A proper generalized decomposition based Padé approximant for stochastic frequency response analysis

Abstract This article presents a proper generalized decomposition (PGD) based Padé approximant for efficient analysis of the stochastic frequency response. Due to high nonlinearity response with respect input uncertainties, classical Galerkin (SG) method utilizing polynomial chaos exhibits slow convergence near resonance. Furthermore, dimension SG is product deterministic and approximation spaces, hence resolution over banded range computationally expensive or even prohibitive. In this study, tackle these problems, PGD first generates solution equations as separated representation components. For computations, vectors are exploited reduced basis in conjunction singular value decomposition. Subsequently, applied on solution, represented by rational function. Through various numerical studies, it demonstrated that proposed framework improves not only accuracy vicinity resonance but also computational efficiency, compared method.