Research On Vibrational,Bucking And Bending Of Piezoelectric Nanobeams With Surface Effects

The one-dimensional piezoelectric nano-beam structure is widely used in micro-nano mechanical and electronic systems,and the piezoelectric nano-beam structure is considered as one of the important components,which is of great important for the study of its electrical and mechanical properties.Based on the finite element method,the finite element simulation of piezoelectric nanomaterials is realized in the finite element software.At the same time,the theoretical model of piezoelectric nanobeams with surface effects are established to study the vibration,buckling and bending related issues of piezoelectric nanobeams.The specific work is as follows:Firstly,in this paper,a method for the numerical simulation of piezoelectric nanomaterials in finite element software is proposed,and the simulation of piezoelectric nanomaterials is efficiently and accurately realized in the finite element software ABAQUS.The unit normalization method and the introduction of surface effects have solved the problem of modeling and scale dependence of piezoelectric nanomaterials simulated by finite element software.Taking the piezoelectric material PZT-5H as an example,the implementation method and calculation process of piezoelectric nanostructures in finite element software are detailed,and the corresponding frequency and vibration mode are calculated.This method not only can solve the beam structure,but also applies to the shell and solid structure,which is versatile.Secondly,Timoshenko beam theoretical model with surface effect and piezoelectric effect is established in this paper,and the vibration and buckling of the piezoelectric nanobeam were studied based on this model.The surface effect is described by Gurtin-Murdoch surface elasticity theory.The governing equations of piezoelectric nanobeam vibration are derived,and the vibration mode and frequency of piezoelectric nanobeam under three boundary conditions of simple support,fixed support and cantilever are solved.The effect of surface parameters,piezoelectric parameters,shear deformation and rotational inertia on frequency modes are discussed.The theoretical results are in good agreement with the aforementioned finite element simulation results.In addition,a theoretical model of buckling of piezoelectric nanobeams considering surface effects was established.The expression for the critical load voltage is derived,and the correlation between critical load voltage and the size and surface effect of the nanobeam are analyzed.The numerical simulation results show that the surface residual stress,surface elasticity and surface piezoelectricity have significant effects on the critical buckling voltage of piezoelectric nanobeams.Finally,the theoretical bending model of piezoelectric beam with surface effect is established to study the bending problem of piezoelectric nanobeam.The bending control equation of piezoelectric nanobeams considering surface effects is derived,and the deflection expression for piezoelectric nanobeams under cantilever boundary conditions is obtained.The effects of surface residual stress,surface piezoelectricity,and surface elasticity on bending deflection are discussed.The result demonstrates that surface effects have a great effect on the deflection of piezoelectric nanobeams.