Dynamics of thermally activated shape memory alloy autoparametric systems with two pendulums

The nonlinear dynamics of a three-degree-of-freedom autoparametric system with two pendulums connected by an shape memory alloy (SMA) spring in the neighbourhood of internal and external resonance is presented in this work. The system consists of the body of mass m1, which is hung on a spring and a damper, two pendulums of the length l, and masses m2 and m3 mounted to the body of mass m1 and connected by a SMA spring. The considered concept of adaptive control is based on the ability to change the spring parameters during a temperature activated, reversible, martensitic transition that is specific to SMAs. The equations of motion have been solved numerically and the influence of temperature on the energy transfer between the modes of vibration was studied. Solutions for the system response are presented for specific values of the parameters of the system. It was shown that in this type of system one mode of vibration might excite or damp another mode, and that as well as different kinds of periodic vibration, chaotic vibrations may also appear.