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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 typical TM-AFM setup.
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f1-sensors-09-03854: Schematic of the typical TM-AFM setup.

Mentions: Atomic force microscopy (AFM) has been developed to a nearly ubiquitous tool for studying physics, chemistry, biology, medicine and engineering at the nano-scale [1-5]. AFM could significantly impact many fabrication and manufacturing processes due to its advantages such as 3D topography of nano-fabrication and metrology for MEMS [2]. As a typical dynamic mode, the tapping mode (TM) is widely used in the operation of AFM where the cantilever is driven at a fixed frequency close or equal to the fundamental resonance frequency of vertical bending [4,6]; a schematic of the TM-AFM setup is shown in Figure 1. Moreover, the vibration amplitude of the cantilever is much bigger than the equilibrium separation between the tip and the sample. The TM-AFM has attracted extensive attention due to its ability to deal with compliant materials as well as to overcome adhesion forces.


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 typical TM-AFM setup.
© Copyright Policy
Related In: Results  -  Collection

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

f1-sensors-09-03854: Schematic of the typical TM-AFM setup.
Mentions: Atomic force microscopy (AFM) has been developed to a nearly ubiquitous tool for studying physics, chemistry, biology, medicine and engineering at the nano-scale [1-5]. AFM could significantly impact many fabrication and manufacturing processes due to its advantages such as 3D topography of nano-fabrication and metrology for MEMS [2]. As a typical dynamic mode, the tapping mode (TM) is widely used in the operation of AFM where the cantilever is driven at a fixed frequency close or equal to the fundamental resonance frequency of vertical bending [4,6]; a schematic of the TM-AFM setup is shown in Figure 1. Moreover, the vibration amplitude of the cantilever is much bigger than the equilibrium separation between the tip and the sample. The TM-AFM has attracted extensive attention due to its ability to deal with compliant materials as well as to overcome adhesion forces.

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