Analytical Study On Bending,Buckling And Vibration Properties Of Nanometer Rectangular Laminates

Nano-laminate structure is widely used in nano-electromechanical systems because of its excellent mechanical properties.However,most of the studies on the nanoplate structure only consider the single-layer nanoplate.Compared with the macro-structure,the nano-size structure has obvious size effect.Therefore,based on Gurtin-Murdoch surface elasticity theory,a variety of new laminate models considering surface effects are established to study the mechanical properties of nano-laminates.A double-layer nanoplate model with surface effects is developed,the governing equations under simple boundary conditions are derived by the method of force balance.The analytical solutions of bending deflection and natural frequency are obtained respectively.The influences of surface parameters on bending deflection and the first four orders of natural frequencies are discussed.For double-layer nanoplates with complex boundary conditions,it is very difficult to obtain the exact solutions of bending deflection and frequency.Therefore,the approximate solutions of bending deflection and natural frequency of nano-laminates under complex boundary conditions are obtained by variational method.And the influences of surface effects under different boundary conditions are discussed.A multi-layer nano-laminate model considering both surface energy and interface energy is established.The influences of surface effects on the buckling and post-buckling behaviors of nano-laminates are studied based on this model.The analytical solution of the critical buckling load and the approximate solution of the nonlinear post-buckling critical load are obtained respectively.The influences of the geometric size of the plate and the number of layers on the buckling and post-buckling critical loads are discussed.Functionally graded materials can combine the advantages of different materials to meet the practical needs of engineering.Therefore,this work further discusses the influences of material properties on the stability of the nano-laminate by developing a functionally graded sandwich nanoplate model with surface effects.The approximate solutions of nonlinear free and forced vibrations considering surface effects are obtained by using Galerkin method.The influences of surface effects on nonlinear amplitude-frequency responses of functionally graded sandwich nanoplates are discussed.The results of this paper are compared with the existing results to verify the correctness and reliability.At the same time,the methods and conclusions of this paper also provide a theoretical basis for other numerical and theoretical results of nano-laminates.