Polynomial chaos‐based extended Padé expansion in structural dynamics

E. Jacquelin · O. Dessombz · Jean-Jacques Sinou · Sondipon Adhikari · Michael I. Friswell

26 citations0/0 files storedInternational Journal for Numerical Methods in Engineering

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Abstract

Summary The response of a random dynamical system is totally characterized by its probability density function (pdf). However, determining a pdf by a direct approach requires a high numerical cost; similarly, surrogate models such as direct polynomial chaos expansions are not generally efficient, especially around the eigenfrequencies of the dynamical system. In the present study, a new approach based on Padé approximants to obtain moments and pdf of the dynamic response in the frequency domain is proposed. A key difference between the direct polynomial chaos representation and the Padé representation is that the Padé approach has polynomials in both numerator and denominator. For frequency response functions, the denominator plays a vital role as it contains the information related to resonance frequencies, which are uncertain. A Galerkin approach in conjunction with polynomial chaos is proposed for the Padé approximation. Another physics‐based approach, utilizing polynomial chaos expansions of the random eigenmodes, is proposed and compared with the proposed Padé approach. It is shown that both methods give accurate results even if a very low degree of the polynomial expansion is used. The methods are demonstrated for two degree‐of‐freedom system with one and two uncertain parameters. Copyright © 2016 John Wiley & Sons, Ltd.

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References

1991Stochastic Finite Elements: A Spectral Approach 1969The eigenvalue problem for structural systems with statistical properties.2007Efficient characterization of the random eigenvalue problem in a polynomial chaos decomposition 2003Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties 2005Analysis of Eigenvalues and Modal Interaction of Stochastic Systems 2009Padé–Legendre approximants for uncertainty analysis with discontinuous response surfaces 2007Stochastic convergence acceleration through basis enrichment of polynomial chaos expansions 2014Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems

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