摘要:

The spectral method is considered in solving boundary integral equations. By subtracting known solutions from the Helmholtz integral equation, the singularities of the Helmholtz integral equation are removed. Therefore, any order of basis functions, used in spectral methods, that times nonsingular kernels in the modified Helmholtz integral equation can be integrated easily and efficiently. Instead of solving the variables at collocation points using conventional methods, the generalized Fourier coefficients are solved by the spectral method which reduces the number of unknowns and the storage of matrix elements in computation. Scattering and radiation problems from a sphere are used to illustrate the technique in the present paper.

ISSN:0001-4966    

DOI:10.1121/1.419717

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

The propagation of elastic plane waves in orthotropic incompressible materials is examined under plane strain conditions in a plane of symmetry. The slowness surface is obtained by aligning a material axis of symmetry with the direction of minimum phase speed. The existence of incident homogeneous waves and reflected homogeneous and nonhomogeneous waves in the presence of a planar interface separating two half-spaces is subsequently examined. A surface which separates the range of existence of two homogeneous reflected waves from that of one homogeneous and one nonhomogeneous is obtained in terms of the angle of incidence, the orientation of the interface with respect to the material axis of symmetry, and one elastic parameter. The critical orientation beyond which there exist two homogeneous reflected waves is derived in explicit form in terms of the elastic parameter. Reflection coefficients are obtained and discussed when the interface is a free surface. Exclusion points are defined in the range of existence of the reflected waves as points for which only one reflected (homogeneous) wave exists. The analysis is complemented with numerical examples.

ISSN:0001-4966    

DOI:10.1121/1.419767

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

A general time-domain approach is presented to address the acoustic transient radiation and scattering problem from fluid-loaded elastic shells. The approach is based on utilizing anin-vacuoeigenvector expansion with time-dependent coefficients for the velocity field of the shell. The time-dependent modal velocity coefficients of the shell are described by a universal set of coupled convolution integral equations. Substitution of the eigenvector expansion into the Kirchhoff integral solution leads to the external pressure field being expressed as a modal sum of convolution integrals of mode and space-dependent pressure impulse response functions with the modal velocity coefficients. Special cases which include an unbaffled finite plate and an arbitrarily shaped shell of revolution are addressed using the general approach. Simple closed-form expressions are presented for the pressure impulse response functions for the unbaffled finite plate and the on-axis response of a general shell of revolution. The characteristics of the mode and space-dependent far-field pressure impulse response functions for an unbaffled simply supported plate and a spherical shell are presented to illustrate the general characteristics of the impulse response functions.

ISSN:0001-4966    

DOI:10.1121/1.419768

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

Two-dimensional boundary element simulations are conducted to investigate the properties of Rayleigh-type fracture interface waves generated by a line source located near a single fracture. The fracture is modeled as a displacement–discontinuity boundary condition between two elastic half-spaces with identical properties. Numerical simulations are performed for different fracture stiffnesses, source polarizations, and source depths. Symmetric and antisymmetric fracture interface waves are observed with amplitudes and velocities that are controlled by the ratio of the fracture impedance to the half-space shear wave impedance, as predicted by plane-wave theory [Gu et al., J. Geophys. Res.101, 827–835 (1996); Pyrak-Nolte and Cook, Geophys. Res. Lett.14, 1107–1110 (1987)]. When the source is located off the fracture, these waves develop at incidence angles that decrease with source depth.

ISSN:0001-4966    

DOI:10.1121/1.419769

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

This study consists of laboratory measurements of dilatational waves propagating through an air-filled unconsolidated sand. One excitation technique consists of a loudspeaker suspended in the air above the packing of sand. A second excitation technique uses a mechanical shaker in contact with the sand. The transmitted signals are received using microphones and geophones located at various depths within the sand. An interpretation based on measured phase speeds indicates that the transmitted energy from the suspended loudspeaker source is partitioned primarily but not exclusively into the type-II dilatational wave. This wave attenuates rapidly and is only detected at depths of less than about 15 cm for this particular sample. At the deeper depths the detected signal is associated with the type-I dilatational wave. The mechanical shaker produces only a type-I dilatational wave. Both the geophone and microphone sensors can detect both types of dilatational waves.

ISSN:0001-4966    

DOI:10.1121/1.419770

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

A structure with two periodicities can couple up to six modes under a case of simultaneous resonance resulting in a stop-band interaction. The method of multiple scales is employed to analyze the modal coupling in a two-dimensional acoustic duct with rigid periodically undulated walls as well as in an elastic plate having periodically corrugated outerfaces, leading to the coupled-mode equations. The comparison between the three possible cases of interaction under simultaneous resonance are given in terms of the power reflection coefficient spectrum as a function of frequency. The strength of the stop-band interaction is found to be strongly related to the number of direct couplings between the incident and reflected modes.

ISSN:0001-4966    

DOI:10.1121/1.419771

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

This paper reports analytical research on the effect of surface roughness on ultrasonic guided waves in plates. The theoretical model is constructed by exploiting the phase-screen assumption that takes advantage of the Kirchhoff approximation, where, on a local scale, the roughness degrades only the signal phase. The effect of the rough surface on the guided wave is treated by decomposing the wave modes into their constituent partial waves and considering individually the effect of the roughness on the partial wave components as they reflect from the plate surfaces. An approximate dispersion relation is derived for the traction-free rough waveguide that is formally identical to the conventional Lamb wave equation, but incorporating the roughness parameter as a complex plate thickness. A more accurate version of the model calculation is generalized to fluid-immersed plates having only a single rough surface either on the same, or opposite, side of the plate as the incident ultrasonic field. Calculations of the reflection coefficients in the presence of roughness serve to illustrate the phenomena for the case of the guided waves.

ISSN:0001-4966    

DOI:10.1121/1.419772

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

In this artice are reported fundamental experimental measurements on guided waves in plates with surface roughness; the experimental data are critically compared to theoretical calculations presented in Part I. All experiments, in either immersion or contact coupling mode, are modeled by the theory developed in I that exploits the phase-screen approximation. In this theory the effect of the rough surface on the received signal, on a local scale, is assumed to be restricted to the signal phase. The comparisons between experiment and predictions show good agreement in most regimes, despite the rather simplifying approximations contained in the calculation. The model is shown to fail only when the guided wave vector is close to a branch point, that is when the guided wave phase velocity approaches the compressional or shear wavespeeds of the plate. Near these values the internal partial waves comprising the guided wave strike the surfaces at grazing incidence or are evanescent, and a simple phase-screen model cannot account for this behavior. Elsewhere in the guided wave spectrum, agreement is quite good. Of practical significance is the finding that the rough-surface damping contrast can be maximized by configuring the experimental conditions to measure just below and well above the compressional critical angle. Aluminum samples, prepared by indenting or sandblasting and independently profiled to determine rms roughness, are measured in immersion and in contact transduction, the latter with wedge couplers and line sources. The influence of the roughness in immersion experiments is strongly affected by whether the upper or lower plate surface is rough, but only in the interaction zone between specular and nonspecular reflection components.

ISSN:0001-4966    

DOI:10.1121/1.419773

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

This paper concerns itself with how the cut-off frequencies and modal shapes of cylindrical acoustic waveguides are altered by the presence of temperature gradients induced by an applied temperature distribution along the duct walls. A physical model is first formulated which incorporates an inhomogeneous sound speed as well as a density gradient. The associated mathematical model is then a generalized eigenproblem. This is then discretized via the control region approximation (a finite difference scheme) yielding a generalized matrix eigenproblem. Under the assumption that the boundary temperature distribution is nearly constant, we apply a procedure of Schrödinger to express the propagation constants and modal functions as perturbation series whose successive terms can be generated recursively. The case of a rectangular duct with temperature variations in the cross section is considered in detail. All numerical computations are performed usingMATLAB©.

ISSN:0001-4966    

DOI:10.1121/1.419774

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

The classical two-duct Herschel–Quincke tube is generalized to ann-duct configuration. A closed-form expression is developed for the transmission loss characteristics, as well as for the resonance locations. While the results are illustrated in the present study in terms of three-duct configurations alone and in comparison with the two-duct arrangements, the developed expressions hold for any number of ducts and cross-sectional area combination.

ISSN:0001-4966    

DOI:10.1121/1.419775

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP