Influences of non-uniform initial stresses on vibration of small-scale sheets reinforced by shape memory alloy nanofibers

.In the present paper, an attempt is made to investigate the influences of biaxial preload on the vibrational behavior of small-scale composite sheets reinforced by shape memory alloy nanofibers. Three small-scale reinforced sheets are employed to form the system. In order to cover more practical cases, the biaxial preload and the compression ratio are assumed to be non-uniform. In addition, the three-layered composite sheet is embedded in a matrix with elastic properties. The Brinson model, nonlocal elasticity and Pasternak foundation model are used to take into account shape memory alloy effects, the influences of being size-dependent and the effects of the elastic matrix on the vibrational behavior, respectively. Performing a work/energy balance via Hamilton's principle yields the differential equations of motions. Finally, the natural frequencies are calculated via Galerkin's procedure. It is found that the natural frequencies of reinforced sheets under a preload of quadratic variation are higher than those of uniform and linear variations.