Article2011

STOCHASTIC STRUCTURAL MODAL ANALYSIS INVOLVING UNCERTAIN PARAMETERS USING GENERALIZED POLYNOMIAL CHAOS EXPANSION

Kian K. Sepahvand · Steffen Marburg · Hans‐Jürgen Hardtke

33 citations0/0 files storedInternational Journal of Applied Mechanics

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Probabilistic and Robust Engineering Design Structural Health Monitoring Techniques Model Reduction and Neural Networks

Abstract

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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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2008The stochastic finite element method: Past, present and future 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations 1986Probabilistic finite elements for nonlinear structural dynamics 1987Structural Dynamics with Parameter Uncertainties 2004Random matrix theory for modeling uncertainties in computational mechanics 1984Probabilistic Methods in the Theory of Structures

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