Theoretical and numerical analyses were conducted to investigate the bending-tension coupling vibration of shape memory alloy Hybrid Composite(SMAHC) beams under thermal load caused by the asymmetric distribution of SMA wires in laminated beams. Based on the force equilibrium of the elemental segment, the differential equation for the coupling vibration of the SMAHC beam under thermal load was derived, and the first two modal vibrations of the SMAHC beam were separated by employing the modal superposition method. Based on the Galerkin method, the equation of motion was discretized by considering the boundary conditions and was solved using the Newmark-β method to obtain the time-history curve of structural vibration, which was then subjected to Fourier transform to obtain the frequencies and the corresponding amplitudes of each order of SMAHC beam’s vibration. The validity of the proposed analyses was verified by comparing the numerical solutions with the finite element results. The influences of the pre-strain, the position of SMA fibers, the volume fraction, the temperature, and the bending-tension coupling stiffness of the SMAHC beam on its vibration characteristics under thermal load were analyzed. It was found that the temperature of SMA wires significantly affects the vibration characteristics of the SMAHC beam.
Jin et al. (Sun,) studied this question.