Three-Dimensional Vibration Analysis of Thick FGM Plate Strips Under Moving Line Loads

Abstract

An exact three-dimensional analysis for steady-state dynamic response of an arbitrarily thick, isotropic, and functionally graded plate strip due to the action of a transverse distributed moving line load which is propagating parallel to the infinite simply supported edges of the plate at constant speed is presented based on the linear elasticity theory. The inhomogeneous plate is approximated by a laminate model, for which the solution is expected to gradually approach the exact one as the number of layers increases. The problem solution is derived by using Fourier transformation with respect to a moving reference frame in conjunction with the classical transfer matrix approach entailing the continuity of displacement and stress components at the interfaces of neighboring layers. The analytical results are illustrated with numerical examples in which a metal-ceramic (ZrO ₂–Al) FGM plate strip of unit width is subjected to a half-sine normal line load of constant amplitude traveling along the strip at uniform speeds. Four types of FGM plate strips are configured, and the effects of load velocity, material compositional gradient, and plate thickness on the basic dynamic field quantities are evaluated and discussed. Also, the response curves for the FGM plates are compared with those of equivalent bilaminate plates containing comparable total volume fractions of constituent materials. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.

Keywords:

• traveling load
• inhomogeneous plate strip
• critical velocity
• dynamic stress concentrations