Longitudinal wave speed in rectangular slabs with mixed restraints in lateral directions

Abstract

Practical problems in structural elements are not confined to simple boundary conditions; often the boundary conditions are mixed. The question of longitudinal wave speed through a rectangular slab is solved herein for the case where the top and bottom surfaces are elastically restrained in the thickness direction while the side surfaces are fully constrained from motion in the width direction. Unlike the classical approach, the current analysis permits changes to the cross-sectional area and density of the considered elemental volume to be accounted for. While it is well established that the wave speed increases and decreases with Young's modulus and density, respectively, the present results additionally show that the wave speed increases with Poisson's ratio magnitude and stiffness of the elastic restraint acting in the thickness direction. Results also indicate that tensile and compressive strains tend to increase and decrease, respectively, the wave speed. The availability of more influencing parameters, arising from the removal of simplifying assumptions, paves a way to greater design options for the practising engineer.