Vibration Characteristics Analysis Of Functionally Graded Sandwich Nanoshells

A functionally graded material(FGM)is a composite material composed of two or more materials.It has some prominent advantages of avoiding cracks,avoiding delamination,reducing stress concentration,and eliminating residual stress.So once put forward,a wave of research and development upsurge was set off.The functionally graded(FG)sandwich shell of nanometer scale not only have high strength and light weight advantages,but also show excellent characteristics in mechanics,electricity,magnetism,etc.,and has applications in various fields such as aerospace,MEMS,and micro/nano medical systems Therefore,it is very important to analyze the vibration characteristics of the structure.The main work of this paper is shown as follows:(?)The linear free vibration characteristics of FG sandwich cylindrical nanoshells under various boundary conditions are studied.The dynamic equations of FG sandwich cylindrical nanoshells are derived using first-order shear deformation theory(FSDT)and Hamilton's principle.Then Galerkin's method is used to obtain the eigenvalue equation of the system.Finally,the effects of surface stress,surface Lame parameters,surface mass density and geometry parameters of the shell on the natural frequency are discussed.(?)The nonlinear free vibration characteristics of FG sandwich cylindrical nanoshells under the simply supported boundary condition are studied.Based on the classical shell theory and Hamilton principle,the nonlinear dynamic equations of nanoshells are derived.The nonlinear dynamic equations of transverse vibration of nanoshells are derived.The nonlinear frequency of the nanoshell is obtained by solving the dynamic equation with multiple scale method.The effects of power law index,intermediate layer thickness,surface stress and shell geometry parameters on the nonlinear free vibration characteristics of FG sandwich nanoshells are analyzed.(?)The nonlinear free vibration of FG sandwich cylindrical nanoshells containing flowing fluid is studied.The internal fluid is ideal,inviscid,incompressible,and the flow is isentropic and irrotational.The nonlinear dynamic equations of FG sandwich cylindrical nanoshells containing flowing fluid are solved by using the multiple scale method.The results show that flow velocity and fluid density have important effect on the nonlinear free vibration of the nanoshells.