摘要:

The elastic response of a solid sphere to a continuous train of plane waves is shown to consist principally of rotational waves, rather like smoke rings, where the rotational motion of a particular wave is centered at points on an annulus perpendicular to the axis of sound propagation. The rotational waves are most clearly evidenced in the standing modes of free vibration of the sphere, with the waves meshing together like a system of gears. Calculated plots of the displacement vector show how these modes are excited in the sphere by incident sound, and how, during a cycle of the excitation, a first harmonic briefly changes into the nearest fundamental as it changes direction during the oscillation. Other results are presented, including a demonstration that the rotational waves also occur in solid cylinders, with the rotation centered at points along lines parallel to the cylinder axis. It is speculated that the rotational waves occur in any closed body.

ISSN:0001-4966    

DOI:10.1121/1.400641

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

This paper presents in detail the resonant bar technique used to measure acoustic properties of materials in the sonic frequency range (≃5–20 kHz). Measurements are corrected for the effects of added mass and jacketing; extrinsic effects such as the sample diameter or the dispersion at higher frequencies can mask intrinsic properties of material and are analyzed here. When this technique is used on porous saturated media such as rocks, it is important to avoid the “Biot–Gardner–White” effect; this intrinsic effect can lead to erroneous high attenuations in unjacketed saturated samples. Experimental evidence of its occurrence on water-saturated rods is presented. Experimental results of velocity and attenuation obtained on various rock types such as limestones and sandstones show the drastic sensitivity of these measurements to effective pressure. Hertz’s theory can be applied to describe the behavior of under-consolidated sandstones. Under high confining pressure, sonic attenuation in water-saturated limestone samples is found to be very low(Q⩾100);attenuation in sandstones is always low(Q⩾50),except for some shaly sandstones.

ISSN:0001-4966    

DOI:10.1121/1.400643

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

Numerical results for the scattering cross section (S) ofN=3–26 equally spaced monopole resonators on a circle (of radiusb) indicate regularities in the values of the normalized diameter (2kb=4πb/λ=ρwith λ as the wavelength) corresponding to maximal scattering for symmetrical excitation. The peaksS∧(N)occur forρ=ρ∧(N)betweenNand 2N, i.e., for circle circumference betweenNλ/2 andNλ. With increasingN, the values ofρ∧(N)in successive alternating sets (shells) of three or four values ofNare close toρm=2mπ−π/4;shell-1 consists ofN=3–5, shell-2 ofN=6–9, shell-3 ofN=10–12, etc. The basis for the shell structure is delineated by a simple asymptotic approximation (for large ρ andNin the range ρ<2N) or a cylindrical wave representation for a sum of spherical waves. A simple approximation is also derived fo the shift in resonance frequency that occurs for ρ small enough for the array to respond as a collective monopole.

ISSN:0001-4966    

DOI:10.1121/1.400644

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

A fast variation of the surface impedance of two layers of different thicknesses of the same material has been observed at low frequencies. These variations, which are predicted by the Biot theory, appear at the λ/4 resonance of the frame.

ISSN:0001-4966    

DOI:10.1121/1.400642

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

Dispersion curves for4 the modes of noncircular fluid-filled boreholes in homogeneous elastic formations are calculated with a boundary integral formulation. Results are displayed for the propagatory modes of several borehole shapes in both fast and slow formations. Any departure from circularity reduces the tube wave speed. Agreement with exact analytical results is obtained for elliptical boreholes, while a simple approximate relation involving borehole perimeter and area is verified for arbitrary cross sections. Higher-order surface modes such as the flexural and screw modes split into two distinct branches distinguished by their orientation with respect to the principal axes of the borehole cross section. Modal dispersion characteristics in elliptical boreholes may be approximately by scaled circular borehole results. In fast formations the effective scaled radii are related to transverse dimensions of the borehole, but in slow formations they are more closely related to local radii of curvature of the borehole. For more complex cross sections with a single axis of symmetry, dispersion of the flexural mode is well modeled by that in elliptical boreholes of similar dimensions, while that of Stoneley and screw modes is not. In asymmetrical boreholes, significant torsional and out-of-phase motion may occur.

ISSN:0001-4966    

DOI:10.1121/1.400522

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

A study of the propagation and interaction of two collinear finite amplitude sound beams, presented in a previous paper [Naze Tjo/tta et al., “Propagation and interaction of two collinear finite amplitude sound beams,” J. Acoust. Soc. Am.88, 2859–2870 (1990)] is extended to include the effects of focusing. The validity of the parabolic equation when applied to strongly focused sound beams is discussed. Equations and algorithms based on a transformed parabolic equation are presented and used to compute the interaction between two collinear, focused sound beams, and between one plane wave and a focused sound beam. Numerical results are shown, with special emphasis on parametric generation and parametric reception of sound.

ISSN:0001-4966    

DOI:10.1121/1.400523

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

Nonlinearity in the propagation and interaction of sound beams in real fluids is considered, with special emphasis on the effects of absorption. Asymptotic formulas are derived for the sum and difference frequency sound generated by two harmonic sound beams. The amplitude and phase conditions of the sources are arbitrary, within the limits imposed by the parabolic approximation. A distinction is made between two main contributions to the nonlinearly generated sound in the far field, the continuously pumped sound and the scattered sound. The relative amplitudes of the pumped and scattered waves are shown to depend critically on the frequency dependence of the absorption coefficients. Numerical results are presented for the noncollinear interaction of Gaussian primary beams, and also for second harmonic generation in the field of a circular uniform piston source.

ISSN:0001-4966    

DOI:10.1121/1.400645

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

Weak nonlinearity in the propagation and interaction of real sound beams in a lossless fluid is considered. Special emphasis is given to the effects produced by various boundary conditions at the sound sources and other bounding surfaces. Asymptotic formulas and numerical results are presented for the second harmonic, and for the scattered sum and difference frequency sound generated by two harmonic beams that intersect at an arbitrary angle. The results are derived from a general theory presented earlier [Naze Tjo/tta and Tjo/tta, J. Acoust. Soc. Am.83, 487–495 (1988)], which is valid for any source separation and amplitude distribution. In situations where the parabolic approximation is not legitimate (large angles, broad beams), properly accounting for the boundary conditions may be crucial. Also discussed are implications for the parametric emitting and receiving arrays.

ISSN:0001-4966    

DOI:10.1121/1.400524

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

Higher-order Padé approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover. Accuracy is achieved by placing constraints on the derivatives of the Padé approximations at the point corresponding to the reference wave number. Stability is achieved by requiring that the Padé approximations map part of the lower-left quadrant of the complex plane into the upper half of the complex plane. Elastic parabolic equations based on these Padé series can handle problems involving compressional, shear, and interface waves, very wide propagation angles, and large depth variations and weak range variations in the seismoacoustic parameters. A finite-difference spectral solution is developed for generating reference solutions and starting fields. The rotated elastic parabolic equation is used to investigate the accuracy of the elastic parabolic equation for range-dependent problems.

ISSN:0001-4966    

DOI:10.1121/1.400646

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP

摘要:

It is shown that the standard stair-step representation of a sloping bottom may result in significant prediction errors. In fact, current parabolic equation implementations arenotenergy conserving. The problem is shown to derive from the approximate treatment of the interface conditions at vertical boundaries along the stair steps. Several improved interface conditions are proposed.

ISSN:0001-4966    

DOI:10.1121/1.400525

出版商:Acoustical Society of America    

年代:1991

数据来源: AIP