Acoustic and Elastic Wave Fields in Geophysics, III by Alex A. Kaufman, A.L. Levshin

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 way of Elsevier (2000, 2002) dealt typically 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). * incidence of actual reasoning on formal mathematical derivations * Readers don't have to have a robust history in arithmetic and mathematical physics * specified research of wave phenomena in quite a few different types of elastic and liquid-elastic media

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The particle velocity decreases as, eq. 2 LONGITUDINAL WAVES IN A THIN BAR 37 while the wave velocity increases in the same manner. For this reason, these two effects cancel each other, and inertia does not change. In fact, from eq. 107) and the influence of E vanishes. Consider, as in example four, a transition from an elastic bar to an ideally rigid one. As we already know, with an increase of the Young modulus the wave velocity increases, but the particle velocity becomes smaller. In other words, with an increase of E, both the particle velocity VQ and the time interval T — l/ci, during which the velocity v(t) remains constant, decrease.

6b. Then, due to a reflection, the compressional wave appears, Fig. 6c. The thin line corresponds to this wave. Superposition of both waves shows that at the beginning the resultant wave (thick line) is still extensional. 6: (a) The incident wave is an arbitrary function of x (b-g) A superposition of the incident and reflected waves at different instances near the free end. [After Kolsky, 1963] 34 CHAPTER 1. HOOKE'S LAW, POISSON'S RELATION AND WAVES... because near the bar end, the magnitude of the reflected wave is smaller than that of the incident wave.

72) 22 CHAPTER 1. EOOKE'S LAW, POISSON'S RELATION AND WAVES... However, the strains exx, eyy, and ezz are comparable, eqs. 73) As was shown earlier, the dilatation defines the relative change of an elementary volume, 0 = AV/V, and wave propagation is accompanied by either compression or expansion of the volume. At the beginning, we assumed that the displacement u(x,t) is uniformly distributed over the cross-section. If, in addition, we neglect by components v and w , it is easy to see that curl s = 0.

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