Nonlinear thermomechanical oscillations of shape-memory devices

The nonlinear responses and bifurcations of shape-memory oscillators, based on a thermomechanical model, are investigated employing a numerically refined approach. Because of the discontinuities of the system tangent stiffness, classical gradient-based shooting-type techniques for calculating the periodic responses are not applicable. These solutions are then sought as the fixed points of the Poincare map combined with a path-following procedure. The Jacobian of the map is calculated via a central finite-difference scheme and its eigenvalues, the Floquet multipliers, are computed to ascertain the stability of the solutions and the codimension-one bifurcations. Frequency-response curves are constructed for shape-memory oscillators characterized by different hysteresis loops and for various excitation levels. The investigations are conducted both in isothermal and nonisothermal conditions and the main outcomes are comparatively discussed. A rich class of solutions and bifurcations-including jump phenomena, pitchfork, period-doubling, Hopf bifurcations, complete bubble structures culminating into chaos-is found; quasiperiodic motions arise in nearly adiabatic conditions. (C) 2003 Elsevier Ltd. All rights reserved.