Mechanical Behavior Of Nanobeam With Fi Exoelectricity Based On Nonlocal Theory

With the development of nanotechnology and the rise of nanoelectromechanical system,more nano science and technology have been widely used,covering aerospace,vehicle engineering,medical health,electronic information and other fields,giving great convenience to people’s life.Many micro-functional devices are made of excellent electromechanical coupling of piezoelectric effect,but in nano-scale,besides piezoelectric effect,there is also an effect which is easy to be ignored——the flexoelectric effect.The piezoelectric effect is caused by the coupling of strain and electric field,while the flexoelectric effect is mainly caused by the coupling of strain gradient,which increases significantly at the nanoscale,and electric field,and the smaller the size is,the stronger the electromechanical coupling of flexoelectric effect is.Nanobeam,as a common component of the nanoelectromechanical system,the study of its mechanical properties provides a theoretical basis for the design and optimization of micro devices.The mechanical properties of flexoelectric nanobeam are studied in this paper.Based on the flexoelectricity theory,nonlocal theory and Euler beam theory,the static bending,free vibration and stability with axial motion of nanobeam are studied.Introducing the functional gradient material(FGM),the free vibration and stability with axial motion of the functionally graded nanobeam are studied too.The effects of flexoelectric effect,piezoelectric effect,nonlocal effect and axial velocity on the mechanical behavior of the nanobeam are discussed.The conclusions are as follows:(1)Based on the Euler beam theory,flexoelectricity theory and nonlocal elasticity theory,the displacement field,strain field and constitutive relation of the cantilever nanobeam are derived,and the governing equation can be deduced by Hamilton’s principle,then working out the numerical analysis.The effects of flexoelectric effect,piezoelectric effect,nonlocal effect,temperature and voltage on deflection are analyzed.(2)Based on the Euler nanobeam model,the governing equation of free vibration can be deduced by Hamilton’s principle.The differential quadrature method(DQM)is referred to solve the governing equation,the analysis of the effects of flexoelectric effect,piezoelectric effect,nonlocal effect on the first three dimensionless natural frequencies of the S-S,C-C and C-F nanobeam are inferred based on the numerical results.(3)The stability of nanobeam with axial motion is studied.First,the governing equation of axial motion can be deduced by Hamilton’s principle,and the effect of the axial velocity on the first three dimensionless natural frequencies of the nanobeam is analyzed by using the differential quadrature method,the effects of the flexoelectric effect,nonlocal effect on critical velocity and stability are also discussed.(4)The free vibration and stability with axial motion of the functionally graded nanobeam are further studied.Using the concept of neutral surface derives the displacement field,strain field and constitutive relation,the governing equations for the free vibration and axial motion of the functionally graded nanobeam are derived by Hamilton’s principle,then using differential quadrature method to obtain numerical solution,the effects of flexoelectric effect,piezoelectric effect,nonlocal effect and axial velocity on natural frequencies and stability are analyzed.