摘要:

A method has been developed for the analysis of free‐wave propagation through a combination of two different semi‐infinite, monocoupled, periodic systems joined together without or through a finite periodic/disordered system. The general expressions derived from the analysis have subsequently been adapted to study the free flexural wave propagation in beam‐type systems. Results have been computed and discussed for different combinations of beam systems which include semi‐infinite periodic beams joined (i) through different periodic and disordered finite beams and (ii) without an additional beam at the junction. Attenuation of free waves in such systems, caused by six‐span finite beam disorders, has been studied and compared to the attenuation of free waves in an infinite periodic beam and when one of its elements is different from the rest. Although multispan finite beam disorders generally attenuate the propagating incident waves, at certain discrete frequencies they offer no obstruction to such waves. The conditions under which this can happen have been identified and explained. It has been pointed out what type of finite disordered beams can be employed to prevent vibrational energy from flowing from one periodic system to another. The energy flow through the combined system, as governed by the transmitted free wave, has been discussed. The conditions have been explained under which two interacting attenuating flexural waves can transmit energy, although they are incapable of doing so individually.

ISSN:0001-4966    

DOI:10.1121/1.383924

出版商:Acoustical Society of America    

年代:1980

数据来源: AIP

摘要:

The scattering of stationary acoustic waves by a bounded elastic obstacle in an inviscid fluid is considered. The developed formalism is an extension of the transition matrix method, which has been given by Waterman for acoustic, electromagnetic, and elastic scattering. In fact the problem at hand is more complex than the elastic case, something which is apparent in the solution. It is possible to obtain some different forms for the transition matrix, depending upon whether the Rayleigh hypothesis enters or not. It is worthy of notice that the more general formalism, i.e., the one not assuming the Rayleigh hypothesis, is also the more efficient numerically. Numerical results are given for spheroids and an object resembling the number ’’8.’’

ISSN:0001-4966    

DOI:10.1121/1.383925

出版商:Acoustical Society of America    

年代:1980

数据来源: AIP

摘要:

The transition matrix method for stationary elastic waves is extended to a great class of obstacles characterized by piecewise constant properties. First, the translation properties of the basis functions is used to treat two and, then, several homogeneous obstacles, and thereafter an obstacle with consecutively enclosing layers is considered. It is then indicated how these two basic methods of combination can be applied to treat more complex cases, including an obstacle consisting of several nonenclosing parts. Finally, we give some numerical applications to configurations of spherical and nonspherical obstacles in and below the resonance region.

ISSN:0001-4966    

DOI:10.1121/1.383926

出版商:Acoustical Society of America    

年代:1980

数据来源: AIP

摘要:

The vector potential for an arbitrarily polarized shear wave in an elastic (lossless) medium incident on, and scattered by, a spherical fluid occlusion is expanded in vector spherical harmonics. The boundary conditions are dealt with for this incident vector potential in terms of two (scalar) Debye shear potentials ψ and χ giving rise to what we have termed ’’sandtwaves,’’ respectively. Theswave scatters into both anotherswave and also mode‐converts into a compressionalpwave. Thetwave scatters only into anothertwave with no mode conversion. Scattering amplitudes are cast in a series of resonance terms. The scatteredpandswaves exhibit resonances; however, thetwave does not. We exhibit monostatic and bistatic plots of the first few partial‐wave amplitudes (n=1,2,3,...) for thesp,ss, andttscattering modes. When the background amplitude corresponding to scattering from anevacuatedspherical cavity is removed from each partial‐wave contribution, the remaining portion of the amplitudes is a clear series of liquid‐sphere resonances. We display these resonances as functions of the acoustic sizekdaof the cavity,andof the ordernof each mode. This work completes the determination of the scattering matrix elements for a fluid sphere in an elastic medium which was commenced by us earlier with the study of resonance effects inppandpsscattering.

ISSN:0001-4966    

DOI:10.1121/1.383927

出版商:Acoustical Society of America    

年代:1980

数据来源: AIP

摘要:

Wave propagation in inhomogeneous media is studied by a new method, the ’’cutting‐out’’ Jessel’s method. Emphasis is on transition layers, where both the sound velocity and density variations are taken into account. Several classes of layers are studied and impedance matching by a smooth dioptre is described. By using the analogy between inhomogeneous media and waveguides, this property of impedance matching has been extended to connecting horns, thus leading to the definition of a new family : the aperiodic horns.

ISSN:0001-4966    

DOI:10.1121/1.383928

出版商:Acoustical Society of America    

年代:1980

数据来源: AIP

摘要:

The problem of the scattering of transient antiplane shear electroelastic waves from a crack in a piezoelectric medium possessing 6‐mm symmetry is solved by determining the electric dipole density induced on the crack by the incident wave. An integral equation satisfied by the Laplace‐transformed dipole distribution is derived by appealing to the piezoelectric reciprocity relation. The solution of the integral equation is accomplished by expanding the dipole distribution in a series of first‐order spline functions with unknown coefficients and then applying the method of moments to transform the problem to a vector‐matrix one, which is readily handled by a computer. Inversion back into the time domain is effected by an efficient numerical method of inverting Laplace transforms. Results are given for the cases of normal and oblique incidence of the wave onto the crack.

ISSN:0001-4966    

DOI:10.1121/1.383929

出版商:Acoustical Society of America    

年代:1980

数据来源: AIP

摘要:

In a previous paper [J. Acoust. Soc. Am. 64, 522 (1978)] we obtained a new approximate equation governing the propagation of small perturbations to the pressure in a thin‐walled fluid filled elastomer tube. There, the spatial fluctuations in the pressure perturbation for fixed time were evaluated numerically by a procedure based on the Fast Fourier Transform (FFT) algorithm. Here, by means of an asymptotic analysis, based on a modified steepest descent method, we explain an apparent anomaly in the numerical results by exhibiting the existence of a forerunner wave and investigate the accuracy of the large time asymptotic results, for times which may be regarded as small or intermediate, by comparing them with the results from the FFT algorithm. It is found that the results obtained from the asymptotic analysis are in close agreement with those obtained from the FFT for moderate times and in qualitative agreement for relatively small times. For nondimensional times greater than 100 the positions of the zeros of the pressure perturbation agreed with those obtained from the FFT to better than four significant figures for the main part of the disturbance.

ISSN:0001-4966    

DOI:10.1121/1.383930

出版商:Acoustical Society of America    

年代:1980

数据来源: AIP

摘要:

The two‐dimensional, scalar diffraction theory is developed for a diffusing surface as suggested by Schroeder, consisting of an array of ’’wells’’ of equal widths but different depths, separated by hard, thin walls. Diffusors of finite size as well as infinite, periodic ones are treated. Matching the plane waves in the free half‐space to the wave modes in the wells yields an infinite but discrete linear equation system in either case. For a periodic diffusor based on a quadratic‐residue (QR) sequence, numerical results are compared with measurements on a finite diffusor comprising two periods. The results are also compared with those obtained by approximating the diffusor as a locally reacting surface. The differences are, at most, a few decibels; the mode‐matching results are usually closer to the measurements. The uniformity of scattering is tested over a range of wavelengths of 1:4; QR sequences are superior to pseudorandom sequences.

ISSN:0001-4966    

DOI:10.1121/1.383931

出版商:Acoustical Society of America    

年代:1980

数据来源: AIP

摘要:

The integral equation for the diffraction of a plane scalar wave by a locally reacting, planar, finite scattering surface is treated, the surrounding being either a free space or a uniform locally reacting plane. The surface is described by a ’’generalized reflectivity’’—a bilinear function of the reflection factor containing two free parameters. By proper choice, the validity of Kirchhoff’s Fourier approximation of the diffraction pattern can be extended. Also the analytical treatment of some simple scattering and inverse scattering problems is alleviated. Numerical solution methods are then considered; apart from the direct method, only applicable to small equation systems, an iteration procedure is developed, based on Neumann’s successive‐approximation method. Proper choice of the two free parameters leads to fast convergence in most cases. The methods are tested with Schroeder’s quadratic‐residue‐sequence diffusors. Agreement with the measurements is acceptable but not perfect.

ISSN:0001-4966    

DOI:10.1121/1.383932

出版商:Acoustical Society of America    

年代:1980

数据来源: AIP

摘要:

Backscattering measurements from solid brass, aluminum, and lucite cylinders in water have been performed at akaof approximately 240 using short acoustic pulses. Numerous discrete echoes are received due to multiple internal reflections of the acoustic pulse at the boundary of the cylinders. Excellent agreement between the measured echo arrival times and the echo arrival times predicted by the theory of Brill and Überall [J. Acoust. Soc. Am. 50, 921 (1979)] is obtained for all of the cylinders. The amplitudes of the backscattered echoes from the brass and aluminum cylinders are also compared with theory and fair agreement is obtained.

ISSN:0001-4966    

DOI:10.1121/1.383933

出版商:Acoustical Society of America    

年代:1980

数据来源: AIP