Polynomial Chaos Expansion in Structural Dynamics: Accelerating the Convergence of the First Two Statistical Moment Sequences
E Jacquelin (Universite de Lyon, France), S Adhikari (Swansea University), J-J Sinou (Ecole Centrale de Lyon, France) & MI Friswell (Swansea University)
Journal of Sound and Vibration, Vol. 356, 10 November 2015, pp. 144-154
Polynomial chaos solution for the frequency response of linear non-proportionally damped dynamic systems has been considered. It has been observed that for lightly damped systems the convergence of the solution can be very poor in the vicinity of the deterministic resonance frequencies. To address this, Aitken's transformation and its generalizations are suggested. The proposed approach is successfully applied to the sequences defined by the first two moments of the responses, and this process significantly accelerates the polynomial chaos convergence. In particular, a 2-dof system with respectively 1 and 2 parameter uncertainties has been studied. The first two moments of the frequency response were calculated by Monte Carlo simulation, polynomial chaos expansion and Aitken's transformation of the polynomial chaos expansion. Whereas 200 polynomials are required to have a good agreement with Monte Carlo results around the deterministic eigenfrequencies, less than 50 polynomials transformed by the Aitken's method are enough. This latter result is improved if a generalization of Aitken's method (recursive Aitken's transformation, Shank's transformation) is applied. With the proposed convergence acceleration, polynomial chaos may be reconsidered as an efficient method to estimate the first two moments of a random dynamic response.
This material has been published in the Journal of Sound and Vibration, Vol. 356, 10 November 2015, pp. 144-154. Unfortunately the copyright agreement with Elsevier does not allow for the PDF file of the paper to be available on this website. However the paper is available from ScienceDirect - see the link below.
Link to paper using doi: 10.1016/j.jsv.2015.06.039
Journal of Sound and Vibration on ScienceDirect