Extreme events and their optimal mitigation in nonlinear structural systems excited by stochastic loads: Application to ocean engineering systems

摘要

We develop an efficient numerical method for the probabilistic quantificationof the response statistics of nonlinear multi-degree-of-freedom structuralsystems under extreme forcing events, emphasizing accurate heavy-tailstatistics. The response is decomposed to a statistically stationary part andan intermittent component. The stationary part is quantified using astatistical linearization method while the intermittent part, associated withextreme transient responses, is quantified through i) either a few carefullyselected simulations or ii) through the use of effective measures (effectivestiffness and damping). The developed approach is able to accurately capturethe extreme response statistics orders of magnitude faster compared with directmethods. The scheme is applied to the design and optimization of smallattachments that can mitigate and suppress extreme forcing events delivered toa primary structural system. Specifically, we consider the problem ofsuppression of extreme responses in two prototype ocean engineering systems.First, we consider linear and cubic springs and perform parametric optimizationby minimizing the forth-order moments of the response. We then consider a moregeneric, possibly asymmetric, piecewise linear spring and optimize itsnonlinear characteristics. The resulting asymmetric spring design faroutperforms the optimal cubic energy sink and the linear tuned mass dampers.