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

Research output: Contribution to journalConference article

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 language English 012039 IOP Conference Series: Earth and Environmental Science 16 1 https://doi.org/10.1088/1755-1315/16/1/012039 Published - 01 Jan 2013 26th IAHR Symposium on Hydraulic Machinery and Systems - Beijing, ChinaDuration: 19 Aug 2012 → 23 Aug 2012

### Fingerprint

slug
wave propagation
acoustics
viscosity
Laplace transform
discontinuity
material
parameter

### All Science Journal Classification (ASJC) codes

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

### Cite this

@article{8ae01b2ba34a4c139ce1016e85554687,
title = "Numerical solution of wave propagation in viscoelastic rods (standard linear solid model)",
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.",
author = "Musa, {Abu Bakar}",
year = "2013",
month = "1",
day = "1",
doi = "10.1088/1755-1315/16/1/012039",
language = "English",
volume = "16",
journal = "IOP Conference Series: Earth and Environmental Science",
issn = "1755-1307",
publisher = "IOP Publishing Ltd.",
number = "1",

}

In: IOP Conference Series: Earth and Environmental Science, Vol. 16, No. 1, 012039, 01.01.2013.

Research output: Contribution to journalConference article

TY - JOUR

T1 - Numerical solution of wave propagation in viscoelastic rods (standard linear solid model)

AU - Musa, Abu Bakar

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

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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U2 - 10.1088/1755-1315/16/1/012039

DO - 10.1088/1755-1315/16/1/012039

M3 - Conference article

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JO - IOP Conference Series: Earth and Environmental Science

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SN - 1755-1307

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