某纳米级机械振荡器的非线性自由振动特性分析  

Nonlinear Free Vibration Analysis to Nano-Mechanical-Oscillator

作　　者：杨国来 [1] JIA Lu  陈运生 [1] 杭燚 [1] 

机构地区：[1]南京理工大学,南京,210094 [2]lowa 大学,lowa City,IA52242 USA

出　　处：《应用力学学报》2005年第2期306-309,i014,共5页Chinese Journal of Applied Mechanics

摘　　要：主要对某纳米级振荡器的非线性自由振动特性进行了初步的研究。基于Lennard-Jones势能推导了单位面积的平板与无限长平板间的势能。为计算方便,引入无量纲化变量,给出了纳米级振荡器非线性自由振动的状态方程和Hamilton函数。根据负的Lennard-Jones力曲线和弹簧力曲线的相交特性,对非线性自由振动的平衡位置特性进行了分析,指出了影响平衡位置特性的若干重要参量。对给定参量的非线性自由振动的相位图特性、振动周期等进行了定量及定性研究。Nonlinear free vibration for a nano-mechanical oscillator is investigated. 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 nonlinear 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 nonlinear free vibration are dealt with.

关 键 词：非线性振动 Lennard-Jones势能 HAMILTON函数 平衡位置 相位图 

分 类 号：O32[理学—一般力学与力学基础]