Research On Nonlinear Dynamics Of Piezoelectric Nano Beam Considering Surface Effect

With the progress of technology and science,the application of Nano-electro mechanical system(NMES)and associated equipment are increasingly wide,which are widely used in frontier domains,such as: space exploration,deep-sea exploration,military,and biomedical engineering.Compared with Micro-electro mechanical system,NEMS devices can maintain a higher mechanical sensitivity while smaller size,and can be smaller size,lower cost,lower power consumption and higher base wave frequency.Owing to its superior electrical and mechanical feature,one dimensional piezoelectric nano-material has been widely used in NEMS,such as nano-resonator.As was well known,the dynamics of nano beam structure had very obvious nonlinear effect under the larger extrinsic motivation effect or when the vibratio n amplitude of the structure is relatively bigger,so there is greater error to analyze nano-beam structure by adopting linear theory.Besides,the performance of Nano scale structure in mechanical,physical and electrical is different from the macroscopic shape materials,so it is very important to study the related mechanical performance of the piezoelectric nano material.Based on the surface piezoelectric model and the geometric nonlinearity of Feng kamen,the mechanical property of nonlinear free,vibration and dynamic stability of piezoelectric nano beam considering surface effect are studied in this paper.Based on the surface piezoelectric model,the forced vibration and free vibration mechanical model of piezoelectric nano-beam with both ends clamped are established.And,the control equation of nonlinear forced vibration and free vibration with piezoelectric nano-beam are deduced based on Euler-Bernoulli and the geometric nonlinearity of Feng Kamen.The equations are partial differential equation which can be transformed into the Dafen equations.They can be solved by using Lin Zi Ted-Poincare Law method.In this result discussion,the impact of various factors like free vibration and nonlinear forced vibration surface effect,voltage and size effect are studied on the nonlinear condition.Based on the surface piezoelectric model,the dynamic stability mechanical model of piezoelectric nano-beam with both ends clamped is established.The dynamic stability of piezoelectric nano-beam with both ends clamped is derived based on Euler-Bernoulli and the geometric nonlinearity of Feng Kamen.Then,the dynamic instability zone of piezoelectric nano-beam is determined by using Galerkin method and incremental harmonic balance method.On that basis,the influence of non-linear surface effect,size and voltage on dynamic instabili ty of piezoelectric nano-beam are discussed.