Nonlinear Free Vibration Analysis to Nano-Mechanical-Oscillator
Yang Guolai(1),Jia Lu(2),Chen Yunsheng(1),Hang Yi(1)
(1 School of Mechanical Engineering, Nanjing Unviersity of Science and Technology, Nanjing, 210094)
(2 Department of Mechanical Engineering, Unviersity of lowa, lowa City, IA52242)

Abstract: Nonlinear free vibration for a nano-mechanical oscillator is investig ated. The potential energy between one plate with unit area and one infinite plate is derived based on Lennard-Jones formula, the dimensionless variables are introduced, then the state equations and Hamiltonian of nonlinear free vibration are formulated for the oscillator. The intersection of minus Lennard-Jones force curve and spring force line motivates to analyze the equilbrium positions of nonlincar free vibration. Some significant parameters which can exert effects on equilibrium positions are pointed out. For the given parameters, the quantitative and qualitative analyses to the phase portrait and motion circle of the nonli near free vibration are dealt with.
Keywords: nonlinear vibration, Lennard-Jones potential, hamiltonian, equilibrium position, phase portrait.