Benchmark solutions for stochastic dynamic responses of rectangular Mindlin plates

Abstract

There exist some researches on the benchmark responses of moderately thick plates based on Mindlin theory under static loads. In practice, rectangular Mindlin plates are often subjected to various random excitations. However, the benchmark solutions of analytically stochastic dynamic responses for rectangular Mindlin plates under random excitations were not investigated. In this paper, analytical power spectral density functions and root mean squares for stationary and nonstationary stochastic responses of rectangular Mindlin plates are derived, which provide benchmark solutions for other numerical methods and experimental design. Firstly, based on the closed-form free vibration analyses of rectangular Mindlin plates with two opposite simply supported edges, exact natural frequencies and modal shapes are obtained. Then, the pseudo excitation method is introduced into the decoupled differential equations of motion. By combining the exact solutions of free vibration, the analytical method for random vibration analysis of elastic Mindlin plate is proposed, and the analytical stochastic responses are derived. Due to the low efficiency of the AM based on symbolic operation, the efficient discrete analytical method, which can ensure that the results are exact in the spatial domain, is further developed. Finally, the performance of the proposed approaches is verified by comparing with the commercial software, Monte Carlo simulation, and literature. The remarkable effects of spatial distributions of excitations on the stochastic responses of Mindlin plates are illustrated. The important influences of parameters including relative thickness, elastic modulus, and boundary constraint degree on responses are revealed.