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 via 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 several media together with isotropic and transversely isotropic solids, liquid-solid types, and media with cylindrical inclusions (boreholes). * occurrence of actual reasoning on formal mathematical derivations * Readers should not have to have a robust heritage in arithmetic and mathematical physics * distinctive research of wave phenomena in a variety of sorts of elastic and liquid-elastic media
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Additional info for Acoustic and Elastic Wave Fields in Geophysics, III
This fact greatly simplifies the study of sinusoidal waves. 2. The shape of transient waves is preserved when they propagate along a bar and attenuation is absent. , it is impossible to describe this process by either single function f[a(t — x/c or g[a(t + x/ci\, or by a sum of them. At the same time, even in the presence of attenuation, the sinusoidal wave as a function of time preserves the same frequency. This is the second reason why it is very convenient to study wave phenomena using sinusoidal waves even when part of an elastic energy is transformed into heat.
Because of a reflection at the upper end, the extensional wave arises at the instant t = l/c and travels downward, but the particle motion has an opposite direction. For this reason, the bar stops to move behind the wave front. At the instant t = 2l/c the wave reaches the low end, and the whole bar is at rest. However, at the same moment the compressional 28 CHAPTER 1. HOOKE'S LAW, POISSON'S RELATION AND WAVES... wave appears at the low end and propagates upward. Correspondingly, the direction of the motion of the low end changes.
8d. Since this volume is at equilibrium, the resultant force, acting on each clement of volume, for instance ob\C\, is equal to zero. Taking into account that the face obi is parallel to ab, the stress at its points is equal to TXX, but at the face oc\ it coincides with ryy. Correspondingly, forces applied to these faces are Fx — — Txxob\\ and Fy — — ryyocij because TXX < 0 and Tyy > 0. 138) As is seen from Fig. 139) It is clear that there is only shear strain at all faces of volume aibiCidi (its extension along the z-axis is implied).