大型复杂减隔震结构非线性随机振动时域显式方法研究

The research on nonlinear random vibration method for seismic isolation and mitigation structures is of great concern to the promotion of the seismic isolation and mitigation techniques. Based on the time-domain explicit formulation method, which was originally proposed for non-stationary random vibration analysis of large scale linear systems, two highly efficient methods, i.e. the fast equivalent linearization method and the fast random simulation approach, will be presented for the locally nonlinear random vibration problems of large complex structures with isolation and mitigation devices under non-stationary seismic excitations. On this basis, a set of nonlinear random vibration analytical approach, in which both structural uncertainties and random excitations are taken into consideration, will be proposed for reasonable evaluation of the effects of the uncertain properties of isolation and mitigation devices on the seismic behaviors of structures. Finally, based on the two highly efficient methods proposed, the sensitivity of structural statistical performance indexes with respect to the parameters of seismic isolation and mitigation devices will be obtained, and a set of parameter optimization method will be presented for stochastic optimal control of the seismic isolation and mitigation strucures. This research will improve the theoretical framework for random vibration of seismic isolation and mitigation structures, and will promote the application of the seismic isolation and mitigation techniques.

强震下减隔震结构非线性随机振动方法研究是推动减隔震技术发展的关键问题。针对非平稳地震激励下大型复杂减隔震结构局部非线性随机振动问题，以大规模线性系统非平稳随机振动时域显式解法为主线，系统提出以时域显式降维迭代计算为核心的快速等效线性化方法和高效随机模拟方法，为减隔震结构非线性随机振动提供两种高效实用分析方法。在此基础上，进一步考虑减隔震装置参数的随机变异性，建立一套考虑结构参数和地震激励双重随机性的减隔震结构非线性复合随机振动方法，为合理评估减隔震装置参数随机性对减隔震结构抗震性能的影响提供科学依据。最后，以所发展的两种高效计算方法为平台，提出减隔震结构关键统计性能指标关于减隔震装置参数的敏度计算方法，系统建立基于随机最优控制的减隔震装置参数优化设计方法，实现减隔震结构的随机最优控制。本项目研究对于丰富和完善减隔震结构随机振动理论体系及推动减隔震技术发展具有重要的科学意义和应用价值。

针对随机地震激励的非平稳特性及减隔震结构的局部非线性特性，结合大规模线性系统非平稳随机振动时域显式解法的时空降维计算优势及单域分析特点，提出了非平稳随机激励下演化等效线性系统响应统计矩的降维迭代高效计算方法，建立了减隔震结构非线性随机地震响应分析的快速等效线性化方法，解决了传统等效线性化方法在非平稳随机振动问题中分析效率低下的问题。从随机地震激励下减隔震结构的拟线性运动微分方程出发，针对减隔震装置局部非线性特性，利用拟线性系统动力响应时域显式表达式的降维表征优势，提出了关于减隔震装置局部非线性自由度的显式降维迭代算法，建立了减隔震结构非线性随机地震响应分析的高效随机模拟方法，突破了传统随机模拟方法计算量巨大的瓶颈。相关研究成果已成功应用于虎门二桥坭洲水道桥（主跨1688m双塔双跨悬索桥）和大沙水道桥（主跨1200m双塔单跨悬索桥）两座跨海特大桥的抗震与减震研究专题，检验了方法的有效性，并提出了相关设计建议。