Numerical solution of wave propagation in viscoelastic rods (standard linear solid model)

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1 Citation (Scopus)

Abstract

The studies 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 (3) 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 discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the interface velocity discontinuities.

Original languageEnglish
Article number012039
JournalIOP Conference Series: Earth and Environmental Science
Volume16
Issue number1
DOIs
Publication statusPublished - 01 Jan 2013
Event26th IAHR Symposium on Hydraulic Machinery and Systems - Beijing, China
Duration: 19 Aug 201223 Aug 2012

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slug
wave propagation
acoustics
viscosity
Laplace transform
discontinuity
material
parameter

All Science Journal Classification (ASJC) codes

  • Earth and Planetary Sciences(all)
  • Environmental Science(all)

Cite this

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abstract = "The studies 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 (3) 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 discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the interface velocity discontinuities.",
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AB - The studies 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 (3) 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 discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the interface velocity discontinuities.

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