Stochastic dynamic analysis of a spatial flexible beam

The uncertainty dynamic response of a spatial flexible beam with large overall motion is investigated. The stochastic differential equations of a three-dimensional beam with large overall motion are derived by using the virtual work principle. The polynomial chaos method and monomial cubature rules are applied to derive a set of completely implicit differential equations. Then the polynomial coefficients are obtained by the variable order method and regression method so as to find the numerical characteristics of the response. As an illustrating example, dynamic modeling of a spatial flexible beam by considering the probabilistic of geometric and physical parameters is presented. The accuracy and efficiency of the method are verified by comparing the results with those given by the Monte Carlo simulation method. The results show that the probabilistic parameters have a significant effect on the dynamic response of the flexible beam and that the dynamic modeling with probabilistic parameters can objectively reflect the dynamic behavior of the objective systems.