Polynomial chaos-based extended Pade expansion in structural dynamics

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 Pade 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 Pade representation is that the Pade 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 Pade approximation. Another physics-based approach, utilizing polynomial chaos expansions of the random eigenmodes, is proposed and compared with the proposed Pade 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 (c) 2016 John Wiley & Sons, Ltd.