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Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects
State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
* Author to whom correspondence should be addressed.
Received: 27 March 2009; in revised form: 23 April 2009 / Accepted: 13 May 2009 / Published: 20 May 2009
Abstract: In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale.
Keywords: TM-AFM; microcantilever; squeeze film damping; Lennard-Jones (LJ) potential
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Zhang, W.-M.; Meng, G.; Zhou, J.-B.; Chen, J.-Y. Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects. Sensors 2009, 9, 3854-3874.
Zhang W-M, Meng G, Zhou J-B, Chen J-Y. Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects. Sensors. 2009; 9(5):3854-3874.
Zhang, Wen-Ming; Meng, Guang; Zhou, Jian-Bin; Chen, Jie-Yu. 2009. "Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects." Sensors 9, no. 5: 3854-3874.