Nonlinear random response of mechanical structures under different loading conditions

Two mechanical systems are investigated during the course of the present study. In the first system a simplified offshore structure subjected to wave loading is delineated, through which a unified second-order stochastic averaging approach suitable for practical nonlinear ocean structures exposed to severe wave conditions is developed. The results are compared with those predicted by Gaussian and non-Gaussian closures and by Monte Carlo simulation. In the absence of parametric excitation, the non-Gaussian closure solutions are in good agreement with Monte Carlo simulation. On the other hand, in the absence of hydrodynamic forces, second-order averaging gives more reliable results in the neighborhood of stochastic bifurcation. However, under pure parametric random excitation, the second-order stochastic averaging and Monte Carlo simulation predict the on-off intermittency phenomenon near bifurcation point, in addition to stochastic bifurcation in probability.; The second system deals with bending-torsion nonlinear interaction of a cantilever beam with a tip mass. The beam configuration with respect to the excitation is made in such a way that the two modes are only coupled through parametric excitation and nonlinear inertia forces. This means that both generalized and normal coordinates are the same.; Multiple time scale method is employed to predict the deterministic response while Monte Carlo simulation is used to estimate the statistics of the stochastic response. In an attempt to validate the predicted results, experimental deterministic investigation is carried out for selected excitation levels and frequencies covering the resonance conditions. Additionally, experimental random investigation was attempted to detect the response of the system under narrow and wide band excitations.; Both analytical and experimental results exhibit common features such as nonlinear modal interaction and non-stationarity in the response for certain excitation level. The stochastic response of the structure reveals different characteristics than the deterministic response.