Journal
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
Volume 3, Issue 3, Pages 587-606Publisher
IMPERIAL COLLEGE PRESS
DOI: 10.1142/S1758825111001147
Keywords
Polynomial chaos; uncertain parameter; stochastic modal analysis; Galerkin projection
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In this paper, the application of generalized polynomial chaos expansion in stochastic structural modal analysis including uncertain parameters is investigated. We review the theory of polynomial chaos and relating error analysis. A general formulation for the representation of modal problems by the polynomial chaos expansion is derived. It shows how the modal frequencies and modal shapes are influenced by the parameter uncertainties. The key issues that arise in the polynomial chaos simulation of modal analysis are discussed for two examples: a discrete 2-DOF system and continuous model of a microsensor. In both cases, the polynomial chaos expansion is used for the approximation of uncertain parameters, eigenfrequencies and eigenvectors. We emphasize the accuracy and time efficiency of the method in estimation of the stochastic modal responses in comparison with the sampling techniques, such as the Monte Carlo simulation.
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