Experimental study of bifurcations in an impact oscillator with SMA constraint

In this paper we study bifurcations of an impact oscillator with one sided SMA motion constraint. The excitation frequency is used as a bifurcation parameter and two different values of the excitation amplitude are considered. It is shown that as frequency varies, the system exhibits highly nonlinear behavior. A typical bifurcation diagram has a number of resonance regions separated by chaotic motions with additional windows of periodic responses. The evolution of chaotic attractors is recorded experimentally, and changes in the structure of the attractors are shown.

A mathematical model is developed and the results of the simulations are compared with the experimental findings. It is shown that the model is capable of accurately predicting not only the resonance structure but also the shape of the periodic and chaotic attractors. Numerical investigations also reveal a number of coexisting attractors at some frequency values. In particular, three attractors are found numerically for A = 0.2 mm and f = 29.474 Hz and their basins of attraction are presented. For A = 0.2 mm and f = 33.463 Hz, four coexisting attractors are found. For both parameter sets, one of the numerically detected attractors was validated experimentally.

The undertaken analysis has shown that the hysteretic behavior of the restraint affected the dynamic responses only at the resonances, when the displacements are sufficiently large to trigger phase transformations in the SMA restraint. In nonresonant frequency ranges the restoring force in the SMA constraint is elastic. These findings are consistent with the numerical analysis carried out in [Sitnikova et al., 2008] for a similar system, which showed that the hysteretic behavior of the SMA affects resonant responses and provides a substantial vibration reduction in those regions.