NONLINEAR RANDOM RESPONSE OF OCEAN STRUCTURES USING FIRST-ORDER AND 2ND-ORDER STOCHASTIC AVERAGING

This paper deals with the dynamic response of nonlinear elastic struct ure subjected to random hydrodynamic forces and parametric excitation using a first- and second-order stochastic averaging method. The gover ning equation of motion is derived by using Hamilton's principle, taki ng into account inertia and curvature nonlinearities and work done due to hydrodynamic forces. Within the framework of first-order stochasti c averaging, the system response statistics and stability boundaries a re obtained. Unfortunately, the effects of nonlinear inertia and curva ture are not reflected in the final results, since the contribution of these nonlinearities is lost during the averaging process. In the abs ence of hydrodynamic forces, the method fails to give bounded response statistics, and the analysis yields stability conditions. It is the s econd-order stochastic averaging which can capture the influence of st iffness and inertia nonlinearities that were lost in the first-order a veraging process. The results of the second-order averaging are compar ed with those predicted by Gaussian and non-Gaussian closures and by M onte Carlo simulation. In the absence of parametric excitation, the no n-Gaussian closure solutions are in good agreement with Monte Carlo si mulation. On the other hand, in the absence of hydrodynamic forces, se cond-order averaging gives more reliable results in the neighborhood o f stochastic bifurcation. However, under pure parametric random excita tion, the stochastic averaging and Monte Carlo simulation predict the on-off intermittency phenomenon near bifurcation point, in addition to stochastic bifurcation in probability.