The moment stability of response on a rectangular thin plate under in-plane narrow band random excitation

A dynamical model of a thin rectangular plate under in-plate parametrical narrow band noise excitation was proposed based on the elastic theory and the Galerkin’s method. Firstly, the model was perturbed applying the multiple scale method, subsequently the averaged equation in Ito form was obtained. Subsequently, the stochastic moment stability of the steady state responses was studied by Floquet theory and the moment method. Finally, the second order moment of the system was calculated. The moments can be used to estimate the statistical characters such as mean and variance of the responses. The numerical simulation was carried out and the results are consistent with the theatrical analysis