A Numerical Solution of Wave Motion in Viscoelastic Rods (Standard Linear Solid Model)
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Abstract
This study is about the propagation of waves through a short rod (or slug) of viscoelastic material. The viscoelastic material are modelled as standard linear solids which involve three material parameters. and the motion is treated as one-dimensional. In this study, a viscoelastic slug is placed between two semi-infinite elastic rods and a wave initiated in the first rod is transmitted through the slug into the second rod. The objective is to relate the transmitted signal to the material parameters of the slug. We solve the governing system of partial differential equations using Laplace transform. We invert the Laplace transformed solution numerically to obtain the transmitted signal for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. Finally, we discuss the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the interface velocity discontinuities.
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