Free Vibration And Buckling Analysis Of Four-sides Compressed FGM Rectangular Plate On Two-parameter Foundation

With the development of society,functional gradient materials(FGM)and nanostructures are widely used in various engineering fields.It is of great significance to study and analyze the mechanical behavior of structures and systems.In this paper,differential transformation method(DTM)is used to analyze the free vibration and buckling behavior of FGM rectangular plate and FGM rectangular nanoplate on Winkler-Pasternak elastic foundation,and the main work includes:Based on the classical thin plate theory,the Hamilton's principle was used to derive the corresponding governing differential equation and dimensionless.Then using the differential transform method makes the original control differential equation of the boundary conditions and transform algebraic equation of discrete function,through iteration to work out the buckling critical load and the dimensionless natural frequencies,at the same time the problem was reduced to the case of no foundation functionally gradient plate and homogeneous material plate with foundation.The DTM solution is compared with the exact solution in existing literatures,and the results are consistent,indicating the applicability and accuracy of DTM.Finally,the relationship between boundary conditions,gradient index,elastic stiffness coefficient,shear stiffness coefficient,length to width ratio and the dimensionless natural frequency and critical buckling load of FGM rectangular plate is analyzed.The research can provide a basis for the design of FGM plate.Based on the Eringen nonlocal theory and the classical thin plate theory,the free vibration and buckling of FGM rectangular nanoplate under four sides compression on Winkler-Pasternak elastic foundation were investigated.Firstly,the generalized Hamilton's principle was used to derive the corresponding governing differential equation and dimensionless.Then using the differential transform method makes the original control differential equation of the boundary conditions and transform algebraic equation of discrete function,through iteration to work out the buckling critical load and the dimensionless natural frequencies.Finally,the influences of boundary conditions,gradient index,non-local parameters,coefficient of elastic foundation,shear modulus of foundation,aspect ratio and other factors on the natural frequency and critical buckling load of FGM rectangular nanoplates are analyzed.The results show that,the stronger the boundary condition,the greater the elastic stiffness coefficient,the shear stiffness coefficient and the length-width ratio of foundation,and the greater the dimensionless natural frequency.The larger the in-plane pressure load,non-local parameter and gradient index,the smaller the dimensionlessnatural frequency.The larger the nonlocal parameter,the smaller the critical buckling load.