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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。
The kinetic equations of the tapping mode atomic force microscope (AFAM) excited by the sample were established by using the Euler-Bernoulli beam theory and the DMT tip-sample force model. The nonlinear dynamic analysis of AFAM microcantilever vibration Characteristics of research. The phenomena of superharmonic, subharmonic, quasi-periodic and chaotic vibration of micro-cantilever were simulated by reasonably changing the parameters of ultrasonic excitation amplitude, ultrasonic excitation frequency and tip-sample initial spacing. Time series, frequency spectrum, Poincare sections and Lyapunov exponents were used to characterize different nonlinear vibration characteristics. The mechanism of the micro-cantilever beam with different nonlinearities is explored by analyzing the force characteristics of the micro-cantilever tip-sample under different model parameters. In addition, the bifurcation characteristics of AFAM micro-cantilever were studied. It was found that the periodic, quasi-periodic and chaotic motions alternated when the amplitude of ultrasonic excitation and the tip-sample initial gap continuously changed. The results provide a theoretical reference for the nonlinear dynamic behavior analysis and chaotic vibration control of AFAM system.