Nonlinear Vibration Analysis Of Fractional Viscoelastic Nanobeam

With the advent of the nanotechnology era,viscoelastic nanomaterials and structures with viscoelastic and size effect characteristics are widely used in aerospace,industry,military,biomedicine,and other fields.Viscoelastic nanobeam is commonly used as components in nanoelectromechanical systems(NEMS),sensors,actuators,etc.It is very important to study the mechanical properties of viscoelastic nanobeam for the design and manufacture of nanodevices.At present,the nonlinear vibration of viscoelastic nanosbeam is a hot topic in the field of nanomechanics.This paper takes viscoelastic nanobeam as the research object,using non-classical continuum mechanics theories and fractional viscoelastic model,proposes a non-classical Euler-Bernoulli beam model and Timoshenko beam model that consider both small-scale and surface effects to study the nonlinear vibration time response of fractional viscoelastic nanobeam.The specific research contents are as follows:(1)Based on the nonlocal-couple stress elasticity and surface elasticity theories,a new fractional viscoelastic Euler-Bernoulli nanobeam model is established by using the vonK’arm’an geometrical nonlinear relation and fractional Kelvin-Voigt viscoelastic model.The governing equation and corresponding boundary condition of a fractional viscoelastic EulerBernoulli nanobeam under transverse harmonic excitation are derived by using Hamilton’s principle,and the fractional integral-partial differential governing equation is solved by Galerkin’s and predictor-corrector methods.Firstly,the influence of nonlocal effect,microstructure effect,surface effect,and their coupling on the nonlinear vibration time response of fractional viscoelastic Euler-Bernoulli nanobeam are studyed.Then,in the frame of nonlocal couple-stress elasticity and surface energy theories,the effects of different parameters on the nonlinear time responses of free and forced vibration of fractional viscoelastic nanobeam are analyzed.The numerical results show that the fractional order greatly influences the nonlinear vibration behavior of the viscoelastic nanobeam,the system’s damping can increase by increasing the fractional order,and the fractional order must be considered in the modeling of viscoelastic nanobeam.And the fractional order has different effects on the nonlinear free and forced vibrations because there is an important correlation between the fractional order and excitation frequency.(2)Based on the nonlocal strain gradient and surface elasticity theories,a new nonclassical Timoshenko beam model is proposed.The governing equations and corresponding boundary conditions of a fractional viscoelastic Timoshenko nanobeam under transverse harmonic excitation are derived by the method of study content(1),and the fractional integral-partial differential governing equations are solved by Galerkin’s and predictorcorrector methods.The effects of surface parameters,nonlocal parameter,length scale parameter,initial displacement,fractional order,viscoelasticity coefficient,damping coefficient,length-to-thickness ratio,force amplitude,and excitation frequency on the nonlinear time responses of free and forced vibration of fractional viscoelastic Timoshenko nanobeam are further analyzed.The new fractional viscoelastic nanobeam model established in this paper can be used as a basic model to study the nonlinear vibration behavior of fractional viscoelastic nanostructures.Meanwhile,this study accurately measures the mechanical properties of viscoelastic nanobeam and designs related measurement techniques and devices based on them.