Response Statistics of a Shape Memory Alloy Oscillator with Random Excitation

Abstract

This paper aimed to explore analytically the influences of random excitation on a shape memory alloy (SMA) oscillator. Firstly, on the basis of the deterministic SMA model under a harmonic excitation, we introduce a stochastic SMA model with a narrow-band random excitation. Subsequently, a theoretical analysis for the proposed SMA model was achieved through a multiple-scale method coupled with a perturbation technique. All of the obtained approximate analytical solutions were verified by numerical simulation results, and good agreements were observed. Then, effects of the random excitation and the temperature value on the system responses were investigated in detail. Finally, we found that stochastic switch and bifurcation can be induced by the random fluctuation, which were further illustrated through time history and steady-state probability density function. These results indicate that the random excitation has a significant impact on dynamics of the SMA model. This research provides a certain theoretical basis for the design and vibration control of the SMA oscillator in practical application.