单自由度超弹性SMA减振结构随机振动控制理论研究

利用形状记忆合金（Shape Memory Alloy，简称SMA）丝的超弹性，提出了一种具有复位功能的阻尼器。在SMA丝的Graesser本构模型基础上，建立了阻尼器恢复力的滑移双线性模型；假定滞回面积相等，提出了恢复力的滑移刚塑性模型以近似简化滑移双线性模型。采用等价线性化法建立了单自由度超弹性SMA减振结构在高斯白噪声激励下的平稳随机振动分析公式。通过一算例，考虑不同激励谱密度和结构阻尼比：比较了等价线性法和蒙特卡罗（Monte Carlo）模拟法计算的结构振动响应（位移标准差和速度标准差），证明了SMA减振结构随机振动控制理论的有效性；比较了等价线性减振结构和无控结构的动力特性（刚度和阻尼比）和振动响应，说明了SMA阻尼器能提高结构的刚度和阻尼比，因而可有效抑制结构的振动。

RESEARCH ON RANDOM VIBRATION CONTROL THEORY OF SINGLE-DEGREE-OF-FREEDOM STRUCTURE WITH SUPERELASTIC SHAPE MEMORY ALLOY DAMPER

Using superelastic shape memory alloy (SMA) wire, a re-centring damper is presented. Based on the Graesser’s constitutive model of SMA wire, the slip bilinear restoring force model of the damper is set up. Given that the two models have the same hysteretic areas, a simplified slip rigid-plastic model is put forward to approximate the slip bilinear model. Using an equivalent linearization method, analyses of the stationary random vibration of a single-degree-of-freedom structure with the SMA damper subjected to a Gaussian white noise excitation are formulated. Numerical simulations are carried out, considering various excitation’s spectrum densities and damping ratios of the structure. Comparisons of the vibration responses (displacement standard deviation and velocity standard deviation) of the SMA-damped structure between the equivalent linearization method and the Monte Carlo simulation method testify the validity of the random vibration control theory. Comparisons of the dynamic properties (stiffness and damping ratio) and the vibration responses between the equivalent linearized damped structure and the uncontrolled structure prove that the SMA damper can decrease the structural vibration effectively attributed to its capabilities of increasing the stiffness and the damping ratio of the structure.