Recent Developments on Nonstationary Parametric Responses of Rectangular Plates

Abstract

Abstract The non-stationary parametric response of a rectangular plate during a logarithmic sweep of the excitation frequency through a system resonance is studied using five different techniques of solution. Considering only the case of principal parametric resonance, the continuous system is spatially discretized by means of a single-term modal approximation for the lateral displacement. The general form of the resulting nonlinear temporal equation of motion for the damped parametric vibrations in any spatial mode is analyzed using the multiple time scales method and the method of asymptotic series expansion developed by Mitropolsky, in the first and second approximation. The non-stationary response of the plate during transition through parametric resonances is also evaluated by direct integration of the temporal equation of motion and the results obtained by the different techniques are compared. The non-stationary response displays several phenomena depending on the conditions of in-plane loading, the amount of damping, the initial conditions, and the rate as well as the direction of the sweep. The validity of these results is ascertained experimentally.