Effect of longitudinal stress on wave propagation in width‐constrained elastic plates with arbitrary Poisson's ratio

Abstract

The Helmholtz wave equation is derived for longitudinal waves in an elastic plate of arbitrary thickness placed in a rigid gantry ensuring a constant width. The whole range of Poisson's ratio allowed for isotropic elastic media constrained in this way is considered. The wave speed is shown to increase under a constant longitudinal compressive stress applied to the front face of the plate and to decrease when the applied stress is tensile. The effect is most pronounced for zero Poisson's ratio and it vanishes for the limiting permitted values, i.e., 1 or −1. The reported results also describe the combined effect of longitudinal stress and Poisson's ratio on the wave speed. These findings provide guidelines for designing devices aimed at a passive control of propagation of longitudinal waves in thin‐walled structures.