The Probabilistic Solutions of the Cantilever Excited by Lateral and Axial Excitations Being Gaussian White Noise

Abstract

The multi-degree-of-freedom system with both external and parametric excitations is formulated with Galerkin’s method from the typical problem of the cantilever excited by both lateral excitation and axial excitation being correlated Gaussian white noises. The probabilistic solution of this multi-degree-of-freedom stochastic dynamical system is obtained by the state-space-split method and exponential polynomial closure method. The way for selecting the sub-state vector in the dimension reduction procedure with the state-space-split method is given for the analyzed cantilever. The solution procedure with the state-space-split method is presented for the system excited by both external excitation and parametric excitation being correlated Gaussian white noises. Numerical results are presented. The results obtained with the state-space-split method and exponential polynomial closure method are compared with those obtained by Monte Carlo simulation and Gaussian closure method to verify the effectiveness and efficiency of the state-space-split method and exponential polynomial closure method in analyzing the probabilistic solutions of the multi-degree-of-freedom stochastic dynamical systems with both external excitation and parametric excitation similar to that formulated from the cantilever excited by both lateral excitation and axial excitation being correlated Gaussian white noises.