Abstract
The paper investigates the path integral solution method combined with the gamma-distribution approximation for exciting forces, for calculating the response statistics of nonlinear dynamic systems whose equations of motion can be modelled by the use of Ito stochastic differential equations. The state vector process of motions is generally a diffusion process, and the transition probability density function (TPDF) of the process satisfies a Fokker-Planck-Kolmogorov (FPK) equation. The method solve FPK equation for short time TPDF. Naess assumed that second order wave exciting force is described by one term of square of Rayleigh process, but this assumption is not actual. Authors propose the new path integral solution method which express the wave exciting force by gamma process. In this paper the new method is applied to the cases whose exact solution exist, and is verified its effectiveness.
