摘要:

A new method to calculate the diffraction of elastic waves by cracks or cavities is presented. The method yields the complete diffracted wave field and is valid at any frequency. It is based on a discretization of the inclusion surface and on the assumption of a periodic repetition of the diffracting inclusion. Body forces are applied at the discretized points along the inclusion surface and the discrete wavenumber method is used to evaluate the resulting radiation. The application of the boundary conditions then leads to a linear system of equations, which is solved by matrix inversion. Examples of calculation and comparisons with results from other techniques are presented in the case of plane incident waves as well as in the case of a line source. The presence of a free surface is also considered.

ISSN:0001-4966    

DOI:10.1121/1.394779

出版商:Acoustical Society of America    

年代:1987

数据来源: AIP

摘要:

The scattering problem of an incident plane sound wave by a soft arbitrarily shaped body as well as its allied diffraction problem by a disk is discussed. A first‐class Fredholm integral equation is posed which, for low frequencies, yields a potential equations sequence for a wavenumber power solution expansion. The power solution expansion coefficients of the scattering cross section and the farfield amplitude up toO(κ6), where κ is the wavenumber, are found to be related through only a few low‐order solutions of the above equations. Reciprocity relations between them were exploited. The following new general formulas are obtained. The scattering cross‐section coefficient σ4ofO(κ4) is found in terms of three solutions up toO(κ2), rather than six solutions up toO(κ5). As for the farfield amplitude, the sixth (fifth, fourth, and third) coefficient ofO(κ5) (κ4, κ3, and κ2) is related to only six (five, four, and two) solutions up toO(κ3) (κ2, κ, and κ). As an application of the above results, the coefficient σ4is explicitly calculated using newly found solutions for an elliptic disk. Also, the circular disk results are shown for an arbitrary angle of incidence.

ISSN:0001-4966    

DOI:10.1121/1.394780

出版商:Acoustical Society of America    

年代:1987

数据来源: AIP

摘要:

The transition matrix (Tmatrix) for acoustic waves scattered by a multilayered inclusion with arbitrary geometry is reformulated by applying the Green’s identity for scalar wavefunctions. The derivation of theTmatrix is much simpler than previous formulations based on the Helmholtz integral formula. Further simplification is accomplished by a new combination of basis functions for refracted waves. The final answer is different but can be reduced to previous results.

ISSN:0001-4966    

DOI:10.1121/1.394781

出版商:Acoustical Society of America    

年代:1987

数据来源: AIP

摘要:

The acoustic field in an automobile cabin can be calculated using a Green’s function method. A method for calculating the acoustic field of an arbitrary volume bounded by an arbitrary surface is shown. The eigenvalues of the system, including the effects of arbitrary shape and surface impedance, are found. Alternatively, the acoustic response is calculated when one or more of the surfaces is in vibration without first calculating the eigenvalues. The method works equally well in one, two, or three dimensions.

ISSN:0001-4966    

DOI:10.1121/1.394782

出版商:Acoustical Society of America    

年代:1987

数据来源: AIP

摘要:

This article provides theoretical results for the acoustic power output from point sources moving with an arbitrary subsonic speed along a general trajectory. Applications to steady and nonsteady rotational motions and to rectilinear and elliptical motions are presented. A harmonic analysis of the power output from one or more point sources in steady rotational motion is given, which includes an account of the distribution among individual modes at different speeds.

ISSN:0001-4966    

DOI:10.1121/1.394783

出版商:Acoustical Society of America    

年代:1987

数据来源: AIP

摘要:

Noncollinear wave interaction in a rectangular duct is investigated both theoretically and experimentally. An inhomogeneous wave equation, exact to second order in the field variables, is derived for the sum and difference frequency pressure waves generated by noncollinear interaction of two finite amplitude plane waves in a lossless fluid. This equation is extended to the interaction of waves in higher‐order modes of a rectangular duct. Quasilinear solutions are obtained, and tube wall attenuation is includedadhoc. Experimental results are reported for the interaction of waves in the (0,0) and (1,0) modes of an air‐filled rectangular duct. Theory and experiment are in excellent agreement with regard to oscillatory structure of the sum and difference frequency wave fields. Although overall agreement between theory and experiment is reasonable (±2 dB), it is not within estimated experimental error (±1 dB). It is shown that because local rather than cumulative nonlinear effects dominate the interaction, knowledge of the proper second‐order source condition is of crucial importance. Discrepancies between the predicted and measured amplitudes are attributed to an inadequate description of the source condition.

ISSN:0001-4966    

DOI:10.1121/1.394784

出版商:Acoustical Society of America    

年代:1987

数据来源: AIP

摘要:

Random waves in one‐dimensional nonlinear elastic materials are considered. An integrodifferential equation is derived that governs the variation of the strain spectrum during propagation. By discretizing the spectrum with respect to the frequency, the spectral equation reduces to a system of ordinary differential equations for the discrete values of the spectrum. Numerical results are given for plane random longitudinal waves in an aluminum alloy. It is found that harmonic sound waves are generated for a narrow‐band spectrum, the power spectrum grows faster for higher frequencies for a wideband spectrum, and secondary waves are generated due to the interaction of two bands of spectra.

ISSN:0001-4966    

DOI:10.1121/1.394785

出版商:Acoustical Society of America    

年代:1987

数据来源: AIP

摘要:

In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results are compared with predictions of conservation theorems for energy and momentum.

ISSN:0001-4966    

DOI:10.1121/1.394786

出版商:Acoustical Society of America    

年代:1987

数据来源: AIP

摘要:

As intense, initially sinusoidal waves propagate in fluids, shocks form and excess attenuation of the wave occurs. We present data indicating that shock formation is not necessary for the occurrence of excess attenuation in nonlinear, lossy media, i.e., air‐saturated, porous materials. An empirical equation is used to describe the excess attenuation of intense sinusoids in porous materials. The acoustic nonlinearity of and the excess attenuation in porous materials may be predicted directly from dc flow resistivity data. An empirical relationship is used to relate an acoustic nonlinearity parameter to the fundamental frequency and relative dc nonlinearity of two structurally different materials.

ISSN:0001-4966    

DOI:10.1121/1.394787

出版商:Acoustical Society of America    

年代:1987

数据来源: AIP

摘要:

This article presents a new method for studying wave propagation in an unbounded medium where the square of the refractive index is of a general three‐dimensional quadratic form. By this method, the Green’s function can be expressed exactly by a onefold integral, for which the integrand is derived from a path integral. The numerical results for one‐dimensional Green’s functions in linearly stratified media are first checked with those obtained from the well‐known Airy function expressions. The method is then applied to obtain the three‐dimensional Green’s functions for linear stratified media and for parabolic profiles with range‐dependent (horizontal) variations. Some interesting phenomena caused by the horizontal variations (i.e., range dependence) of the medium will be shown and interpreted by simple ray pictures whenever appropriate. For the special case of a parabolic profile with symmetric turning points, a wave duct is formed and the Green’s function can be expanded as a series of wave modes. It will be shown that an evanescent mode in a purely stratified medium may switch to a propagating mode due to the range dependence of the medium property. Application of the results to acoustic wave propagation in the atmosphere and in the ocean will be discussed.

ISSN:0001-4966    

DOI:10.1121/1.394788

出版商:Acoustical Society of America    

年代:1987

数据来源: AIP