Research On Vibration And Stability Of Nonlocal Piezoelectric Nanoplates

Due to its instinct electro-mechanical coupling effect,the piezoelectric material possesses promising application potential in the engineering fields like sensor technology,information technology,intelligent material systems,etc.With the development of modern material manufacturing technology,the piezoelectric nanostructures have extensive applications in the micro-/nano-electro-mechanical systems(MEMS/NEMS),which attracted world-wide attentions.Numerous studies have indicated that in nanometer scale,the scale effect is essential in the performances of the piezoelectric nanostructures,which leads to significant different characteristics compared with their macroscopic counterparts.To better characterize the scale effect in piezoelectric nanostructures,this paper applies the nonlocal theory proposed by Eringen to study the vibration and stability of the piezoelectric nanoplate,including the linear and nonlinear vibration,buckling and post buckling behaviors.Afterwards,further discussion is taken on the nonlinear vibration of the magneto-electro-elastic(MEE)nanoplate.Compared with the piezoelectric nanoplate,the MEE nanoplate possesses more complicated constitutive relationships due to the instinct magneto-electro-elastic coupling effect.Through theoretical derivation and analytical/numerical solution,this paper mainly discusses the influences of different factors(such as nonlocal parameters,thermo-electro-mechanical loads,boundary conditions,etc.)on the linear and nonlinear vibration,buckling and post buckling behaviors of the piezoelectric nanoplate,as well as the nonlinear vibration of the MEE nanoplate.Specifically,the discussion of this paper is mainly divided into following sections:1.This paper firstly concerns about the free vibration of the piezoelectric nanoplate.Based on the nonlocal constitutive relationship,the Kirchhoff and Mindlin piezoelectric nanoplate models are established to study the free vibration behaviors under the thermo-electro-mechanical loads.The Kirchhoff piezoelectric nanoplate is assumed with all edges simply supported,while different boundary conditions are considered for the Mindlin piezoelectric nanoplate.The governing equations and corresponding boundary conditions of the linear vibration are derived by applying the Hamilton's principle,and then solved analytically and numerically for the natural frequencies and shape modes for free vibration of the piezoelectric nanoplate.2.Based on the above analysis of free vibration,the nonlinear vibration properties of the piezoelectric nanoplate under the thermo-electro-mechanical loads are further investigated.For the Kirchhoff piezoelectric nanoplate with all edges simply supported,the Navier method is applied to achieve the analytical solutions for the nonlinear frequencies.However,for the Mindlin piezoelectric nanoplate with different boundary conditions,the governing equations are solved by the iterative differential quadrature(DQ)method to achieve the numerical solutions for the nonlinear vibration frequencies and shape modes.3.The buckling and post buckling behaviors of the Mindlin piezoelectric nanoplates under axial loads with different boundary conditions are examined.The governing equations and corresponding boundary conditions are derived through the principle of minimum potential energy.For the buckling problem with a linear strain-displacement relationship,the governing equations can be directly solved by the DQ method for the critical buckling loads;while for the post buckling problem with von Karman nonlinearity,the iterative DQ solution is applied to obtain the post buckling response of the piezoelectric nanoplate.4.Additionally to the previous investigations,the nonlinear vibration of the MEE nanoplate is discussed.Compared with the piezoelectric nanomaterials,the MEE nanomaterial is more complicated in the nonlocal constitutive relationship.Based on the Mindlin plate theory,the nonlocal theory and the von Karman nonlinearity,this section investigates the thermo-electro-magneto-mechanical nonlinear vibration of the MEE nanoplate under different boundary conditions.This paper has established the nonlocal piezoelectric nanoplate and MEE nanoplate models,and examined the scale effect and multiple-field coupling effect on the vibration and stability properties of the piezoelectric nanoplates and MEE nanoplates,which provides reliable theoretical evidences to the design and development of micro-/nano-electro-mechanical systems(MEMS/NEMS).