Derivation of Effective Ratio of Acoustic Impedance for Impacting Viscoelastic Slug (Standard Linear Solid Model) and Elastic Rod

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 impacts a semi-infinite stationary viscoelastic rod. In order to validate the numerical results, we derive the effective ratio of acoustic impedance for impacting rods which will be used in the viscoelastic discontinuity analysis. The objective of this study 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 viscoelastic discontinuity analysis 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.

• Periodical: Applied Mechanics and Materials (Volume 554)
• Pages: 701-711
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.554.701
• Online since: June 2014
• Authors: Abu Bakar Musa*
• Keywords: Acoustic, Interface, Stress, Viscoelastic, Viscosity

References

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DOI: 10.1090/qam/78848