Non-linear axisymmetric transient analysis of orthotropic thin annular plates with a rigid central mass

The geometrically non-linear, axisymmetric transient elastic response is determined of cylindrically orthotropic thin annular plates with a rigid central mass subjected to a uniformly distributed load on the plate as well as a central load on the rigid mass. The dynamic analogue of the von Kármán equations in terms of the normal displacement w and the stress function Ψ are employed. The displacement w and stress function Ψ are expanded in finite power series and the orthogonal point collocation method in the space domain and the Newmark β scheme in the time domain are used. The response of isotropic and orthotropic, clamped as well as simply supported, annular plates with a rigid central mass, subjected to step function and sinusoidal pulse loads, has been calculated for two values of the annular ratio. The influence of the mass ratio and the magnitude of the step load on the deflection response has been determined. The effect of mass ratio, amplitude and duration of sinusoidal pulse on the deflection response has also been studied.