Validation of numerical solution of wave propagation in vicoeslastic material (standard linear solid model) through perturbation

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The study is about impact of a short viscoelastic slug on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when a viscoelastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to investigate how the viscosity time constants in the slug and in the rod give rise to different interface stresses and interface velocities following wave transmission in the slug. After modeling the impact and solving the governing system of partial differential equations in the Laplace transform domain, we invert the Laplace transformed solution numerically to obtain the stresses and velocities. In inverting the Laplace transformed equations we used the complex inversion formula (Bromwich contour). In validating the numerical results, the method of multiple scales in perturbation is engaged to determine the first discontinuity jump at the interface. Finally, we discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the viscoelastic impacts obtained numerically and the predictions acquired using the multiple scales in perturbation.

Original languageEnglish
Title of host publicationProceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences
Subtitle of host publicationA Catalyst for Creativity and Innovation
Pages148-157
Number of pages10
Volume1522
DOIs
Publication statusPublished - 06 May 2013
Event20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012 - Putrajaya, Malaysia
Duration: 18 Dec 201220 Dec 2012

Other

Other20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012
CountryMalaysia
CityPutrajaya
Period18/12/1220/12/12

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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    Haji Musa, A. B. (2013). Validation of numerical solution of wave propagation in vicoeslastic material (standard linear solid model) through perturbation. In Proceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation (Vol. 1522, pp. 148-157) https://doi.org/10.1063/1.4801118