A new approach for nonlinear transient dynamic analysis of micro SMA beam considering size effect and instantaneous phase transformation

Abstract

Shape Memory Alloys (SMAs) have attracted lots of attraction in the recent years due to their unique characteristics. However, studies in the field of behavior of SMAs at micro scale is not enough and more research is required. The present paper presents a nonlinear dynamic solution for a micro made of NiFeGa SMA, located on a viscoelastic foundation. The recommended approach takes into account instantaneous variations of martensite volume fraction and size effect which are the main novelties of the present study. In this regard, the formulation proposed by Hernandez and Lagoudas is used to capture and model the size effect of the SMAs. The governing differential equations obtained for Euler-Bernoulli micro beam using the Hamilton’s principle, considering the Von-Karman nonlinear strain. The nonlinear equation of motion is solved applying the semi-exact method. In this study, the return mapping convex cutting plane is used, in order to overcome the material nonlinearity of the problem. The obtained results are compared with the reference papers which shows the accuracy of the present model. Results show that with considering the size effect, the loss factor of vibration will increase by increasing the thickness of the micro SMA beam. While regardless of the size effect, this factor remains almost constant. The reason for this phenomenon is that when size effect is taken into account, the thermodynamic properties and critical stresses of phase transformation will change with resizing the SMA. Outputs also show that by increasing the damping coefficient and decreasing the stiffness of foundation, more energy is wasted in the vibration of the micro SMA beam. In addition, it was observed that micro beams with lower thicknesses are more sensitive to foundation characteristics meanwhile the loss factor of vibration with lesser thicknesses changes more by changing the foundation stiffness and damping coefficients.