Nonlocal Longitudinal Vibrations And Wave Propagation Of Viscoelastic Nanorods

With the rapid development of nanotechnology,nanoelectromechanical systems and nano-devices are gradually applied to various fields of technology and life.As an indispensable element in nano-devices and nanoelectromechanical systems,it is necessary to systematically research the mechanical behavior especially the dynamic characteristics of the rod-shaped nanostructures.Therefore,based on Eringen nonlocal theory and Kelvin-Voigt viscoelastic theory,this paper firstly established the viscoelastic nanorod model and solved the axial vibration and longitudinal wave propagation problems of the nanorod.Secondly,based on the nonlocal strain gradient theory,the nonlocal viscoelastic Love rod model and the Rayleigh-Bishop rod model were established respectively using the classical Love rod theory and the Rayleigh rod theory.The wave propagation problems in the magnetic field environment were studied,and analyzed the effects of the two small-scale parameters,magnetic field strength and viscosity coefficient on wave propagation characteristics.The main contents were as follow:(1)Based on the traditional nonlocal theory and Kelvin viscoelastic theory,the differential governing equations of the axial dynamics of viscoelastic nanorods were derived.The vibration characteristics under three typical boundary conditions were discussed by the separation variable method.The results show that small-scale effect makes the first and second frequencies decrease persistently and the third frequency increases at first then decreases,which indicates that the nonlocal stiffness of the nanostructure is weakened or strengthened.(2)Based on the nonlocal viscoelastic nanorods model,the longitudinal wave propagation of viscoelastic nanorods is solved.The results show that the circular frequency and wave velocity decay rapidly to zero because of the viscosity coefficient.Under the same conditions,the damping ratio increases with the viscosity coefficient The effect of damping effect can be effectively reduced by enhancing nonlocal effect.(3)Based on the nonlocal strain gradient theory and the classical Love rod theory,the axial dynamic governing equation was derived,and the longitudinal wave propagation problem under the transverse magnetic field was solved.It shows that wave velocity decreases and the nonlocal stiffness is weakened if the nonlocal parameters are larger than the strain gradient parameters.If the opposite,wave velocity increases and the nonlocal stiffness enhances.Strengthening of magnetic field,the wave velocity increases and the damping ratio decreases(4)Based on the nonlocal strain gradient theory and the Rayleigh rod theory,the Rayleigh rod model under axial magnetic field is built.And the wave propagation characteristics of three kinds of bar models are compared by an example.In the classic rod model,the wave velocity is the highest,followed by the Love model and the Rayleigh model.The damping effect of the material causes the wave velocity to decay rapidly.However,damping ratio can be effectively reduced by increasing magnetic field intensity,increasing nonlocal parameters or decreasing the strain gradient parameters.