Probabilistic Solutions of a Nonlinear Plate Excited by Gaussian White Noise Fully Correlated in Space

This paper addresses the nonlinear random vibration of a rectangular von Kármán plate excited by uniformly distributed Gaussian white noise which is fully correlated in space. The state-space-split method and exponential polynomial closure method are jointly utilized to analyze the probabilistic solutions of the plate. The computational efficiency and numerical accuracy of the methodology for analyzing the nonlinear random vibration of the plate are verified by comparing the computational effort and numerical results with those obtained by Monte Carlo simulation and equivalent linearization, respectively. Meanwhile, the convergence of the probabilistic solution in the sense of Galerkin’s approximation is examined by analyzing the plate modeled as single-degree-of-freedom and multi-degree-of-freedom systems. Some phenomena are discussed after numerically studying the behaviors of probabilistic solutions of the deflection at different locations of the plate.

The Nonlinear Random Vibration of a Clamped Rectangular Thin Plate in Magnetic Field

In this paper, the magneto-elastic nonlinear random vibration of a clamped rectangular thin plate in magnetic field is studied. According to the magneto-elastic theory of plates and shells and the theory of structural random vibration, the magneto-elastic nonlinear random vibration equation of a clamped rectangular thin plate in a magnetic field is derived. Then the nonlinear random vibration equation is transferred into the Ito differential equation, and the Ito differential equation is solved using FPK equation method. Thus the numerical characteristics of displacement response and velocity response of the rectangular thin plate are obtained. Finally, through a numerical example, the influences of magnetic field parameters on the numerical characteristics are discussed, and some methods which can be used to effectively control the random vibration responses of the plate are given.