A numerical method is developed for the analysis of one-dimensional wave propagation in viscoelastic media with temperature-dependent properties when thermomechanical coupling is significant. The method is applied to a specific case of longitudinal wave propagation in a finite rod with essentially sinusoidal stress variation at the two ends. The results show that, contrary to the usual assumption, such a system does not have the same response as a single-degree-of-freedom elastic system with viscous damping, as long as a realistic stress-strain relation is used.
Wave Propagation in a Viscoelastic Material With Temperature-Dependent Properties and Thermomechanical Coupling
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Petrof, R. C., and Gratch, S. (September 1, 1964). "Wave Propagation in a Viscoelastic Material With Temperature-Dependent Properties and Thermomechanical Coupling." ASME. J. Appl. Mech. September 1964; 31(3): 423–429. https://doi.org/10.1115/1.3629658
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