Finite Element Formulation and Numerical Simulation of the Large Deflection Random Vibration of Laminated Composite Plates

A theoretical large deflection finite element formulation is developed for the purpose of simulating the random vibration of thin generally laminated composite plates. The random acoustic load is taken to be stationary and Gaussian with zero mean and uniform magnitude and phase over the surface of the plate. In­ plane inertia terms are included in the formulation however rotary inertia terms are assumed negligible. The integration routine is derived from a set of unified single step algorithms, using a weighted satisfaction of the equilibrium equation. The algorithm is second order accurate and unconditionally stable for particular values of its free parameters. The application of this technique to the nonlinear finite element formulation leads to a system of nonlinear algebraic equations in the routines unknowns. A Newton­ Raphson scheme is used to solve this equation at each time step using the previous time values as initial guesses. Probability density, spectral density and autocorrelation functions are presented for various input spectrum levels and mean square values are compared with linear solutions. Classical thin plate boundary conditions and pseudo white noise excitations are used in this investigation.