Wave Propagation in Elastic Solids by J.D. Achenbach (Eds.)

By J.D. Achenbach (Eds.)

This publication goals to give an account of the idea of wave propagation in elastic solids. the cloth is prepared to give an exposition of the fundamental suggestions of mechanical wave propagation inside one-dimensional environment and a dialogue of formal elements of elastodynamic idea in 3 dimensions

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81). ke_ — = dt -Α+ωθ++Α_ωθ-, where Θ+ = exp 0_ = exp i I kx — ωί + γ++ - I i lkx + cot + y_ + -1 . By employing the relation SP = — τχύ, the power per unit area is obtained as 9 = Ekωl{A+)2m(θ+)m{Θ+)-(A_)2m(θ-)m(θJ)~\. It is noted that for waves traveling in opposite directions 0* has no cross terms, so that even the instantaneous values of the energy transmission are simply the differences between the individual fluxes. 87), the time average is immediately obtained as <0>>=iEkco[(A + )2-(A_)2].

Determine the reflected and transmitted waves for the linearized theory. 6. A rod of length / and square cross section (cross-sectional area h2) is resting on one of its lateral sides on a smooth plane surface. At time t = 0 the rod is subjected at one end to an axial force F0H(t). There is no friction between the plane surface and the rod. The total mass of the rod is h2lp, where p is the mass density. If the rod were infinitely rigid the motion of the center of gravity would follow from an application of New­ ton's law.

51). , I ^(0, t)dt = | Jo The first integral assumes the form i'0(O,t)dt = Jo JT(x, t)dx. 65) Jo ~\(\p(s)Yds. 65) can easily be verified. 51). Upon integrating once, we find Τχ = (Α + 2μ) — = dx -p(t), 26 ONE-DIMENSIONAL MOTION OF AN ELASTIC CONTINUUM [Ch. 4. 48). Suppose we consider a monotonically increasing function p(t), and we expand p(t--\ \ ~p(t)--p(t). CTJ CT It is then clear that for given x and /, t > x/cL, the difference between the static and dynamic stresses is small if iL*)

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