随机结构-TMD优化设计与概率密度演化研究
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摘要
针对随机结构提出了TMD的优化设计方法,基于Gegenbauer多项式逼近法将随机结构转化为等效确定性扩阶系统,选取该扩阶系统传递函数的H∞范数为优化目标,采用遗传算法来优化TMD参数。此外,应用概率密度演化理论分析比较了随机结构-TMD系统控制前后的结构随机地震响应和动力可靠度,并用蒙特卡罗法进行了验证。仿真分析结果表明:采用所提方法优化设计的TMD能有效地减小随机结构响应的峰值和方差,明显改善结构在地震激励下的动力可靠度,采用该方法优化设计的TMD具有良好的鲁棒性。
This paper presents a robust optimal design procedure of TMD parameters for stochastic structures based on H∞performance.A stochastic structure is first transformed into its deterministic equivalent system by Gegenbauer polynomial approximation method.Genetic algorithm is used in order to evaluate TMD′s optimum parameters through H∞ norm of the transfer function of the deterministic equivalent system as the objective function.The procedure of the optimal design of TMD is illustrated through a numerical example by the probability density evolution analysis.Numerical results show preliminarily that the optimized TMD can effectively suppress the undesirable vibration and improve structural dynamic reliability of the stochastic structure under the earthquake.
This paper presents a robust optimal design procedure of TMD parameters for stochastic structures based on H∞performance.A stochastic structure is first transformed into its deterministic equivalent system by Gegenbauer polynomial approximation method.Genetic algorithm is used in order to evaluate TMD′s optimum parameters through H∞ norm of the transfer function of the deterministic equivalent system as the objective function.The procedure of the optimal design of TMD is illustrated through a numerical example by the probability density evolution analysis.Numerical results show preliminarily that the optimized TMD can effectively suppress the undesirable vibration and improve structural dynamic reliability of the stochastic structure under the earthquake.
引文
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[18]苏成,徐瑞.非平稳地震作用下随机结构动力可靠度计算[J].振动工程学报,2011,24(2):118—124.Su Cheng,Xu Rui.Dynamic reliability analysis of stochastic structures subjected to nonstationary seismic excitations[J].Journal of Vibration Engineering,2011,24(2):118—124.
[2]吕西林,丁鲲,施卫星,等.上海世博文化中心TMD减轻人致振动分析与实测研究[J].振动与冲击,2012,31(2):32—37,150.Lv Xi-lin,Ding Kun,Shi Wei-xing,et al.Analysis and field test for human-induced vibration reduction with TMD in Shanghai EXPO culture center[J].Journal of Vibration and Shock,2012,31(2):32—37,150.
[3]秦丽,彭凌云,李业学.变摩擦系数式变摩擦TMD及其减震控制效果研究[J].土木工程学报,2013,46(11):81—88.Qin Li,Peng Lingyun,Li Yexue.Study on variable friction TMD with friction coefficient changeable and its seismic control effectiveness[J].China Civil Engineering Journal,2013,46(11):81—88.
[4]樊健生,李泉,李全旺,等.考虑人-结构相互作用的楼盖振动控制研究[J].振动与冲击,2010,29(11):230—236,264—265.Fan Jian-sheng,Li Quan,Li Quan-wang,et al.Floor vibration control considering human-structure interaction[J].Journal of Vibration and shock,2010,29(11):230—236,264—265.
[5]Asami T,Nishihara O,Baz A M.Analytical solutions to H∞and H2 optimization of dynamic vibration absorbers attached to damped linear systems[J].Journal of Vibration and Acoustics,2002,124:284—295.
[6]Zang C,Friswell M I,Mottershead J E.A review of robust optimal design and its application in dynamics[J].Computers and Structures,2005,83:315—326.
[7]Emiliano Matta,Alessandro De Stefano.Robust design of mass-uncertain rolling-pendulum TMDs for the seismic protection of buildings[J].Mechanical Systems and Singal Processing,2009,23:127—147.
[8]Giuseppe Carlo Marano,Giuseppe Quaranta.Robust optimum criteria for tuned mass dampers in fuzzy environments[J].Applied Soft Computing,2009,9:1 232—1 243.
[9]Cun-li Wu,Xiao-ping Ma,Tong Fang.A complementary note Gegenbauer pol-ynomial approximation for random response problem of stochastic structure[J].Probabilistic Engineering Mechanics,2006,21:410—419.
[10]李杰.随机结构动力分析的扩阶系统方法[J].工程力学,1996,13(1):93—102.Li jie.An expanded order system method for the dynamic analysis of stochastic structures[J].Engineering Mechanics,1996,13(1):93—102.
[11]廖俊,孔宪仁,杨正贤,等.随机结构非平稳响应的正交解法[J].工程力学,2011,28(12):13—19.Liao Jun,Kong Xian-ren,Yang Zheng-xian,et al.The orthogonal method for random structural non-stationary response[J].Engineering Mechanics,2011,28(12):13—19.
[12]Jie Li,Jian-bing Chen,Wen-liang Fan.The equivalent extreme-value event and evaluation of the structural system reliability[J].Structural Safety,2007,29:112—131.
[13]Jie Li,Jianbing Chen.The principle of preservation of probability and the generalized density evolution equation[J].Structural Safety,2008,30:65—77.
[14]周克敏,Doyle J C,Glover K.鲁棒与最优控制[M].北京:国防工业出版社,2006.Zhou Ke-min,Doyle J C,Glover K.Robust And Optimal Control[M].Beijing:National Defense Industry Press,2006.
[15]Cheung Y L,Wong W O.H-infinity optimization of a Variant design of the dynamic vibration absorber—Revisited and new results[J].Journal of Sound and Vibration,2011,330:3 901—3 912.
[16]Holland J H.Adaption in Nature and Artificial System[M].The University of Michigan Press,1975.
[17]林家浩,张亚辉,孙东科,等.受非均匀调制演变随机激励结构响应快速精确计算[J].计算力学学报,1997,14(1):2—8.Lin Jia-hao,Zhang Ya-hui,Sun Dong-ke,et al.Fast and precise computation of structural responses to nonuniformly modulated evolutionary random excitations[J].Chinese Journal of Computational Mechanics,1997,14(1):2—8.
[18]苏成,徐瑞.非平稳地震作用下随机结构动力可靠度计算[J].振动工程学报,2011,24(2):118—124.Su Cheng,Xu Rui.Dynamic reliability analysis of stochastic structures subjected to nonstationary seismic excitations[J].Journal of Vibration Engineering,2011,24(2):118—124.
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