Low–frequency decay conditions for a semi–infinite elastic strip

Abstract

In this paper we investigate in–plane harmonic vibrations of a semi–infinite elastic strip with prescribed edge stresses. Low–frequency decay conditions are established demonstrating the deviation from the classical Saint–Venant principle in quadratic terms in frequency. In the case of the symmetric motion (strip extension), the proposed correction is expressed explicitly in terms of given end data, whereas for the antisymmetric motion (strip bending) this also involves unknown edge displacements. Further applications are defined including those related to dynamic analysis of plates and shells excited by statically self–equilibrated edge loads. The derivation is based on a perturbation approach using the Laplace transform technique. We also address methodological aspects dealing with a continuous eigenspectrum and the two–parametric nature of the problem.