On nonlinear vibration of shape-memory-alloy-reinforced system

The nonlinear dynamic properties of a shape-memory-alloy-reinforced system are studied for the purpose of vibration suppression. The shape-memory-alloy-reinforced structure is simplified to a single-degree-of-freedom system by using the constitutive model and internal friction model 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 some 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.