随机结构地震响应的TMD控制

Optimal Design of TMD for Stochastic Structure under Earthquake Excitation

讨论了随机结构地震响应的TMD控制及其优化问题。借Gegenbauer多项式逼近法,首先把随机结构-TMD系统转化为等效的确定性扩阶系统,然后用演变随机响应统一解法求其随机响应。引进响应面法来建立结构随机响应与TMD参数之间的近似关系式,通过优化得到随机结构响应的最优TMD控制系统。算例证实,最优TMD可最有效地控制结构的总体响应,且对随机结构的每一个样本都有很好的控制效果。所以说,最优TMD控制具有鲁棒性。

Aim. TMD is short for Tuned Mass Damper, an effeetive passive strategy for vibration suppression. A stochastic structure we consider is modeled as a structure with bounded random parameters. The earthquake excitation is modeled by an evolutionary random process of the 1964 Niigata type. So this paper is devoted to the optimal design of a TMD for a stochastic structure under evolutionary random excitation. Based on Gegenbauer polynomial approximation, the stochastic structure with TMD is first transformed into its deterministic equivalent system, whose evolutionary random responses can be readily obtained by the available unified approach. Then the relationship between the evolutionary random responses and the parameters of the TMD can be explicitly formulated by means of the response surface methodology. Based on this explicit formulation the optimal parameters of TMD can be found through Matlab package. The procedure of optimal design of TMD is illustrated through an example. Numerical results, shown in Table 1 and Fig. 3 in the full paper, show preliminarily that the optimized TMD can effectively suppress the earthquake responses of the structure. Moreover the TMD works equally well for every sample system.