Dynamical Behaviors And Stability Response Of Axially Moving Two-dimensional Nano-structure

Nano-materials and structures have immense potential for application as structural elements in the field of information technology,sensing technology and biotechnology,owing to their remarkable thermal,electrical,mechanical,physical and chemical properties.The dynamic characteristics of nanostructures is one of the most important theoretical foundations of nanotechnology,as a large number of experiments and atomistic simulations have shown a significant size effect in mechanical properties when the dimensions of these structures become very small.Classical continuum mechanics,which is a scale-independent theory,cannot predict the size effects well.In order to overcome this problem,the nonlocal elasticity theory presented by Eringen has been widely accepted to deal with scale-dependent theory.Among them,the prediction of the mechanical properties of the two dimensional nanostructures is the most popular,because they are widely used in the nano-conveyor belt,telescopic arm of nano-robot and self-powered component of biomedical nano-robot.In this paper,axially moving two dimensional nanostructures are studied.The effect of speed and small-scale parameter on the natural frequencies and stability of the constant mean moving nanostructures and the parametric resonance and stability of the non-uniformly moving nanostructures are discussed in detail.This article's main research content and work are as follows:(1)Firstly,dynamic characteristics of axially moving elastic nanoplates are studied based on the Eringen nonlocal Kirchhoff plate theory.Hamilton's principle is employed to derive partial differential equations governing the transverse motion of the axially moving nanoplates.The effect of small-scale parameter on the transverse vibration in sub-critical region and the instability in super-critical region is analyzed by the Galerkin method.(2)Further,response of the parametric resonance of axially moving viscoelastic nanoplate is studied based on the Kelvin-Voigt viscelastic theory.The parametric resonance and instability behaviors of viscoelastic nanoplate with a simple harmonic variation about the constant mean speed are addressed using the method of multiple scales,and then the expression of the modal function is determined by the specific boundary conditions and the complex mode method.The analyses are mainly focused on the instable regions caused by summation and principal parametric resonance,respectively,of which the summation parametric resonance occurs when the harmonic frequency approaches the sum of any two mode natural frequencies,and the principal parametric resonance occurs when the harmonic frequency approaches two times of certain mode natural frequency.(3)The thermo-electro-mechanical coupling vibrations of axially moving viscoelastic piezoelectric nanoplates are examined based on the nonlocal piezoelectric plate model.The governing differential equations of axially moving piezoelectric nanoplates subjected to biaxial forces,external electric voltage and temperature change are derived,and the natural frequencies are determined numerically.Subsequently,effects of the small-scale parameter,biaxial forces,external electric voltage and temperature change on the thermo-electro-mechanical vibration responses are discussed.Subsequently,the instable behaviors of axially non-uniformly moving counterpart characterized as a sine variation about the constant average speed are addressed using the method of multiple-scales.The analyses are mainly focused on the boundaries of instable regions in combination parametric resonance and principal parametric resonance.