Large vibration of a clamped circular composite plate with a concentric rigid mass

Abstract

The investigation is concerned with the axisymmetric non-linear vibrations of a thin composite circular plate carrying a concentric rigid mass. Hamilton's principle is utilized to derive the von Karman equations and the associated boundary conditions. Harmonic vibrations are assumed and the time variable is eliminated by a Kantorovich averaging method. Numerical solutions are obtainable by introducing the related initial value problem. Responses of the free and forced vibrations of the plate-mass system are obtained. Basic Differential Equations and Approximate Analyses Consider a flat circular plate having an outer radius a, constant thickness h, and an attached concentric rigid mass, M . The radius of the rigid mass is b and equals th: inner radius of the plate. The geometry is shown in Figure 1. The plate material is assumed to be elastic and homogeneous, but the material is made of composites which behave as a cylindrically orthotropic plate. By Hamilton's principle, it can be shown that the equations of motion for a finite amplitude axisymmetric vibration of a circular plate with a concentric rigid mass in nondimensional form are,