试样激励下轻敲模式原子力声显微镜的非线性动力学特性

利用Euler-Bernoulli梁理论和DMT针尖-样品作用力模型建立了试样激励下轻敲模式原子力声显微镜(AFAM)系统的动力学方程,并应用非线性动力学分析方法对AFAM微悬臂梁的振动特性进行研究。通过合理改变超声激励幅值、超声激励频率和针尖-样品初始间距等模型参数模拟得到微悬臂梁的超谐波、次谐波、准周期和混沌振动现象,采用时间序列、频谱、相空间、Poincare截面和Lyapunov指数等方法对不同非线性振动特性进行表征。通过分析不同模型参数条件下微悬臂梁针尖-样品作用力特性,探索了微悬臂梁不同非线性振动现象的产生机制。此外,研究了AFAM微悬臂梁运动的分岔特性,发现当超声激励幅值和针尖-样品初始间隙连续变化时,周期、准周期和混沌运动交替出现。研究结果对AFAM系统非线性动力学行为分析和混沌振动控制提供了理论参考。 

Nonlinear dynamic behavior of atomic force acoustic microscopy using sample vibration excitation and tapping mode

The dynamic equations of atomic force acoustic microscopy (AFAM), which using sample vibration excitation and tapping mode, are built based on Euler-Bernoulli beam theory and DMT tip - sample contact force model, and nonlinear dynamic methods are used to explore nonlinear vibration characteristics of the microcantilever beam of AFAM system. The superharmonic, subharmonic, quasiperiodic and chaotic vibrations of the microcantilever are simulated by changing model parameters such as ultrasonic excitation amplitude, frequency and tip - sample initial gap. The different nonlinear vibration phenomena are characterized by time series analysis, frequency spectrum, phase space, Poincar~ section and Lyapunov exponent. Then the generation mechanisms of different nonlinear vibration are explored by analyzing the interaction force characteristics between the tip and samples. Furthermore, the bifurcation characteristics of the microcantilever vibrations are investigated. It is found that periodic, quasi-periodic and chaotic vibrations of the microcantilever occur alternately when the model parameters such as excitation amplitude and initial gap are varied continuously. The research results provide significant theoretical reference for the analysis of the nonlinear dynamical behavior in AFAM and the control of chaotic vibration.