The Dynamic of an Autoparametrical System With Two Coupled Pendulums Connected by SMA Spring

Abstract

The nonlinear dynamics of a three degree of freedom autoparametric system with two pendulums connected by SMA (Shape Memory Alloys) spring in the neighborhood internal and external resonance is presented in this works. The system consists of the body of mass m1 which is hung on a spring and a damper, and two connected by SMA spring pendulums of the length 1 and masses m2 and m3 mounted to the body of mass m1. It is assumed, that the motion of the pendulums are damped by resistive forces. Shape memory alloys have ability to change their material properties, for example stiffness. The equations of motion have been solved numerically and there was studied the influence of temperature on the energy transfer between modes of vibrations. Solutions for the system response are presented for specific values of the parameters of system. It was shown that in this type system one mode of vibrations may excite or damp another mode, and that except different kinds of periodic vibrations there may also appear chaotic vibrations. It depends on various amplitudes of excitation, frequencies ratio and different system parameters. Also fundamental is the influence of temperature on response of the system. For the identification of the responses of the system various techniques, including chaos techniques such as bifurcation diagrams and time histories, power spectral densities (FFT), Poincare` maps and exponents of Lyapunov may be use.