Response Statistics of a Shape Memory Alloy Oscillator with Random Excitation

Rong Guo,Qi Liu,Yong Xu,Junlin Li

doi:10.3390/app112110175

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.

Highlights

Shape memory alloys (SMAs) are included in certain kinds of smart materials that are relatively lightweight, easy to manufacture, and are able to produce high forces or displacements with low power consumptions [1,2,3]
These reversible transformations lead to the special properties of superelasticity and shape memory
Shang and Wang [12] showed similar periodic and chaotic motions of the shape memory alloy (SMA) model through numerical simulations, which owe to the changing temperature, damping coefficient, and amplitude of the external forces

Summary

Introduction

Shape memory alloys (SMAs) are included in certain kinds of smart materials that are relatively lightweight, easy to manufacture, and are able to produce high forces or displacements with low power consumptions [1,2,3]. It is worth mentioning that, compared with the Gaussian noise, narrow-band random excitation is important and widely present in actual engineering systems. For the SMA oscillation system, it is important to study its nonlinear dynamic behaviors under the excitation of narrow-band noise, which has not been well addressed far. This work is devoted to exploring the stochastic dynamical behaviors of a single-degree-of-freedom (SDOF) SMA oscillator with a polynomial constitutive model under a narrow-band random excitation. The multiple-scale method coupled with a perturbation method was extended to the proposed SMA model in order to achieve the theoretical analysis, and several approximate analytical solutions were derived Both analytical and numerical results were implemented to reveal the influences mechanism of the random fluctuation on structural responses of the introduced SMA oscillator model. The main conclusions are presented to close this paper

Description of the SMA Oscillator Model

Theoretical Analysis of the SMA Oscillator Model

Numerical Verification

CCoonncclluussiioonnss