Exact Solutions of Random Vibration Responses for Orthotropic Rectangular Kirchhoff Plates

Abstract

This paper efficiently determined exact stochastic responses of orthotropic rectangular Kirchhoff plates under stationary and nonstationary random excitations in a semianalytical manner. The transcendental frequency equations of orthotropic plates were solved exactly for the high-order natural frequencies. The power spectral density functions of elastic stochastic responses were derived analytically by means of the pseudoexcitation method. The semianalytical method (SAM) is proposed to ensure the accuracy of differential and integral operations in the space domain and to enhance the computational efficiency of random vibration analysis. The exact stochastic responses of the plates, especially the distribution of stochastic von Mises stress, to various stationary, temporal and spectral nonstationary random excitations were achieved, and the higher efficiency of SAM than of the analytical method, and its higher accuracy than that of Monte Carlo simulation, were illustrated. The remarkable effects of boundary conditions, material, and loading cases on uncertainty propagation of the orthotropic plate were determined. The obtained exact stochastic responses of orthotropic plate can be taken as the benchmark to verify other numerical methods.