Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods

Present analysis, deals with dynamic buckling of sandwich nano plate (SNP) subjected to harmonic compressive load based on nonlocal elasticity theory. The material properties of each layer of SNP are supposed to be viscoelastic based on Kelvin-Voigt model. In order to mathematical modeling of SNP, a novel formulation, refined Zigzag theory (RZT) is developed. Furthermore, the surrounding elastic medium is simulated by visco-orthotropic Pasternak foundation model in which damping, normal and transverse shear loads are taken into account. Using energy method and D′Alembert's principle, the size dependent governing motion equations are derived. In this study, the governing motion equations are solved numerically using new procedure namely differential cubature (DC) method in conjunction with Bolotin method. The effects of some remarkable parameters such as viscoelastic foundation, damping coefficient of viscoelastic plates, aspect ratio, amount of small scale effect, various boundary conditions, different values of fiber orientation of the face sheets, number of grid points and thickness-length ratio on the dynamic instability region (DIR) are investigated. The results show that considering viscoelastic property of system is essential to obtain real mechanical behavior and instability of systems. In addition, the surrounding elastic medium is an effective parameter on the DIR of SNP.