Nonlinear vibration of SMA hybrid composite beams actuated by embedded pre-stretched SMA wires with tension-bending coupling effect

Abstract

Theoretical and numerical analyses for nonlinear vibrations of the shape memory alloy hybrid composite(SMAHC) beam actuated by the pre-stretched shape memory alloy(SMA) fibers with tension-bending coupling effect are presented in this paper. Under the sudden action of thermal temperature, a recovery force and moment are caused in the SMAHC beam due to the phase transition in the SMA fibers, exciting the nonlinear vibration of the SMAHC beam. The one-dimensional Brison constitutive model was adopted to express the influence of the phase transition temperature, initial volume fraction of martensite, and pre-strain on the phase transition in the shape memory alloy. On this basis, the constitutive law of the SMAHC beam is built by considering the tension-bending coupling effect and the phase transition in the SMAHC beam. The equation of motion for nonlinear vibration of the SMAHC beam with geometric nonlinearity and material nonlinearity is derived from the Hamilton principle and is discretized into matrix form using the Galerkin method. According to the algorithm of the NewMark-β method, numerical solutions are computed by developing Matlab program and are compared with the results from ABAQUS analysis. It shows that the frequencies and amplitudes of the theoretical calculations are very consistent with those obtained from ABAQUS analysis. In addition, both the theoretical study and ABAQUS simulation indicates that the high frequency for longitudinal vibration is not observed in the spectrum diagram of transverse vibration, while the low frequencies for transverse vibration are captured in the longitudinal vibration. With the established Matlab program, parametric study is carried out to investigate the effect of the temperature and the location of the SMA fibers on the vibration responses of the SMAHC beam. The results from this study indicate that the transverse vibration of SMAHC beams is characterized as one of low frequency, while the longitudinal vibration has the characteristics of high frequency. Especially in the case of nonlinear vibration, not only the vibration of high frequency but also the vibration of low frequency observed in the transverse vibration will occur in the longitudinal direction of the SMAHC beam. Furthermore, the double and triple fundamental frequencies of the transverse vibration are excited in the nonlinear vibration of the SMAHC beam. The results of this paper can provide a theoretical basis for the evaluation of the safety and stability of smart composite structures.