Analysis of nonlinear dynamic behavior of atomic force microscope using differential transformation method

Summary This paper investigates the nonlinear dynamic behavior of the probe tip of an atomic force microscope using the differential transformation method. The dynamic behavior of the probe tip is characterized by reference to phase portraits, power spectra, Poincaré maps, and maximum Lyapunov exponent plots produced using the time-series data obtained from differential transformation method. Furthermore, the detailed transitions in the dynamic response of the probe tip are examined using bifurcation diagrams of the tip displacement and the tip velocity, respectively, in which the amplitude of the probe tip vibration is taken as the bifurcation parameter. The results indicate that the probe tip behavior is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the probe tip motion changes from T-periodic to 2T-periodic, then from 4T-periodic to multi-periodic, and finally to chaotic motion with windows of periodic motion as the vibrational amplitude is increased from 0 to 1.0. Furthermore, it is demonstrated that the differential transformation method is in good agreement for the considered system.