Convolved Orthogonal Expansions for Uncertainty Propagation: Application to Randomvibration Problems

Physical nonlinear systems are typically characterized with n-fold convolution of the Green’s function, e.g., nonlinear oscillators, inhomogeneous media, and scattering theory in continuum and quantum mechanics. A novel stochastic computation method based on orthogonal expansions of random fields has been recently proposed [1]. In this study, the idea of orthogonal expansion is formalized as the so-called nth-order convolved orthogonal expansion (COE) method, especially in dealing with random processes in time. Although the paper is focused on presentation of the properties of the convolved random basis processes, examples are also provided to demonstrate application of the COE method to random vibration problems. In addition, the relation to the classical Volterra-type expansions is discussed