Buckling And Vibration Analysis Of Functionally Graded Sandwich Nanoplate

In this paper,the research methods of elastic thin plates are introduced.Based on equilibrium differential equation,virtual displacement principle and classical elastic theory and non-local elastic theory,the governing equations of isotropic single-layer plates expressed by internal forces are derived.Using Reissner sandwich plate theory,the buckling loads of nano-scale infinite wide plates under unidirectional compression are obtained.Based on equilibrium differential equation,virtual displacement principle and non-local elasticity theory,the buckling load control equations of simply supported functional gradient sandwich plates with four sides are derived by using classical plate theory,first-order shear deformed plate theory,third-order shear deformed plate theory and sinusoidal shear deformed plate theory.In addition,the natural boundary conditions are obtained by the virtual displacement principle.Based on equilibrium differential equation,virtual displacement principle and D'Alembert's principle and non-local elasticity theory,the governing equations of free vibration of simply supported functionally graded sandwich plates with four sides are derived by using classical plate theory,first-order shear deformed plate theory,third-order shear deformed plate theory and sinusoidal shear deformed plate theory.The above governing equations are solved by using the Navier method,and the expression of the buckling load and the frequency equation are given.The effects of non-local parameters,aspect ratio,axial compression ratio,volume fraction index and buckling modulus on the buckling loads are discussed.The effects of non-local parameters,aspect ratio,thickness ratio,volume fraction index and vibration order on the natural frequencies are discussed.The buckling loads and first-order natural frequencies of functionally graded sandwich plates with different thickness ratios of surface to core are given.