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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

Local bifurcation and Poincaré maps of equilibrium parameter α.
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f16-sensors-09-03854: Local bifurcation and Poincaré maps of equilibrium parameter α.

Mentions: To explain the dynamic responses of the system clearly, Figure 16 shows the local bifurcation diagram and Poincaré maps of the dynamic system at the interval of 1.6 < α < 2. It can be found that the system responses exhibit the alternation of periodic and chaotic motions. The system response comes into steady-state synchronous motion with period-1 from chaotic motion, and enters period-2 motion from period-1 motion as the equilibrium parameter α increases, and then becomes chaotic motion with period-doubling bifurcation. Moreover, at 1.7 < α < 1.9, the system response changes between period-1 and period-2 motions alternately. When α > 1.9, the system response comes into steady-state synchronous motion with period-1. These phenomena indicate that the dynamic responses of the coupled system are very complex. The cantilever tip can undergo a period-doubling cascade to possible chaos about the original equilibrium. It is demonstrated that, away from the surface, the net force on the tip is always in the downward direction and causes the tip to accelerate the sample until it passes the key point, where the repulsive force plus the spring force becomes larger than the van der Waals force, and then the tip is forced away from the sample.


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)

Local bifurcation and Poincaré maps of equilibrium parameter α.
© Copyright Policy
Related In: Results  -  Collection

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

f16-sensors-09-03854: Local bifurcation and Poincaré maps of equilibrium parameter α.
Mentions: To explain the dynamic responses of the system clearly, Figure 16 shows the local bifurcation diagram and Poincaré maps of the dynamic system at the interval of 1.6 < α < 2. It can be found that the system responses exhibit the alternation of periodic and chaotic motions. The system response comes into steady-state synchronous motion with period-1 from chaotic motion, and enters period-2 motion from period-1 motion as the equilibrium parameter α increases, and then becomes chaotic motion with period-doubling bifurcation. Moreover, at 1.7 < α < 1.9, the system response changes between period-1 and period-2 motions alternately. When α > 1.9, the system response comes into steady-state synchronous motion with period-1. These phenomena indicate that the dynamic responses of the coupled system are very complex. The cantilever tip can undergo a period-doubling cascade to possible chaos about the original equilibrium. It is demonstrated that, away from the surface, the net force on the tip is always in the downward direction and causes the tip to accelerate the sample until it passes the key point, where the repulsive force plus the spring force becomes larger than the van der Waals force, and then the tip is forced away from the sample.

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