MOTION OF A RIGID SPHERE IN AN ACOUSTIC WAVE FIELD

Geophysics ◽  
1945 ◽  
Vol 10 (1) ◽  
pp. 91-109 ◽  
Author(s):  
Alfred Wolf
Keyword(s):  
Acoustic Waves ◽  
Response Curve ◽  
Wave Length ◽  
Elastic Solid ◽  
Rigid Sphere ◽  
Resonance Effects ◽  
First Order ◽  
Solid Media ◽  
The Waves ◽  
Scattering Of Acoustic Waves

A rigid sphere in the field of plane acoustic waves in a fluid or in an elastic solid medium is subjected to harmonic forces in the direction of propagation of the waves, and proportional to their amplitude. The response curve is a function of the ratio of the circumference of the sphere to the wave length, and of the ratio of the mass of the sphere to the mass of the displaced medium. In an elastic solid, Poisson’s ratio must also be included among the variables. The response curve in fluids decreases continuously with decreasing wave length. In elastic solid media, the response curve has a maximum which is due to resonance effects. In general, the greater the mass of the sphere the smaller the response except in the neighborhood of resonance in elastic solid media. The scattering of acoustic waves by a rigid sphere is determined. The potential of scattered waves is developed in a series of spherical harmonics; it is shown that only the first order coefficients are affected by the motion of the sphere.

High Resolution Nonreciprocal Microwave Interferometry of Moving Media and Structures

1973 ◽  
Vol 28 (9) ◽  
pp. 1443-1453
Author(s):  
O. Gehre ◽  
H. M. Mayer ◽  
M. Tutter
Keyword(s):  
High Resolution ◽  
Glow Discharge ◽  
Relative Motion ◽  
Wave Length ◽  
Electron Drift ◽  
First Order ◽  
The Third ◽  
Microwave Interferometry ◽  
Moving Media ◽  
The Waves

Three experiments are described in which the relative motion of media or structures causes nonreciprocal effects of first order in ν/c. The first two experiments deal respectively with the Fresnel effect due to the motion of a normal dielectric and the electron drift in the plasma of a glow discharge. The third experiment is a microwave analogon to the historical experiments of Harress, Pogany and Sagnac. To our knowledge these are the first investigations of the well-known effects under conditions where the transverse dimensions of the waves are comparable to the wave length. Under such conditions the nonreciprocal effects when expressed in fringe shifts (or phase angle) remain small. They could, however, be detected after the development of an elaborate microwave interferometry which could resolve fringe shifts down to the order of 10-6.

ON THE PROPAGATION OF RAYLEIGH WAVES ON THE SURFACE OF A VISCO‐ELASTIC SOLID

Geophysics ◽  
1953 ◽  
Vol 18 (1) ◽  
pp. 70-74 ◽  
Author(s):  
C. W. Horton
Keyword(s):  
Rayleigh Waves ◽  
Dimensionless Parameter ◽  
Attenuation Factor ◽  
Wave Length ◽  
Elastic Solid ◽  
Angular Frequency ◽  
Elastic Parameters ◽  
Lissajous Figure ◽  
The Waves ◽  
Horizontal Displacements

The propagation of Rayleigh waves over the surface of a visco‐elastic solid is examined. It is shown that for a Poisson solid (λ=μ), the behavior of the waves can be characterized by a dimensionless parameter δ=ωη/μ which is less than 0.1 for the frequencies and elastic parameters of interest in geophysics. In this expression ω=angular frequency, μ=shear modulus, η=viscosity. For small values of δ it is possible to modify the usual analysis of Rayleigh waves and obtain the new characteristics without much difficulty. It is shown that the motion of a particle on the earth’s surface is changed from an ellipse to a Lissajous’ figure and that the phase angle between the vertical and horizontal displacements is changed from [Formula: see text] to [Formula: see text] radians. The surface wave has an attenuation factor of [Formula: see text] where [Formula: see text] is the wave length of the Rayleigh wave in the absence of internal friction.

The propagation of Rayleigh waves over curved surfaces at high frequency

1971 ◽  
Vol 70 (1) ◽  
pp. 103-121 ◽  
Author(s):  
R. D. Gregory
Keyword(s):  
High Frequency ◽  
Rayleigh Waves ◽  
Elastic Solid ◽  
High Frequencies ◽  
First Order ◽  
Rayleigh Surface Waves ◽  
Dispersion Formula ◽  
Time Harmonic ◽  
The Waves ◽  
Order Dispersion

AbstractA formal asymptotic theory, valid at high frequencies, is developed for the propagation of time harmonic Rayleigh surface waves over the general smooth free surface Σ of a homogeneous elastic solid. It is shown that on Σ these Rayleigh waves can be described by a system of surface rays, which are shown to be geodesics of Σ. The amplitude of the waves on Σ is shown to vary in such a way that the energy propagated along a strip of surface rays is constant. The waves are also shown to be dispersive and an explicit first-order dispersion formula is derived.

scholarly journals Numerical Simulation of Acoustic Scattering by a Cylinder Based on the Enhanced Optimized Scheme

2021 ◽  
Vol 2101 (1) ◽  
pp. 012030
Author(s):  
Siqi Yuan ◽  
Ruixuan Ma ◽  
Conghai Wu ◽  
Shuhai Zhang
Keyword(s):  
Acoustic Waves ◽  
Acoustic Scattering ◽  
Numerical Results ◽  
Acoustic Energy ◽  
Two Dimensional ◽  
Benchmark Problem ◽  
Spatial Redistribution ◽  
Scattered Fields ◽  
The Waves ◽  
Scattering Of Acoustic Waves

Abstract The enhanced optimized scheme we developed in the early work is employed to simulate the scattering of acoustic waves from a two-dimensional cylinder by solving the Euler equations. The numerical results of a benchmark problem are found to be in excellent agreement with the exact solution. Our numerical results show that when acoustic waves propagate through a cylinder, the acoustic scattering results in a spatial redistribution of the acoustic energy as well as an alteration of the phase of the waves. The directivities of the scattered fields change significantly for the different length ratios of acoustic wavelength to the radius of the cylinder.

EFFECTS OF A LIQUID CORE ON THE PROPAGATION OF SEISMIC WAVES

1959 ◽  
Vol 37 (2) ◽  
pp. 109-128 ◽  
Author(s):  
George Duwalo ◽  
J. A. Jacobs
Keyword(s):  
Seismic Waves ◽  
Wave Length ◽  
Liquid Core ◽  
Elastic Solid ◽  
Compressible Liquid ◽  
Diffracted Waves ◽  
Viscous Compressible Liquid ◽  
Method Of Residues ◽  
Propagation Of Elastic Waves ◽  
The Waves

Effects of a spherical cavity in an infinite, homogeneous, isotropic elastic solid, containing non-viscous compressible liquid, on the propagation of elastic waves are investigated mathematically. The waves emitted by a simple harmonic point source in the solid are of the types known as SH and P in seismology. The discussion is restricted to the case ka » 1 (ka = 2 π cavity radius/wave length). Series solutions are transformed into contour integrals by Watson's method. Evaluation of these by the method of residues results in expressions describing the P and S components of the diffracted waves.

Sign in / Sign up

Export Citation Format

Share Document