Linear and Non-Linear Analysis of SMA Based Duffing Oscillators

Gaikwad, Shantanu Rajendra (2016) Linear and Non-Linear Analysis of SMA Based Duffing Oscillators. Masters thesis, Indian Institute of Technology Hyderabad.

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Abstract

Recently, there have been many applications involving shape memory alloy (SMA) to actuate or control small to large vibration in the field of aerospace, automobile, building structures, bioengineering devices, etc. The application of SMA over a wide field is due to its ability to apply large force and displacement with low power. It is also found that SMA can regain its original state after going through the cycle of heating and cooling processes. During the process of loading, the internal temperature change due to phase transformation which causes energy dissipation. Due to its effective energy dissipation capabilities, it can respond to slow loading, fast loading, sudden loading, and time varying loading, respectively. However, to understand the effective control of vibration of a structure, it is important to investigate its linear and nonlinear behavior under the different loadings conditions. In this thesis, we plan to investigate the linear and nonlinear response of SMA controlled cantiliver beam (spring) under different loading conditions. To do the study, we first present the thermomechanical constitutive model of SMA with a single degree of freedom system. Subsequently, we solve the equation to obtain linear frequency and nonlinear frequency response using the method of harmonic balance. To analyze the in uence of cubic and quadratic nonlinearity, we modify the governing equation and discuss the results based on the method of harmonic balance. Additionally, we also describe the method of averaging to obtain the nonlinear frequency response of SMA based oscillators. The analysis of results lead to various ways of controlling the nature and extent of nonlinear response of SMA based oscillators. Such findings can be effectively used to control the external vibration of different systems.

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