Explicit asymptotic modelling of transient Love waves propagated along a thin coating |
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Authors: | M Ahmad E Nolde A V Pichugin |
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Institution: | 1.Department of Mathematics,University of Sargodha,Sargodha,Pakistan;2.Department of Mathematical Sciences,Brunel University,Uxbridge,UK |
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Abstract: | An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples |
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