Non-linear transient and damping analysis of a long cylindrical sandwich panel with embedded SMA wires

In this work, nonlinear dynamic analysis of a cylindrical sandwich panel with embedded SMA wires in the face sheets is performed taking into account the instantaneous and spatial martensite phase transformation. The Boyd and Lagoudas one-dimensional SMA constitutive equation is used to model the pseudoelastic behavior of the shape memory alloy wires. Since the martensite volume fraction depends on the stress distribution, the governing equations and the phase transformation kinetic equations are coupled together and therefore an iterative method is employed to solve the highly nonlinear equations. Moreover, considering that the stress resultants generated by the martensite phase transformation in the wires are path dependent values, an incremental method is used to estimate the increment of the stress resultants at each time step. A new finite-element-based procedure is proposed and Newmark time integration method is used to solve the finite element equations. The results show a gradual decrease in the amplitude of vibration as long as the SMA wires do not reach a fully elastic condition. This feature is of great interest for the vibration suppression of structures especially that which is related to resonance phenomena. Finally, the effect of various parameters such sector angle, operating temperature, wire volume fraction, through the thickness location of the wires and different boundary conditions on the vibration amplitude and loss factor is investigated.