CHAOS ROBUSTNESS AND STRENGTH IN THERMOMECHANICAL SHAPE MEMORY OSCILLATORS PART II: NUMERICAL AND THEORETICAL EVALUATION

Abstract

In this two-part paper the problem of evaluating robustness and strength of chaos in thermomechanically-based Shape Memory Oscillators (SMOs) is addressed. In Part I, several tools for the theoretical prediction of the main features of the pseudoelastic loops of Shape Memory Devices (SMDs) have been proposed. In this Part II, the Method of Wandering Trajectories (MWT), that has already been validated as a systematic, yet affordable, numerical tool for the evaluation of the chaotic response of SMOs, is enhanced by complementing it with a quantitative indicator of chaoticity: the maximum value of the displacement normalized separation over a fixed time interval. The method is used to compute numerical 3D behavior charts for several model parameters sets, properly selected in order to highlight the influence of various model parameters on the nonlinear dynamical response of SMOs. From the numerical analyses it turns out that two main aspects of the SMD behavior do influence the robustness and strength of chaos, namely the hardening of the pseudoelastic plateaus and the area of the hysteresis loop, both of them being meaningfully affected by the model mechanical and thermal parameters. The numerical results are also interpreted by means of the theoretical indicators discussed in Part I, which provide a reliable framework for the prediction of the main features of dynamic response before actual computation of the trajectories.