Wave Propagation in an Elastic Plate Resting on an Elastic Foundation

Author: Lloyd, James Reily

Year: 1962

Degree: Dissertation (Ph.D.)

Advisor: Miklowitz, Julius

Committee Member: Unknown, Unknown

Option: Mechanical Engineering

Abstract

Presented is an analysis of wave propagation in an infinite elastic plate or beam on an elastic foundation. The results are presented in two parts:

The frequency spectra (frequency as a function of wave number) for the problem based on existing approximate bending theories are compared with the spectra based on the exact equations of motion from linear elasticity theory. The existence of complex wave numbers is established in each case. A distinct similarity is found between the spectrum representing the more exact theory of bending (Timoshenko bending mechanism) and the exact Rayleigh-Lamb spectrum for symmetric waves in a free elastic plate. Good agreement between approximate theories and the exact equations is found for soft foundations under the usual restrictions of low frequency-long waves.
The transient response is considered for the exact theory and the more exact theory of bending. In both cases suddenly applied line loads are considered. In the latter case the related point load problem is also studied. Two distinct integral transform methods of solution are presented and used in these problems. For one of these methods the contributions from the various modes, including the complex arms, are identified with certain integrals that are components of the solution. Results from numerical computation of these integrals are presented and analyzed for the more exact theory of bending using two different foundation stiffnesses.