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Linearized of Electrostatic Force in the Carbon Nanotube for Dynamic Behavior Analysis  

Lee, Jongkil (안동대학교 사범대학 기계교육과)
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대한공업교육학회지 / v.30, no.2, 2005 , pp. 115-122 More about this Journal
Abstract
For an analysis of dynamic behavior in carbon nanotube(CNT) which is widely used as micro and nano-sensors, an electrostatic force of CNT was investigated. For larger gaps in between sensor and electrode the van der Waals force can be ignored. The boundary condition in the CNT was assumed to clamped-clamped case at both ends. In this paper electrostatic force is expressed as linear equation along deflection using Taylor series. The first and second terms(${\zeta}_0$ and ${\zeta}_1$) of the linear equation are analyzed. Based on the simulation results nondimensional number ${\Phi}_0$ and ${\Phi}_1$ which came from ${\zeta}_0$ and ${\zeta}_1$ were decreased according to the increment of the gap. Reduction ratio of the second term ${\zeta}_1$ is increased up to 99% along to the increment of the gap. The higher order terms can be ignored and therefore, electrostatic force can be expressed using the first two terms of the linear equation. This results play an important role in analyzing the nonlinear dynamic behavior of the CNT as well as the pull-in voltage of simply supported switches.
Keywords
Carbon nanotube; Electrostatic force; Linearized equation;
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1 Dequesnes, M., Rotkin, 5., Aluru, N. (2002). Calculation of Pull-in Voltages for Carbon-nanotube-based nanoelectromechanical switches. Nanotechnology, 13, 120-131   DOI   ScienceOn
2 Bajaj, A., Johnson, J. (2002). On the Amplitude Dynamics and Crisis in resonant Motion of Stretched Strings. Phil. Trans. R. Soc. Lond. A, 338, 1-41
3 Yakobson, B., Brabec, C. Bernholc, J. (1996). Nanomechanivs of Carbon Tubes: Instabilities beyond Linear Response. Physical Review Letters, 76, 2511-2514   DOI   ScienceOn
4 Pirio, G. et. al. (2002). Fabrication and Electrical Characteristics of Carbon Nanotube Field Emission Microcathodes with an Integrated Gate Electrode. Nanotechnology, 13, 1-4
5 Jang, Y. et. al. (2002). Suppression of Leakage Current via Formation of a Sidewall Protector in the Microgated Carbon Nanotube Emitter. Nanotechnology, 14, 497-500   DOI   ScienceOn
6 Tuzun, R. et. al. (1997). Dynamics of $He/C_{60}$ Flow Inside Carbon Nanotubes. Nanotechnology, 8, 112-118   DOI   ScienceOn
7 Younis, M., Nayfeh, A. (2003). A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation. Nonlinear Dynamics, 31, 91-117   DOI   ScienceOn
8 Osterberg, P., Senturia, S. (1997). M-Test: A Test Chip for MEMS Material Property Measurement Using Electrostatically Actuated Test Structures. J. of Microelectromechanical Systems, 6, 107-118   DOI   ScienceOn
9 Wu, Y., Shannon, M. (2004). Theoretical Analysis of the Effect of Static Charges in Silicon-Based Dielectric Thin Films on Micro- to Nanoscale Electrostatic Actuation. J. of Micromechanics and Microengineering, 14, 989-998   DOI   ScienceOn
10 Lee, S. et al. (2004). Nonlinear Tapping Dynamics of Multi-Walled Carbon Nanotube Tipped Atomic Force Microcantilevers. Nanotechnology, 15, 416-421   DOI   ScienceOn
11 Ono, T., Miyashita, H., Esashi, M. (2002). Electric-field-enhanced growth of carbon nanotubes for scanning probe microscopy. Nanotechnology, 13, 62-64   DOI   ScienceOn
12 Mitrofanov, V., Styazhkina, N., Tokmakov, K. (2002). Test Mass Damping Associated with Electrostatic Actuator. Classical and Quantum Gravity, 19, 2039-2043   DOI   ScienceOn
13 Dharap, P., Li, Z., Nagarajaiah, S., Barrera, E. (2004). Nanotube Film Based on Single-wall Carbon Nanotubes for Strain Sensing. Nanotechnology, 15, 379-382   DOI   ScienceOn
14 Levy, R., Maaloum, M. (2002). Measuring the Spring Constant of Atomic Force Microscope Cantilevers: Thermal Fluctions and Other Methods. Nanotechnology, 13, 33-37   DOI   ScienceOn
15 Hayt, W. (1981). Engineering Electromagnetics. McGraw-Hill, New York
16 Younis, M., Abdel-Rahman, E., Nayfeh, A. (2003). A Reduced-Order Model for Electrically Actuated Microbeam-Based MEMS. J. of Microelectromechanical Systems, 12, 672-680   DOI   ScienceOn
17 Wang, G. et al. (2004). Pull-in instability study of carbon nanotube tweezers under the influence of van der Waals forces. J. of Mocromechanics and Microengineering, 14, 1119-1125   DOI   ScienceOn
18 Abdel-Rahman, E., Younis, M., Nayfeh, A. (2002). Characterization of the Mechanical Behavior of an Electrically Actuated Microbeam. J. of Micromechanics and Microengineering, 12, 759-766   DOI   ScienceOn
19 Lin, W., Zhao, Y. (2003). Dynamic Behavior of Nanoscale Electrostatic Actuators. Chin. Phys. Lett., 20, 2070-2073   DOI   ScienceOn