Transient Lamb's Solution for Surface Strip Impulses

Abstract

An alternative integral‐form solution of the Lamb's problem is developed for the transient response inside of the medium as well as at the surface, when subjected to impulsive/sudden application of surface strip loads. A distributed‐source solution that yields a Green's function for the boundary‐integral equation for half‐space problems has more advantages for the effective use for actual boundary‐value problems when compared to the Lamb's classical point/line source solution of 1904. The present procedure applies the Fourier‐Laplace integral transform to the governing equation so that after getting the Fourier (wavenumber) Laplace domain solution, it performs the inverse Fourier transform analytically and the inverse Laplace transform by contour integration. Such obtained expressions are amenable to numerical computation with excellent accuracy. The interior and surface responses of the medium under the uniform surface loading are the focus of the illustrative computations. The results are verified by comparing the surface response at the extreme loading state with the existing closed‐form solution for line source. The interior response features are stated.