Free Vibration Analysis of Functionally Gradient Sandwich Composite Plate Embedded SMA Wires in Surface Layer  
[PERSON]  
1 State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China; yizhehuang@hust.  
method. Integration of SMA temperature characteristics and pre-strain performance in a composite plate was further studied analytically and experimentally, which has received considerable attention in the past decades [4; 5; 6; 7]. [PERSON] et al. [8; 9; 10; 11] investigated the dynamic behavior of thermally-buckled composite plates embedded with SMA wires. In addition, among the scientific research on SMA wires applied to composite structures, more investigations have been performed into the vibration behavior of SMA composite structures, such as low velocity impact [12; 13], active buckling control [14; 15; 16], thermal stability [17; 18], and nonlinear free vibration response [19; 20].  
Modern sandwich structures consist of two very thin surface sheets, which may be embedded with SMA to give prominence to the unique property of large recoverable strain on vibration and buckling. In terms of core, honeycomb materials and polymeric foam are the mainstream choices for soft cores; simultaneously, laminated composites or functionally graded materials enhance the structural properties of the core layer in structural form [21; 22]. For instance, an analytical study was carried out by [PERSON] et al. [23], to study the frequency of a sandwich plate with active SMA hybrid composite face sheets and a temperature-dependent flexible core. [PERSON] et al. [24] carried out a non-linear layerwise dynamic response analysis of sandwich plates with soft auxetic cores and embedded SMA wires experiencing cyclic loadings. In another work, [PERSON] et al. [25] analyzed the thermal vibration of a double curved sandwich panel with embedded pre-strained SMA wires hybrid composite face sheets and a soft core. However, still fewer studies have taken into consideration the vibration analysis of sandwich structures with SMA fibers, especially the application of gradient distribution in the core layer. In this work, free vibration analysis of functionally gradient sandwich composite plate embedded SMA wires in the surface layer was investigated. According to the foregoing literature survey, novelties of the present research are that a new type of composite gradient sandwich plate structure which the core layer composed of epoxy resin and graphite-reinforced materials is proposed, and graphite acts as a functionally gradient material in the core layer. Particularly noteworthy is that the gradient parameter is used as the distribution index of graphite in the core layer under a certain content; the large modulus and distribution form of graphite are fully utilized to affect the overall rigidity of the sandwich plate. Reddy shear deformation theory is employed to improve the calculation accuracy of the mechanical properties, which doesn't require computing the shear correction factor. Then, based on SMA stress-strain relation and the Hamilton principle, we derived the governing partial differential equations of motion and frequency equation. The influence of SMA wires on the vibration behavior of a sandwich plate was examined by varying the volume fraction and pre-strain with temperature rise. The modal performance results in this study provide a theoretical basis and design concept for vibration control of a gradient sandwich composite plate with embedded SMA.