By Alex A. Kaufman, A.L. Levshin
This monograph is the final quantity within the sequence 'Acoustic and Elastic Wave Fields in Geophysics'. the former volumes released by means of Elsevier (2000, 2002) dealt commonly with wave propagation in liquid media.
The 3rd quantity is devoted to propagation of aircraft, round and cylindrical elastic waves in numerous media together with isotropic and transversely isotropic solids, liquid-solid versions, and media with cylindrical inclusions (boreholes). * occurrence of actual reasoning on formal mathematical derivations * Readers wouldn't have to have a robust heritage in arithmetic and mathematical physics * specified research of wave phenomena in numerous varieties of elastic and liquid-elastic media
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Additional resources for Acoustic and Elastic Wave Fields in Geophysics, III
This behavior of A/ poses the following question. How does the low end of the bar, Fig. 4c, "know" where the opposite end is located? In order to find an explanation, consider the motion of the low end under action of the constant force FT: Fr = 0 if t <0 and FT — const if t > 0. provided that the upper end of the bar is fixed. Since the force Fx is directed downward, an extensional wave arises at the instant t = 0 and propagates toward the upper end. At the same time, the low end moves with constant velocity along the :r-axis.
128 (c) Stresses inside elementary volume (d) Forces acting on the rectangular parallelepiped aibiCidi 44 CHAPTER 1. HOOKE'S LAW, POISSON'S RELATION AND WAVES... —Fy. In equilibrium, both forces Fy and — Fy have equal magnitudes but opposite directions. Their resultant force is equal to zero, but they form the couple, which tries to rotate the volume counterclockwise. Such motion causes a deformation of a medium in the vicinity of the horizontal faces and, correspondingly, the tangential (shear) forces F x and -F, T appear, which act on these faces, Fig.
Finally, in many cases, sources of waves generate sinusoidal oscillations that create harmonic waves. 3 LONGITUDINAL SINUSOIDAL WAVES IN A BAR 39 As before, we will often deal with sinusoidal waves, and so let us recall the basic features of a sinusoidal wave. 109) Certainly, the sinusoidal wave is generated and propagates away from the source. In accordance with eq. 110) Q Here UJ is an angular frequency and fc=- (1-111) Q is the wave number. By definition, ujt — kx is the phase of the outgoing wave and, in the same manner, ujt + kx is the phase of the incoming wave.