Stochastic fem method to vibration problems with uncertain parameters

In this work, we employ non-sampling techniques based on the generalized polynomial chaos expansions to numerical simulation of vibrational problems including random material Parameters. The method is used to discretize the random space using the same basis as the deterministic FEM to approximate the random parameters locally. The numerical algorithm has this potential to use commercial FEM codes as black box to discretize the spatial deterministic space. The hybrid stochastic collocation FEM method is implemented to generate samples of the parameters for the FEM deterministic code from which the polynomial chaos expansion of system responses are determined. To compute response statistics, the sparse grid stochastic collocation method uses approximate solutions, corresponding to a deterministic set of points in the random input space. Efficiency and convergence of the method are studied numerically by modal analysis investigation of a cantilever beam with uncertain E-modulus as a random field.