Non-linear dynamic analysis of a sandwich beam with pseudoelastic SMA hybrid composite faces based on higher order finite element theory

In the present work a non-linear dynamic response of a continuous sandwich beam with SMA hybrid composite face sheets and flexible core is analyzed taking into account the phase transformation and also the material non-linearity effects, for every point along the face sheets. The one-dimensional constitutive equation of SMA proposed by Brinson is employed. Equations of motion are derived using Hamilton's principle and a new finite element is proposed based on a higher order sandwich panel theory. Due to the phase transformation, the equations of motion are coupled with the phase transformation's kinetic equations of SMA wires. A new finite-element-based approach along with an iterative incremental method is developed to study the dynamic response of sandwich beam with SMA hybrid composite face sheets and flexible core. A damped response of the sandwich beam is observed, which is due to the hysteresis behavior of SMA wires. The influence of the SMA wires on the vibration suppression related to the resonance phenomena of a sandwich beam as well as the effect of the through thickness location of the SMA wires inside the composite face sheets and also the effect of different boundary conditions on the dynamic response are analyzed.