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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

The Poincaré maps and phase portraits of different equilibrium parameters α.
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f18-sensors-09-03854: The Poincaré maps and phase portraits of different equilibrium parameters α.

Mentions: To illustrate the various motions, Figure 18 shows the nonlinear characteristics of the coupled system with the plots of the Poincaré maps and phase portraits for different equilibrium parameters α at different conditions. The motion of the coupled system changes between periodic and chaotic motions alternately. At α = 1.2, the motion with period-1 represented by a point in the Poincaré maps and characterized by a close curve in phase portraits is shown in Figure 18(a). As illustrated in Figure 18(b), the system response comes into period-6 motion at α = 1.42 from synchronous motion with period-1 at α = 1.2, as displayed in Figure 18 (a), then leaves period-6 motion and enters chaotic motion at α = 1.6, which can be seen from Figure 18(c). The strange attractor has a fractal structure and the corresponding largest Lyapunov exponent is positive. With the increase of the equilibrium parameter coefficient, as shown in Figure 18(d), the system response becomes periodic motion from chaotic motion again, and one can find the period-3 motion marked by three isolated points in Poincaré map and three circles in phase portrait at α = 1.74. It is indicated that the components of chaotic motions of the coupled system increases obviously with the increase of the amplitude of the force term. In general, the effect of equilibrium parameter on the system response should be considered for the design of the TM-AFM.


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)

The Poincaré maps and phase portraits of different equilibrium parameters α.
© Copyright Policy
Related In: Results  -  Collection

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

f18-sensors-09-03854: The Poincaré maps and phase portraits of different equilibrium parameters α.
Mentions: To illustrate the various motions, Figure 18 shows the nonlinear characteristics of the coupled system with the plots of the Poincaré maps and phase portraits for different equilibrium parameters α at different conditions. The motion of the coupled system changes between periodic and chaotic motions alternately. At α = 1.2, the motion with period-1 represented by a point in the Poincaré maps and characterized by a close curve in phase portraits is shown in Figure 18(a). As illustrated in Figure 18(b), the system response comes into period-6 motion at α = 1.42 from synchronous motion with period-1 at α = 1.2, as displayed in Figure 18 (a), then leaves period-6 motion and enters chaotic motion at α = 1.6, which can be seen from Figure 18(c). The strange attractor has a fractal structure and the corresponding largest Lyapunov exponent is positive. With the increase of the equilibrium parameter coefficient, as shown in Figure 18(d), the system response becomes periodic motion from chaotic motion again, and one can find the period-3 motion marked by three isolated points in Poincaré map and three circles in phase portrait at α = 1.74. It is indicated that the components of chaotic motions of the coupled system increases obviously with the increase of the amplitude of the force term. In general, the effect of equilibrium parameter on the system response should be considered for the design of the TM-AFM.

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