Nonlinear Free Vibration of Hybrid Composite Moving Beams Embedded with Shape Memory Alloy Fibers

The aim of this paper is to investigate the free vibration of hybrid composite moving beams embedded with shape memory alloy (SMA) fibers. The nonlinear equations of motion are derived based on the Euler–Bernoulli beam theory in conjunction with the von Karman type of nonlinearity in strain–displacement relations via the extended Hamilton principle. Also, the recovery stress induced by the SMA fibers is computed by applying the one-dimensional Brinson model and Reuss scheme. Then, an analytical approach in used to solve the nonlinear equation of motion for the simply supported shape memory alloy hybrid composite (SMAHC) moving beams. Based on the analytical solution, several parametric studies are presented to show the effects of various parameters such as volume fraction, pre-strain in the SMA fibers, temperature rise and velocity on the fundamental frequency of the SMAHC moving beams. Due to the lack of similar results in the specialized literature on the subject of interest, this paper is likely to fill a gap in the state of the art of the related research.