Vibration reduction of the impact system by an SMA restraint: numerical studies

Abstract

The dynamic behaviour of an impact oscillator with a shape memory alloy (SMA) restraint is modelled and analyzed. This impact oscillator has the secondary support made from an SMA and the thermo-mechanical description of the SMA element follows the formulation proposed by Bernardini et al. [1,2]. The thermo-mechanical coupling terms included in the energy balance equation allow to undertake the non-isothermal analysis. Due to the mechanical characteristics of the SMA element and the non-smooth nature of the impacts, five different modes of operation can be distinguished. The undertaken numerical investigations suggest that the system can exhibit complex dynamic responses, which if appropriately controlled can be used for vibration reduction. A comparison with an equivalent elastic oscillator is made. It is found out that the low amplitude regimes are not affected by the SMA element. On contrary, for the large amplitude responses, a significant vibration reduction may be achieved due to the phase transformation hysteresis loop. Various bifurcation scenarios are constructed and the influence of the SMA element is discussed. In particular, the analysis of the frequency and amplitude variations of the external excitation is given and the parameter ranges where the vibration reduction is possible are identified.