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Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects.

Zhang WM, Meng G, Zhou JB, Chen JY - Sensors (Basel) (2009)

Bottom Line: 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.Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China; E-Mails: gmeng@sjtu.edu.cn (G.M.); giantbean@sjtu.edu.cn (J.-B.Z.); jerrysmiling@hotmail.com (J.-Y.C.).

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.

No MeSH data available.


Related in: MedlinePlus

Schematic of the lumped spring-mass-damping model for the TM-AFM cantilever vibrating near a sample surface.
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f2-sensors-09-03854: Schematic of the lumped spring-mass-damping model for the TM-AFM cantilever vibrating near a sample surface.

Mentions: The AFM is composed of an elastic cantilever and the achievable sensitivity and resolution of AFM depend largely on the geometry of the cantilever [11,26]. Considering only the first vibration mode, the cantilever can be modeled as a simplified spring-mass-damping system, as shown in Figure 2. The tip is modeled as a sphere of radius R, and the cantilever-sample distance is characterized by z0, which is the distance between the equilibrium position of the cantilever and the sample when only the gravity acts on it. The cantilever position is given by x measured from the equilibrium position.


Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects.

Zhang WM, Meng G, Zhou JB, Chen JY - Sensors (Basel) (2009)

Schematic of the lumped spring-mass-damping model for the TM-AFM cantilever vibrating near a sample surface.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3297151&req=5

f2-sensors-09-03854: Schematic of the lumped spring-mass-damping model for the TM-AFM cantilever vibrating near a sample surface.
Mentions: The AFM is composed of an elastic cantilever and the achievable sensitivity and resolution of AFM depend largely on the geometry of the cantilever [11,26]. Considering only the first vibration mode, the cantilever can be modeled as a simplified spring-mass-damping system, as shown in Figure 2. The tip is modeled as a sphere of radius R, and the cantilever-sample distance is characterized by z0, which is the distance between the equilibrium position of the cantilever and the sample when only the gravity acts on it. The cantilever position is given by x measured from the equilibrium position.

Bottom Line: 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.Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China; E-Mails: gmeng@sjtu.edu.cn (G.M.); giantbean@sjtu.edu.cn (J.-B.Z.); jerrysmiling@hotmail.com (J.-Y.C.).

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.

No MeSH data available.


Related in: MedlinePlus