Benchmark solutions of stationary random vibration for rectangular thin plate based on discrete analytical method

This paper aims to accurately and efficiently achieve the benchmark solutions of stationary stochastic responses for rectangular thin plate. Firstly, the exact solutions of free vibration for thin plate with SSSS, SSSC, SCSC, SFSF, SSSF and SCSF boundary conditions are introduced to random vibration analysis. Based on pseudo excitation method (PEM), the analytical power spectral density (PSD) functions of the transverse deflection, velocity, acceleration and stress responses for thin plate under random base acceleration excitation are derived. Subsequently, to enhance computational efficiency, the discrete analytical method (DAM) that realizes the discretization for the modal coordinates and frequency domain is proposed. Finally, the efficiency of DAM and the accuracy of benchmark solutions are scrutinized by comparison with the analytical solutions and finite element solutions.