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Elastic wave propagation, deriving characteristic equations in generalized curvilinear coordinates using linear elastic, isotropic and homogeneous constitutive equations
Unified approach to propagation of plane, cylindrical and spherical dilation waves in elastic media, using method of characteristics
Unified approach to propagation of plane, cylindrical and spherical dilation waves in elastic media, using method of characteristics
Wavefront singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d to the -1/2 power, where d measures distance away from the front. However, in certain exceptional cases singularities of order d to the -n power, where n = 1/4, 2/3, 3/4, may be encountered.
Plane elastic waves of finite amplitude in Hadamard materials and harmonic materials
The extended method of equivalent inclusion developed is applied to study the specific wave problems of the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and of the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. The eigenstrains are expanded as a geometric series and the method of integration for the inhomogeneous Helmholtz operator given by Fu and Mura is adopted. The results obtained by using a limited number of terms in the eigenstrain expansion are compared with exact solutions for the layer problem and for a perfect sphere. Two parameters are singled out for this comparison: the ratio of elastic moduli, and the ratio of the mass densities. General trends for three different situations are shown.
Elastic wave problems involving one space variable solved by hyperbolic partial differential equations
One-dimensional elastic wave problems treated by hyperbolic partial differential equations and analyzed by method of characteristics
The solution of the nonlinear differential equation which describes an initially sinusoidal finite-amplitude elastic wave propagating in a solid contains a static-displacement term in addition to the harmonic terms. The static-displacement amplitude is theoretically predicted to be proportional to the product of the squares of the driving-wave amplitude and the driving-wave frequency. The first experimental verification of the elastic-wave static displacement in a solid (the 111 direction of single-crystal germanium) is reported, and agreement is found with the theoretical predictions.
Computer program for one dimensional elastic wave problems connected with structural members
Unified approach to one-dimensional elastic waves by method of characteristics
Elastic wave velocities of two Apollo 14 rocks, 14053 and 14321, three Apollo 15 rocks, 15058, 15415, and 15545, and one Apollo 16 rock 60315 have been determined at pressures up to 10 kb. For sample 14321, the variation of the compressional wave velocities with temperature has been measured over the temperature range from 27 to 200 C. Overall elastic properties of these samples except sample 15415 are very similar to those of Apollo 11, 12, and 14 rocks and are concordant with Toksoz et al.'s (1972) interpretation that lunar upper crust is of basaltic composition. Temperature derivative of the P wave velocity for sample 14321 is a half to one order of magnitude larger than that for single crystalline minerals. This suggests that the seismic velocity in the lunar crust may be affected significantly by the temperature distribution.
Elastic wave propagation along cylindrical cavity filled with conducting fluid
Phase difference due to elastic waves produced by cyclic heating of targets by impacting ions from pulsed beam
Elastic wave propagation in two dimensions using theory of characteristics
Elastic surface wave amplitude and propagation velocity in lunar rocks, calculating Poisson ratio
The propagation of elastic waves in the moon, where the first seismograms were characterized by the presence of a long coda attributed to strongly scattered waves, is modeled with the aid of the time-dependent equation of radiative transfer. The average energy density as a function of time and space is described by the diffusion equation with linear dissipation on the assumption that all the energy present has been scattered many times and the time and distance scales of the problem are long compared to the scales of the scattering process. Ultrasonic experiments in the laboratory confirm the applicability of the formalism.
Apollo 11 lunar sample elastic wave velocities at high pressures, examining P and S waves, Q value and geophysical implications