Research On Vibration Characteristics Of Nanoplate Shell And Coupling Plate Structures By Nonlocal Theory

The design and manufacture of small and lightweight intelligent electronic equipment is the development trend of China’s future manufacturing industry.The use of nanomaterials to process and produce electronic equipment can provide technical support for the lightweight design,miniaturization research and equipment development.It provides a power source for the development of nano-electromechanical system.Therefore,expanding the research methods of the dynamic properties revealing the vibration characteristics of nanostructures and analyzing the effects of external physical fields can effectively promote the study of the dynamic properties of nanostructures.It has important scientific value,theoretical value and engineering significance.This paper has an analysis on the dynamic performance of three kinds of important basic components in nano-electro-mechanical system.Combined with the wave based method,the vibration characteristics of nanobeam structure,nanoplate structure,cylindrical nanoshell structure and coupled nanoplate structure are analyzed in turn.The main research work of this paper is as follows:The vibration characteristics analysis models of functionally graded nanobeams and multi-physical fields magnetoelectric nanobeams on the elastic foundation are established.Based on the Timoshenko beam theory,combined with the nonlocal theory,the governing equations of functionally graded nanobeams and magnetoelectric nanobeams are derived.In the one-dimensional wave solution form,the displacement solution vector is constructed,and the displacement vector matrix,force vector matrix,and boundary matrix are set.Based on the wave based formulations,the overall control equations of the vibration characteristic model of functionally graded nanobeam and multi-physical field magnetoelectric nanobeam structure are established.Furthermore,the inherent characteristics of nanobeam structures under different boundary conditions are obtained.Constructing the external load vector,the forced vibration of functionally graded nanobeam and multi-physical field magnetoelectric nanobeam structure is analyzed.Through the comparison of data examples,the correctness of the functionally graded nanobeam and multi-physical field magnetoelectric nanobeam vibration characteristic models are verified.On this basis,the effects of various parameters on the dynamic properties of functionally graded nanobeams and multi-physical field magnetoelectric nanobeams under different boundary conditions are discussed.The vibration characteristics analysis models of functionally graded nanoplates and multi-physical fields piezoelectric nanoplates on the two-parameter elastic supporting foundation are established.The governing equations of functionally graded nanoplates and piezoelectric nanoplates are obtained by using Kirchhoff plate theory and Eringen nonlocal relationship.The structural displacement variables of functionally graded nanoplates and piezoelectric nanoplates are set by using the Lévy type solution.Combined with the wave formulation,the overall control equation of the vibration characteristic analysis model for functionally graded nanoplate and piezoelectric nanoplate structure under different boundary conditions are assembled.Furthermore,the inherent characteristics of the nanoplate structure are solved.The external load vector is constructed,and then the forced vibration of the nanoplate structure is studied.Through the comparison of data examples,the calculation correctness of the vibration characteristics model is conducted.Furthermore,the influence of several parameters on the inherent characteristics and steady-state response of nanoplate structure are analyzed.The vibration characteristics analysis models of the functionally graded cylindrical nanoshell and multi-physical fields piezoelectric cylindrical nanoshell under different boundary conditions are obtained.Combined with the nonlocal theory,the governing equations of functionally graded cylindrical nanoshells and piezoelectric cylindrical nanoshells are constructed with the First-order shear deformation theory and Kirchhoff-Love shell theory.Based on the wave function form,the displacement solution form of cylindrical nanoshell is set,and the displacement vector matrix is constructed.Furthermore,the overall control equations of the vibration characteristics analysis model for the functionally graded cylindrical nanoshell and multi-physical field piezoelectric cylindrical nanoshell are obtained,the inherent characteristics of cylindrical nanoshell structures under different boundary conditions are obtained.The external force vector matrix is set up to solve the steady-state response of the cylindrical nanoshell structure.Through the comparison of numerical examples,it is proved that the vibration characteristic analysis model of functionally graded cylindrical nanoshell and multi-physical field piezoelectric nanocylindrical shell is correct.The influence mechanism of nonlocal effects and external physical field parameters on inherent characteristics and steady-state response of nanoshell structure are analyzed.The vibration characteristics analysis models of nonlocal coupled nanoplates under different coupling forms are established.Based on the Kirchhoff plate theory and the nonlocal constitutive relationship,the differential equations for controlling in-plane vibration and bending vibration of nanoplate structures are obtained.In the form of the Lévy solution,the in-plane displacement vector and bending displacement vector are set,and the force vectors are obtained.According to the connection forms of different coupled plates and the boundary matrix,the overall control equations for the analysis of vibration characteristics of coupled nanoplates with different coupling forms are constructed and the inherent characteristics of nano-coupled plates are solved.According to the external force,the external load matrix is set up to further solve the forced vibration of the coupled nanoplates.After verifying the correctness of the established vibration analysis model,the influence of various parameters on the inherent characteristics and steady-state response of coupled nanoplates under different boundary conditions is systematically analyzed.