Some analytical aspects of viscoelastic Lamb’s problem for improving its numerical evaluation

Two analytical modifications of the original viscoelastic time-harmonic Lamb’s problem expressions are presented with the aim of improving their numerical integration efficiency. Firstly, a new change of variable in the Lamb’s problem integrands is proposed, which allows a standardization of the integration sampling vector and a complete spatial-frequency field solution after performing only one numerical integration/transformation. Secondly, the Lamb’s problem static integrands are modified and introduced into the original integrands to reduce their spectral content at high wavenumbers and, therefore, the sampling vector lengths needed to avoid aliasing.

► A new change of variable is proposed for the viscoelastic Lamb’s problem. ► New integrands are not frequency-dependant. ► The complete spatial-frequency solution can be obtained by numerically solving only one integral. ► The spectral content at high wavenumbers is significantly reduced by using modified static solutions.