Chaotic vibration of atomic force microscopes based on the modified couple stress theory

M. Molavian Jazi, S. Ziaei-Rad and R. Ebrahimi

Archive of Applied Mechanics, Volume 92, Issue 12, September 2022, Pages 3683–3694

ABSTRACT

Sensitivity and resolution of an atomic force microscope (AFM) can be affected by the nonlinear vibrational behavior of its microcantilever. So, the main purpose of this paper is to analyze the chaotic vibration of an AFM microcantilever under base excitation. Based on the modified couple stress theory (MCST) and the Euler–Bernoulli beam model, the nonlinear governing equations of motion are derived using the Hamilton's principle. Also, the squeeze film damping and the nonlinear microcantilever tip–sample surface interaction descripted by the Lennard–Jones potentials is considered. The governing partial differential equation is discretized by means of the single-mode Galerkin’s method and solved using the Runge–Kutta method. The effects of the initial distance between the microcantilever tip and sample surface, excitation amplitude and damping on the nonlinear dynamic response of the system are investigated by the bifurcation diagrams, maximum Lyapunov exponent, phase plane portrait, time history and Poincare´ map. The results indicate that the vibrational behaviors of the microcantilever include 6T-periodic and chaotic motions. Based on the classical continuum mechanics theory, it is found that chaotic behavior initiates at much higher initial distances than predicted by MCST.

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