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Waves in a Linear Viscoelastic Medium: Asymptotic Theory

机译：线性粘弹性介质中的波：渐近理论

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Uniformly valid asymptotic solutions are developed for the one-dimensional wave equation in a linear viscoelastic solid. In particular, the long-time behaviors resulting from an impulse, a unit step function, and a harmonic oscillation are investigated. The asymptotic solutions illustrate the effect of the dispersive-attenuation process. Results show a small-amplitude precursor, a diffusive main wave, and a boundary layer. The precursor propagates at a speed corresponding to the instantaneous modulus and decays exponentially with distance. The main wave travels at a speed corresponding to the equilibrium modulus and spreads diffusively. The approximating equations using perturbation methods reveal that the decay of the precursor results from relaxation processes and that the diffusive behavior results from cumulative dispersion. (ERA citation 05:027997)

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