Polynomial Chaos based on Extended Padé Expansion in Structural Dynamics
E Jacquelin (Universite de Lyon, France), O Dessombz, J-J Sinou (Ecole Centrale de Lyon, France), S Adhikari & MI Friswell (Swansea University)
International Journal for Numerical Methods in Engineering, Vol. 111, No. 12, 21 September 2017, pp. 1170-1191
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 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.
This material has been published in the International Journal for Numerical Methods in Engineering, Vol. 111, No. 12, 21 September 2017, pp. 1170-1191. Unfortunately the copyright agreement with Wiley InterScience does not allow for the PDF file of the paper to be available on this website. However the paper is available from the Wiley website - see the link below.
Link to paper using doi: 10.1002/nme.5497
International Journal for Numerical Methods in Engineering on Wiley InterScience