Polynomial Chaos Expansion and Steady-state Response of a Class of Random Dynamical Systems

E Jacquelin (Universite de Lyon, France), S Adhikari (Swansea University), J-J Sinou (Ecole Centrale de Lyon, France) & MI Friswell (Swansea University)

ASCE Journal of Engineering Mechanics, Vol. 141, No. 4, April 2015, paper 04014145

Abstract

The first two moments of the steady-state response of a dynamical random system are determined through a polynomial chaos expansion (PCE) and a Monte-Carlo simulation (MCS) that gives the reference solution. It is observed that the PCE may not be suitable to describe the steady-state response of a random system harmonically excited at a frequency close to a deterministic eigenfrequency: many peaks appear around the deterministic eigenfrequencies. It was proved that the PCE coefficients are the responses of a deterministic dynamical system, the so-called PC-system. As a consequence these coefficients are subjected to resonances associated to the eigenfrequencies of the PC-system: the spurious resonances are located around the deterministic eigenfrequencies of the actual system. It is shown that the polynomial order required to obtain some good results may be very high, especially when the damping is low. These results were shown on a multi-dof (degree-of-freedom) system with a random stiffness matrix. A 1-dof system was also studied and new analytical expressions that make the polynomial chaos expansion possible even for high order were derived. The influence of the PC order was also highlighted. The results obtained in the paper improve the understanding and scope of applicability of PCE for some structural dynamical systems while harmonically excited around the deterministic eigenfrequencies.

Paper Availability

This material has been published in the ASCE Journal of Engineering Mechanics, Vol. 141, No. 4, April 2015, paper 04014145. Unfortunately the copyright agreement with ASCE does not allow for the PDF file of the paper to be available on this website.


Link to paper using doi: 10.1061/(ASCE)EM.1943-7889.0000856

Link to the Journal of Engineering Mechanics website