摘要:

The stress tensor in a continuously twisted structurally chiral medium (CTSCM) is symmetric and the stiffness tensor varies helicoidally about the axis of spirality. Exact analytic solutions are found for elastodynamic wave propagation along the axis of spirality in a CTSCM.

ISSN:0001-4966    

DOI:10.1121/1.408420

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

A new method is presented to evaluate the acoustic transient radiation from fluid‐loaded shells of revolution which are excited by axisymmetric mechanical or acoustical excitations. This method is based on the use of anin‐vacuomodal vector (eigenvector) expansion with time‐dependent coefficients to describe the velocity field of the fluid‐loaded shell. Modal acoustic impulse responses which account for the coupling between thein‐vacuomodal vectors for the fluid‐loaded shell are introduced in the formulation of the general solution. The time‐dependent modal velocity coefficients are expressed as the solution of a set of coupled convolution integral equations which are readily solved by marching forward in time. The associated time‐dependent surface pressure is subsequently expressed as a modal vector expansion in which the time‐dependent coefficients are readily related to the modal velocity coefficients. Since the surface velocity and pressure are then known, the time‐dependent pressures in the field are simply obtained via quadrature methods from the space‐time Kirchhoff integral solution. The special case of a fluid‐loaded spherical shell is addressed to illustrate the application of the method to determine the general characteristics of the transient velocity response of the shell and the associated pressure field resulting from axisymmetric mechanical force excitations of spherical shells. Numerical results are presented to illustrate the effects on the velocity response and pressure field of time‐dependent fluid coupling between the modal vectors corresponding to the upper and lower branches of thein‐vacuofrequency spectrum of the spherical shell.

ISSN:0001-4966    

DOI:10.1121/1.408421

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

Considered in this paper are two boundary‐value problems: first, a plane wave incident upon a planar interface separating an achiral elastic half‐space from a chiral elastic half‐space; second, a plane wave incident upon a chiral slab interposed between two achiral elastic solid half‐spaces. The inability of the achiral solid medium to support the microrotation field and the couple‐stress dyadic provides the option of two distinct sets of boundary conditions at achiral/chiral interfaces. It is observed from numerical computations that using either set of boundary conditions in either of the two boundary‐value problems results in the satisfaction of the principle of conservation of energy. Thus, it appears that the physically proper set of boundary conditions for a chiral/achiral interface may have to be decided experimentally.

ISSN:0001-4966    

DOI:10.1121/1.408422

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

A new analytical expression for the impulse response of a transducer in the form of a curved strip is derived. The radiator is defined as part of a concave spherical shell delimited by two horizontal parallel planes and two vertical parallel planes. The field of the transducer is obtained by means of the impulse response method proposed by F. Oberhettinger [J. Res. Natl. Bur. Stand.65, 1–6 (1961)] and P. R. Stepanishen [J. Acoust. Soc. Am.49, 841–849 (1971)] and the formalism developed by M. Ardittietal. [Ultrason. Imag.3, 37–61 (1981)]. Exact analytical expressions of the impulse response and of the continuous pressure field were obtained in the three planesxOy,xOz,yOz, whereOzis the propagating axis of the ultrasound andOthe focal point. The results of numerical modeling were compared with experimental results obtained using a 5‐MHz rectangular spherical strip (7×21 mm) focused at 75 mm. The agreement was excellent.

ISSN:0001-4966    

DOI:10.1121/1.408423

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

Many scenarios in underwater acoustics involve radiation from, or scattering by, configurations with periodic or quasiperiodic features. Depending on the operating conditions, the acoustic field generated by these processes carries the gross imprint of periodicity or quasiperiodicity, without or with effects of truncation, regardless of the detailed structure in each unit cell. To understand and quantify the phenomenology under time harmonic and pulsed excitation, especially in the mid‐ to high‐frequency regime where the width of each cell can cover many wavelengths, it is instructive to explore alternative parametrizations that emphasize, respectively, the nondispersive direct radiation from each cell and the dispersive collective treatment of strict or weakly perturbed periodicity, without and with truncations. The prototype configuration for this two‐dimensional study is a finite periodic array of linearly phased parallel filamentary elements. The formulation makes use of Poisson summation and subsequent asymptotics applied to the finite array, and is parametrized in the configuration‐spectrum phase space; it highlights the connection between local and global phenomena in both the space‐time and wave‐number‐frequency domains, with a view toward phase‐space data processing. Formal aspects and general principles are presented in this paper and are applied to infinite and truncated periodic arrays to illustrate how known results obtained by other methods are recovered with the Poisson‐based algorithm. The outcome is a new frequency and time domain Bragg‐modulated ray acoustic model that generalizes the nonuniform and uniform ray fields of the geometrical theory of diffraction, so as to include effects of periodic dispersion, with truncations. Under transient conditions, such dispersion gives rise to new time domain Bragg modes.

ISSN:0001-4966    

DOI:10.1121/1.408424

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

The transient response of a wave front that forms a transverse cusp caustic is studied. The travel time surface of a simple cuspoid caustic is known to have the general shape of the singular surface of the next higher order cuspoid catastrophe. Though the transverse cusp wave front considered here is curved in two dimensions, it is also shown to have a travel time surface with the general shape of the singular surface of the swallow tail catastrophe. Ultrasonic experiments to image the travel time surface of the transverse cusp caustic were performed. The imaged travel time surface has the shape of the swallow tail singular surface imposed on a slowly varying travel time surface due to the spherical nature of the source. Imaged cuts through the travel time surface compare very well to calculated travel time curves. The calculated curves are a superposition of a smooth background contribution and a contribution due to the shape of the reflecting surface. It is the second contribution that describes the merging and disappearance of rays as the cusp caustic is crossed. There are no adjustable parameters used in the comparison. It is possible to infer at least qualitative information about the reflecting surface from the imaged travel time surface.

ISSN:0001-4966    

DOI:10.1121/1.408425

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

Characteristics of surface Stoneley (Scholte) waves propagating along the interface bismuth germanate–water solution of glycerol are investigated both theoretically and experimentally. These waves have been generated and detected using interdigital transducers (IDT). The phase velocity of the Stoneley wave and its energy distribution between the two media are measured at frequencies between 15 and 50 MHz over a wide region of sound speeds in the liquidvL, including those exceeding the speed of the Rayleigh wave in the solidvR. It is shown that atvL≳vRthe speed of the Stoneley wave markedly differs (≳10%) from the speed of the longitudinal wave in the liquid. The former remains limited byvR, and the major part of wave energy propagates in the solid. The insertion and transducer losses (TL) were measured for the generation of Stoneley waves by the IDT; the minimal value of TL was close to 10 dB per transducer. This suggests that it is feasible to use this method for the generation of Stoneley waves.

ISSN:0001-4966    

DOI:10.1121/1.408426

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

The integral‐equation method is applied to study the diffraction of acoustic waves by rigid plane baffles, such as a circular disk and a ring. A set of six real Fredholm integral equations of the second kind is solved simultaneously to determine the velocity potentials on a circular disk. These equations are transformed into discrete forms by applying the Gauss–Legendre quadrature formula in the radial direction and the best possible numerical integration formula in the angular direction. The discrete equations are solved by the method of successive approximations, which is also called the direct integral‐equation method. A new method is also developed to take care of integrations involving the Cauchy principal values, which occur when the moving point coincides with the fixed point. The accuracy of the present numerical approach has been tested by computing the excess‐pressure ratio ‖p/p0‖ on the surfaces of a circular disk exposed to a plane wave and by comparing it with both analytical and experimental results. Our numerical results coincide with both results quite well, especially on the shadow side, where the diffraction field is not sensitive to the thickness of the circular disk. The effect of different parameters on the diffracted acoustic field about a circular disk due to a monochromatic acoustic source is systematically studied and compared. These parameters include the location of the acoustic source, the wave number, and the disk thickness. Some interesting results are obtained. As the wave number increases, the excess‐pressure ratio approaches two on the ‘‘illuminated’’ side and zero on the ‘‘shadow’’ side of the disk, which indicates that Kirchhoff’s approximation is appropriate at higher wave numbers. As the acoustic source moves away from the symmetric axis toward one side, the bright spot on the shadow side moves toward the opposite side and has the same peak value. Finally, following the same approach as that for a circular disk, the diffraction of acoustic waves by a rigid ring is studied. Instead of six, a set of eight real Fredholm integral equations is solved simultaneously. The effect of different parameters on the diffraction field is also systematically studied and compared.

ISSN:0001-4966    

DOI:10.1121/1.408427

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

Few problems in elastodynamics have a closed‐form analytical solution. The others can be investigated with semianalytical methods, but in general one is not sure whether these methods give reliable solutions. The same happens with numerical techniques: for instance, finite difference methods solve, in principle, any complex problem, including those with arbitrary inhomogeneities and boundary conditions. However, there is no way to verify the quantitative correctness of the solutions. The major problems are stability with respect to material properties, numerical dispersion, and the treatment of boundary conditions. In practice, these problems may produce inaccurate solutions. In this paper, the study of complex problems with two different numerical grid techniques in order to cross‐check the solutions is proposed. Interface waves, in particular, are emphasized, since they pose the major difficulties due to the need to implement boundary conditions. The first method is based on global differential operators where the solution is expanded in terms of the Fourier basis and Chebyshev polynomials, while the second is the spectral element method, an extension of the finite element method that uses Chebyshev polynomials as interpolating functions. Both methods have spectral accuracy up to approximately the Nyquist wave number of the grid. Moreover, both methods implement the boundary conditions in a natural way, particularly the spectral element algorithm. We first solve Lamb’s problem and compare numerical and analytical solutions; then, the problem of dispersed Rayleigh waves, and finally, the two‐quarter space problem. We show that the modeling algorithms correctly reproduce the analytical solutions and yield a perfect matching when these solutions do not exist. The combined modeling techniques provide a powerful tool for solving complex problems in elastodynamics.

ISSN:0001-4966    

DOI:10.1121/1.408428

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP

摘要:

The coherent component of the field scattered at grazing angles from a slightly rough pressure release surface is found. This is valid for multiple scattering and is based upon the parabolic integral equation method. Also examined are the scattering of planes waves under the method and in particular, the effect of truncating the boundary integral. It is shown that the coherent field remains invariant when the source and receiver are displaced vertically by equal and opposite distances, as was found numerically in a previous paper. In general, this can be shown to hold because the coherent field due to any plane wave is specular; however, under the parabolic equation method reflection isnotspecular, and thus the result is of particular interest. Reflection coefficients are given in closed form for several surface statistics, valid asymptotically at large distances.

ISSN:0001-4966    

DOI:10.1121/1.408429

出版商:Acoustical Society of America    

年代:1994

数据来源: AIP