Nonlinear Vibration Analysis of Composite Plates with SMA Wires, Considering Instantaneous Variations of the Martensite Volume Fraction

In the past few years, extensive improvements have been accomplished in reinforcing the structures through using shape memory alloys (SMAs). These materials absorb or dissipate energy through establishing a reversible hysteresis loop during a cyclic mechanical loading. This unique characteristic of the SMAs has made them appropriate for sensing, actuation, absorbing the impact energy, and vibration damping applications. Instantaneous and local variations of the phases of the SMA wire in the successive loading and unloading events of the vibration have not been accurately investigated by the works published so far. In the present paper, vibrations of composite plates reinforced by SMA wires are investigated, by employing an algorithm that overcomes the mentioned shortcomings. Governing equations are derived based on the Hamilton’s principle and the first-order shear-deformation plate theory. Furthermore, Brinson’s constitutive equations are used to model material properties of the SMA and the time-dependent partial deferential equations are solved using Newmark’s numerical time integration method. The governing equations are solved by a finite element code written in MATLAB software. In the present research, the influence of the instantaneous variations of the volume fraction of the Martensite volume fraction due to variations of the stress components on the material properties of the SMA, hybrid composite, and the recovery load is considered for the first time. Finally, effect of the volume fraction of the SMA wires of each layer and the influence of the amplitude of the abruptly applied load on the vibration behavior of the composite plate is investigated, too.