Nonlinear Systems Under Gaussian White Noise Excitation

In Chap. 4, the Wiener path integral technique developed in Chap. 3 is generalized to account for multi-degree-of-freedom systems exhibiting various nonlinear behaviors. An integral part of the approach relates to the derivation of a nonlinear functional minimization problem to be solved numerically for determining the most probable path to be used for approximating the associated functional integral. To this aim, a simple, yet computationally demanding, brute-force numerical implementation scheme is proposed for determining the multi-degree-of-freedom system response joint transition probability density function. The chapter concludes with two representative examples for demonstrating numerical aspects of the technique.