Modeling of Flexural Wave Propagation in a Plate with Contacting Interfaces

Abstract

Propagation characteristics of a flexural wave in a thin plate which surfaces are in imperfect contact with solid bodies are examined theoretically as well as numerically. To this purpose, a nonlinear interface model of solid-solid contact is incorporated in the Mindlin plate theory. The governing differential equations are derived for a plate in contact with rigid bodies on both surfaces, and the dispersion relation for infinitesimal amplitudes is obtained theoretically. The derived equations are solved by the finite difference method to examine the propagation of a flexural wave packet. The numerical results show that the interfacial stiffnesses influence the velocity and the broadening of the propagating wave packet, and the contact nonlinearity brings about harmonic generation. It is discussed how these features are influenced by the linear and nonlinear interface parameters, the wave amplitude and the propagation distance.