SMA阻尼器控制单自由度结构在地震激励下的平稳随机振动研究

RESEARCH ON STATIONARY RANDOM VIBRATION OF SINGLE-DEGREE-OF-FREEDOM STRUCTURE WITH SHAPE MEMORY ALLOY DAMPER SUBJECTED TO EARTHQUAKE EXCITATION

对安装有超弹性形状记忆合金(shape memory alloy,简称SMA)阻尼器的单自由度结构在地震激励下的平稳随机振动进行了理论研究:假定地震地面运动是具有平稳过滤有色噪声模型的随机过程,确定了与《建筑抗震设计规范》(GB 50011-2010)相对应的随机地震动模型参数(平稳持时和谱强度因子);建立了SMA阻尼器控制的单自由度结构在平稳地震动过程下的状态方程,并采用随机等价线性化法推导了其平稳反应公式以及基于首超破坏准则的结构动力可靠性公式;通过算例,证明了随机振动解析式是可行的,并指出SMA阻尼器能消耗地震能量,从而有效抑制结构的振动,增加结构动力可靠性。

Theoretical researches on the stationary random vibration of a single-degree-of freedom structure with the superelastic shape memory alloy （SMA） damper subjected to earthquake excitations are carried out. The earthquake ground motion is assumed to be a stationary filtered color noise process, and the parameters of the random earthquake ground motion model （i.e. the stationary duration and the spectral intensity parameter） are determined according to the Code for seismic design of buildings （GB50011-2010）. Random state equations of the SMA-damped structure under the stationary filtered color noise excitation are set up. Then, using an stochastic equivalent linearization method, the stationary random seismic responses of the SMA-damped structure are formulated, and the dynamic reliability of the structure is obtained on the basis of the first threshold crossing failure criterion. Numerical simulations prove that the proposed random vibration formulations are correct, and that the SMA damper can decrease the vibration of the structure effectively, and increase the dynamic reliability of the structure attributed to its capability of dissipating the earthquake energy.