Dynamic analysis of a shape memory alloy beam

In this study a novel solution method for dynamic analysis of clamped-free shape memory alloy beams is presented. It is assumed that the beam is entirely made of shape memory alloy. Based on Euler-Bernoulli beam theory the governing equations of motion and corresponding boundary conditions are derived by using extended Hamilton principle. In the derived PDEs the transformation strain is behaved as external force that changes with time and position. The Galrkin approach is employed to convert PDEs to ODE system equations of motion. The derived equations of motion are solved by using Newmark integration method. The shape memory alloy constitutive model that presented by Souza is applied for specifying the phase of material all over beam. The transformation strain as internal variable that is coupled with states of equations of motion is identified in every time and every position of beam by using return map algorithm. A parametric study on the control variables has been adopted and the results of parametric study are discussed. The results show that the hysteresis damping is increased by increasing the operating temperature. Moreover the damping of system is faster by increasing the initial displacement in free vibration.