Transient Response of Two-Dimensional Cantilevered Semi-Infinite and Finite Elastic Plates, Subjected to Base Motions

This research is concerned with the response of a two-dimensional, isotropic, homogeneous, elastic, cantilevered plate subjected to a step transverse velocity at the base. The investigation uses a method by Miklowitz which is based on a double Laplace transform and a boundedness condition on the solution. The case of a semi-infinite plate is solved, for long-time, to find the shear and normal stresses at the base. The solution in the interior of the plate is shown to agree with that obtained by the Bernoulli-Euler approximate theory. The solution is then extended to the case of the finite length plate, with traveling wave and vibrational forms of the solution being found for the interior of the plate. At the base of the plate the investigation shows that the normal stress is singular at the corners while the shear stress is non-singular.