形状记忆合金复合材料系统非线性动力学研究

研究了形状记忆合金复合材料系统的非线性动力学特性。基于Brinson的形状记忆合金本构关系和Dejonghe的内耗模型,提出了单自由度简化系统的模型建立方法。考虑材料系统刚度和阻尼的变化,在弱非线性和较强非线性两种情况下给出近似-解析解法。算例表明:形状记忆合金可以作为良好的耗能材料,用于结构的被动控制。

ON NONLINEAR VIBRATION OF SHAPE-MEMORY-ALLOY-REINFORCED SYSTEM

The nonlinear dynamic properties of a shape memory alloy reinforced system for the purpose of vibration suppression are studied. The shape memory alloy reinforced structure is simplified to a single degree of freedom system by using the constitutive and internal friction models proposed by Brinson and Dejonghe, respectively. The internal friction is then expressed as the damping ratio of the shape memory alloy. In the case of weak nonlinear vibrations, the analytical solution of free vibration of the simplified system by using a small parameter method is obtained, while the weak nonlinear responses of the system excited by a simple harmonic force and forces in more generalized forms are proposed as well. The paper also presents an iterative algorithm for solving the system in a stronger nonlinear case. In this case, the total load history is divided into steps at which changes of stiffness and damping of the shape memory alloy reinforcement caused by martensite transformation and its inverse are taken into account. For each step, the problem is formulated as a weak nonlinear one and then solved by the aforementioned approach. Three examples of free and forced vibrations are provided. The results show that shape memory alloy reinforcement can be used as an efficient component in passive vibration control.