piezoelectric medium. Piezoelectric resonators are treated in detail from the point of view of normal mode expansions. A general network representation is obtained and is applied to the disk transducer, as an example. Normal mode theory of piezoelectric waveguides is briefly sketched and a perturbation theorem, which can be applied to both resonator and waveguide problems, is derived.

Interaction of a Ring-Reinforced Shell and a Fluid Medium

This work is concerned with the transient dynamic response of a periodically ring-reinforced, infinitely long, circular cylindrical shell to a uniform pressure suddenly applied through the surrounding acoustic medium. The incident particle velocity is zero, and the rings are assumed to be slightly flexible. A classical theory of the Donnell type is used to analyze the shell while the fluid is described by the linear acoustic field equation. The solution is obtained by assuming a power series expansion in the ring stiffness parameter and utilizing a technique which reduces the transient dynamic problem to an equivalent steady-state formulation. Numerical results are presented for a steel shell immersed in salt water for different ring spacings. For the case of rigid rings, a cylindrical and plane wave approximation was also used to represent the fluid field. It is shown that the cylindrical wave approximation yields reasonably accurate results. Flexible ring results, although limited, indicate that undamped or nonradiating components of the shell vibration are activated.