An approximate nonlinear dynamic theory for plates

Summary In this paper an approximate theory for the moderately large motion of transversely isotropic (orthotropic) plates is presented. Unlike other methods used in the past, the method used here involves no artificial assumptions. The method of approach begins with the equations of a partially non-linear elasticity theory and utilizes a method of asymptotic integration to arrive at successive two-dimensional approximations of increasing accuracy. The first approximation theory obtained here is the dynamic counterpart of Karman's plate theory. It includes the effect of rotatory inertia.