单自由度SMA阻尼结构在高斯白噪声激励下的平稳随机振动分析  

ANALYSES OF STATIONARY RANDOM VIBRATION OF SINGLE-DEGREE-OF-FREEDOM STRUCTURE WITH SHAPE MEMORY ALLOY DAMPER SUBJECTED TO GAUSSIAN WHITE NOISE EXCITATION

作　　者：任文杰[1,2] 李宏男[3] 

机构地区：[1]河北工业大学土木工程学院,天津300401 [2]河北省土木工程技术研究中心,天津300401 [3]大连理工大学海岸和近海工程国家重点实验室,大连116024

出　　处：《工程力学》2014年第2期35-40,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(50978081);中国博士后科学基金面上项目(2013M541165);教育部高等学校博士学科点专项科研基金项目(20091317120002);河北省教育厅百名优秀创新人才支持计划项目(CPRC011);住宅与城乡建设部科学技术项目(2011-K3-18);大连理工大学海岸和近海工程国家重点实验室开放基金项目(LP0902)

摘　　要：设计了一种超弹性形状记忆合金(Shape Memory Alloy,SMA)阻尼器。在SMA丝的Graesser本构模型基础上,建立了SMA阻尼器的常规力学模型,进而提出了其简化力学模型。采用随机等价线性化法建立了单自由度SMA阻尼结构在高斯白噪声激励下的平稳随机振动分析公式。算例比较了随机等价线性化法和蒙特卡罗(Monte Carlo)模拟法计算的结构振动响应,证明了随机等价线性化法的有效性;比较了无控结构和SMA阻尼结构的动力特性和振动响应,说明了SMA阻尼器能增加结构的刚度和阻尼比,因而可有效抑制结构的振动。A superelastic shape memory alloy （SMA） damper is designed. Based on the Graesser＇s constitutive model of SMA wire, the conventional mechanical model of the SMA damper is set up. Further, a simplified mechanical model of the SMA damper is put forward. Using a stochastic equivalent linearization method, the analyses of the stationary random vibration of a single-degree-of freedom structure with the SMA damper subjected to Gaussian white noise excitation are formulated. Numerical simulations are carried out to compare the vibration responses of the structure between the stochastic equivalent linearization method and the Monte Carlo simulation method, and the results testify that the stochastic equivalent linearization method is valid. The dynamic properties and the vibration responses of the structure without and with the SMA damper are computed, and the results show that the SMA damper can decrease the vibration of the structure effectively due to its capability of increasing the stiffness and the damping ratio of the structure.

关 键 词：形状记忆合金 阻尼器 力学模型 随机振动 随机等价线性化法 蒙特卡罗模拟法 

分 类 号：TU352.1[建筑科学—结构工程] TB123[理学—工程力学]