By J.D. Achenbach (Eds.)
This publication goals to provide an account of the idea of wave propagation in elastic solids. the cloth is prepared to offer an exposition of the fundamental techniques of mechanical wave propagation inside of one-dimensional atmosphere and a dialogue of formal facets of elastodynamic conception in 3 dimensions
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Additional info for Wave Propagation in Elastic Solids
This result is known as Jordan's lemma. 104) we close the contour in the upper half-plane for t — xjcL < 0, and in the lower half-plane for t — x/cL > 0, in order that the integration over the semicircle vanishes. Since there are no poles in the upper half-plane, we find τχ(χ, ή Ξ 0 for cLt < x. 107) In the lower half-plane there is a pole at ω = — ίη, whose contribution yields τχ = -Po exp ~η It- —) for cLt ^ x. 3. Although the foregoing example displays the features of Fourier integral analysis, the example is rather simple.
Other conditions are possible on the boundary of the body. In the dis cussion of the uniqueness theorem in chapter 3 the boundary conditions will be stated in detail. To complete the problem statement we define initial conditions; in V we have at time t = 0 Ui(x, 0) = iii(x) ύ ί ( χ , 0 + ) = έι·(χ). C h . 2, § 2 . 6 . 6. One-dimensional problems If the body forces and the components of the stress tensor depend on one spatial variable, say x1, the stress-equations of motion reduce to τη,ι+Pfi =püi.
83) only those which have a nodal point at x = I can be used. Thus we require sin (kl) = 0, which implies kl = — = nn A n = 1, 2, 3, 4, . . The distance between nodal points is half the wavelength, and thus this distance must be /, //2, //3, etc. The corresponding circular frequencies are ω = kcb — . The circular frequency of the lowest or fundamental mode, which is called the fundamental frequency, is ω 0 = ncjl radians per second; in cycles per second the fundamental frequency is f0 = cb/2l.