摘要:

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converge slowly for high frequency waves. In this paper, a fast numerical solution is presented for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single‐ and double‐layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, it is shown that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

ISSN:0001-4966    

DOI:10.1121/1.410559

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

A prominent feature predicted for the backscattering of tone bursts by thin spherical shells is an enhancement of a guided wave contribution near the first longitudinal resonance. This has been explained with a backward ray model of a leaky Lamb wave where energy is leaked off without having circumnavigated the far side of the shell [P. L. Marstonetal., J. Acoust. Soc. Am.90, 2341 (1991); D. H. Hughes, Ph.D. thesis, Washington State University (1992)]. The relevants2bLamb wave has opposing group and phase velocities giving rise to prompt radiation following the direct specular echo. The present research gives a comparison between a ray theory approximation and experiments in which tone bursts having carrier frequencies in the range 585

ISSN:0001-4966    

DOI:10.1121/1.410560

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

Reflection, diffraction, and higher order diffractions from a finite width wedge construction on an effectively infinite plane were studied experimentally and theoretically. The construction consisted of a 12.6‐cm‐width angle iron on dry wall board or sheet rock. The experiments used a spark as a point source with a separated receiver at the same side of the wedge. The reflected pressure signals were well separated in time domain. Higher order diffractions from the apex and troughs of the wedge were observed. The experimental geometry is in the reflections and is different [Medwinetal., J. Acoust. Soc. Am.72, 1005–1013 (1982)] transmission and shadow geometry. Medwinetal.’s Huygens based constructions were used to compute the double diffraction events.

ISSN:0001-4966    

DOI:10.1121/1.410561

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

An original formalism that allows a thorough understanding of cross‐correlation‐based phase aberration correction techniques in a scattering medium is developed. This formalism is based on the analysis of the second‐order statistics of the pressure field scattered by a random distribution of scatterers. One of the major interests of this analysis is the ability it provides to evaluate and monitor the convergence of phase aberration correction techniques. This is achieved by the computation of a single parameterCthat serves as a focusing criterion. The theoretical developments are validated experimentally.

ISSN:0001-4966    

DOI:10.1121/1.410562

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

The boundary element method is applied to acoustic radiation and scattering from three‐dimensional objects submerged in a perfect waveguide. To simulate an idealized shallow‐water environment, the top surface is assumed to be perfectly soft and the bottom surface perfectly rigid. The waveguide Green’s function is calculated by either the image solution at short ranges or the normal‐mode solution at long ranges. Empirical rules of thumb for determining the so‐called ‘‘long ranges’’ are given. Since computation of the Green’s function is very time consuming, a so‐called ‘‘Green’s‐function interpolation technique,’’ recently developed for multifrequency acoustical analysis, is adopted to speed up the matrix formation procedure. It is found in many cases that the total CPU time is reduced to only one third of the conventional integration approach. The use of an improved CHIEF method to overcome the well‐known nonuniqueness difficulty at certain fictitious eigenfrequencies is also explored. An estimate of the matrix condition computed from a QR‐decomposition least‐squares solver is used to monitor the quality of the CHIEF solution.

ISSN:0001-4966    

DOI:10.1121/1.410563

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

This paper deals with a three‐dimensional elasticity investigation of wave propagation in an infinitely long hollow cylinder whose homogeneous or layered structure is made by generally orthotropic or monoclinic materials. The analysis is based on a recursive formulation of a successive approximation method employed elsewhere by the authors for the study of axisymmetric and flexural vibrations of homogeneous orthotropic and cross‐ply laminated hollow cylinders of finite length. The method has further been applied in connection with static and thermoelastic analyses of orthotropic homogeneous and cross‐ply laminated cylinders and cylindrical panels. In all cases considered, results of this approach converge very rapidly toward corresponding exact three‐dimensional elasticity results. Hence the present study is based on essentially exact three‐dimensional elasticity results and is further expected to serve as a benchmark for corresponding future investigations based on finite element and/or two‐dimensional shell theory formulations.

ISSN:0001-4966    

DOI:10.1121/1.410564

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

An extension of Biot’s theory is proposed for frozen porous media where the solid substrate, ice particles, and unfrozen water can coexist. Elastic, kinetic, and dissipation energy densities are written using the results of continuum mechanics, then the equations of propagation are deduced with the help of Lagrange’s equations and Hamilton’s least‐action principle. The ice parameters are introduced in the model in addition to those used in Biot’s theory. It appears that only the percolation theory is able to describe the transition of the ice matrix between the continuous state and the discontinuous state during a freezing or a thawing process. The resolution of the equations of propagation lead to the existence of three longitudinal and two transverse modes. Their velocities and attenuations are calculated as functions of the physical parameters of the medium. Independently, a thermodynamical argument is developed which allows the mechanical properties to be related to temperature. Experimental results are briefly presented to confirm the theoretical predictions.

ISSN:0001-4966    

DOI:10.1121/1.411336

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

The scattering of guided elastic waves from a circumferential crack in an isotropic hollow cylinder is investigated analytically using theS‐parameter formalism. A general formula, analogous to that of [B. A. Auld,AcousticFieldsandWavesinSolids(Krieger, Malabar, FL, 1990), 2nd ed., Vol. II, p. 200], is derived for the scattered amplitude of an arbitrary mode due to the incidence of an arbitrary mode. The amplitudes are expressed as an integral of the inner product of the crack opening displacement caused by the incident mode and the traction field of the scattered mode. Using a simple approximate form of known elastostatic solutions for the crack opening displacements due to pure tension, a formula is derived for the scattering of guided wave modes of arbitrary circumferential order due to the incidence of axisymmetric wave modes with large wavelength and uniform stress distribution. These results are analyzed and conclusions drawn on the possibility of crack sizing using relatively simple scattering amplitude information.

ISSN:0001-4966    

DOI:10.1121/1.410565

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

An approximate model is proposed for the solution of the problem of the radiation of transient pulses in an elastic medium. The proposed approximation leads to an explicit integral formula for the elastic displacement vector radiated by an arbitrary source of traction applied to an elastic medium. The radiation integral obtained is shown to be closely related to the well‐known Rayleigh integral for the radiation in fluids. To illustrate the potential of our formulation and to test the accuracy of the approximations made in the derivation, the radiation integral is calculated in the case of a flat disc thickness‐mode transducer directly coupled to an elastic half‐space. The similarity of our formula with the Rayleigh integral allows the use of the impulse‐response approach for the calculation. An analytic expression is obtained for the elastic displacement vector which is directly related to the classical solution for the transient acoustical potential radiated in a fluid, as stated by Weight [J. P. Weight, ‘‘A model for the propagation of short pulses of ultrasound in a solid,’’ J. Acoust. Soc. Am.81(4), 815–826 (1987)]. Results obtained with the present model are compared with exact results. It is shown that the approximate model is suitable for predicting the displacement field generated by ultrasonic transducers typical of those used in pulse‐echo measurements in nondestructive testing. Throughout, particular attention is given to the assumptions and approximations made in deriving the model with clear definition of its domain of validity.

ISSN:0001-4966    

DOI:10.1121/1.410566

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

An analytic expression is proposed for the radiation of transient pulses by an ultrasonic shear wave transducer directly coupled to an elastic medium (Y‐cut crystal). The expression of the displacement vector is obtained by combination of the impulse‐response approach with the approximate integral formula for the transient radiation of elastic waves by an arbitrary transducer proposed by Lhémery [A. Lhémery, ‘‘A model for the transient ultrasonic field radiated by an arbitrary loading in a solid,’’ J. Acoust. Soc. Am.96, 3776–3786 (1994)].

ISSN:0001-4966    

DOI:10.1121/1.410567

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP