【摘要】 为了把非线性动力学理论应用于超灵敏质量传感技术,应用积分方程法研究了由两个弹性耦合的纳米尺度Duffing振子构成的非线性受迫振动系统的动力学特性。该方法首先求得控制方程的线性部分对应的级数形式的格林函数,然后把控制方程转化为积分方程,再把积分方程化为代数方程组,最后数值求解该方程组,得到问题的近似解。由数值实验发现,当系统的参数取一组特定数值时,此系统可发生模态局部化现象。而当系统的参数取另一组特定数值时,一个振子的质量的微小变化可引起另一个振子的周期响应发生剧烈变化。更多还原

【Abstract】 In order to apply the nonlinear dynamic theory to the ultrasensitive mass sensing technology,an integral equation approach is employed to investigate the nonlinear dynamic characteristics of a forced nonlinear system consisting of two elastically coupled nanomechanical resonators.Firstly,the Green function of the linear part of the governing equation is expressed into the series form.Then the governing equation is transformed into the integral equation.The integral equation is further reduced into the algebraic equation system which can be solved numerically.It is found that when the system parameters take a group of specific values the mode localization phenomenon can occur.When the system parameters take another group of specific values,the tiny change of the mass of one resonator can cause a drastic change of the periodic response of the other resonator.更多还原