Wave Propagation in an Elastic Beam or Plate on an Elastic Foundation

Abstract

Presented is an analysis of wave propagation in an infinite elastic plate or beam on an elastic foundation, based on a comparison of frequency spectra (or wave-train solutions) from the exact equations and existing approximate bending theories. A distinct similarity is found between the spectrum representing the more exact theory of bending and the Rayleigh-Lamb spectrum for symmetric waves in a free elastic plate, including the existence of complex branches. Good agreement between the approximate theories and the exact equations is found for soft foundations under the usual restrictions on high-frequency, short waves.