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.