Scale-Dependent Dynamic-Pull-In of Functionally Graded Carbon Nanotubes Reinforced Nanodevice with Piezoelectric Layer
Publication: Journal of Aerospace Engineering
Volume 30, Issue 3
Abstract
This paper proposes a scale-dependent model to investigate the dynamic-pull-in characteristics of a functionally graded carbon nanotubes (FGCNTs) reinforced nanodevice with a piezoelectric layer. Based on nonlocal beam theory, the nonlinear thermoelectromechanical coupling dynamic governing equation of an electrostatically actuated nanodevice is derived. The material properties of the functionally graded layer depend on temperature environment, thickness, volume ratio, and distribution of carbon nanotubes (CNTs) reinforcement. The van der Waals interaction and Casimir force are considered in the dynamic-pull-in analysis. The homotopy perturbation method is used to obtain a second-order approximated analytical function of nature frequency with respect to initial amplitude. The influences of piezoelectric effect, temperature change, nonlocal parameters, distribution, and volume ratio of CNTs and initial amplitude on dynamic-pull-in behaviors and natural frequencies of the nanodevice are discussed. The results show that the system has one stable focus point at the domain of small initial amplitude and appears in a particular homoclinic orbit originating point and ends at an unstable saddle point.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors acknowledge financial support from National Science Foundation of China under Grant No. 11172165.
References
Alibeigloo, A. (2013). “Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity.” Compos. Struct., 95, 612–622.
Batra, R., Porfiri, M., and Spinello, D. (2007). “Effects of Casimir force on pull-in instability in micromembranes.” Euro Phys. Lett., 77(2), 20010.
Chao, P. C., Chiu, C., and Liu, T.-H. (2008). “DC dynamic pull-in predictions for a generalized clamped-clamped micro-beam based on a continuous model and bifurcation analysis.” J. Micromech. Microeng., 18(11), 115008.
Cho, C. H. (2009). “Characterization of Young’s modulus of silicon versus temperature using a “beam deflection” method with a four-point bending fixture.” Curr. Appl. Phys., 9(2), 538–545.
Comi, C., Corigliano, A., Ghisi, A., and Zerbini, S. (2013). “A resonant micro accelerometer based on electrostatic stiffness variation.” Meccanica, 48(8), 1893–1900.
Dashtaki, P. M., and Beni, Y. T. (2014). “Effects of Casimir force and thermal stresses on the buckling of electrostatic nanobridges based on couple stress theory.” Arabian J. Sci. Eng., 39(7), 5753–5763.
Degani, B. O., Elata, D., and Nemirovsky, Y. (2002). “An efficient DIPIE algorithm for CAD of electrostatically actuated MEMS devices.” J. Microelectromech. Syst., 11(5), 612–620.
Fakhrabadi, M. M. S., Rastgoo, A., and Ahmadian, M. T. (2014). “Non-linear behaviors of carbon nanotubes under electrostatic actuation based on strain gradient theory.” Int. J. Non-Linear Mech., 67, 236–244.
Fakhrabadi, M. M. S., Rastgoo, A., Ahmadian, M. T., and Mashhadi, M. M. (2014). “Dynamic analysis of carbon nanotubes under electrostatic actuation using modified couple stress theory.” Acta Mech., 225(6), 1523–1535.
Farrokhabadi, A., Koochi, A., and Abadyan, M. (2014). “Modeling the instability of CNT tweezers using a continuum model.” Microsyst. Technol., 20(2), 291–302.
Ghayesh, M. H., Farokhi, H., and Amabili, M. (2013). “Nonlinear behaviour of electrically actuated MEMS resonators.” Int. J. Eng. Sci., 71, 137–155.
Guo, J. G., and Zhao, Y. P. (2006). “Dynamic stability of electrostatic torsional actuators with van der Waals effect.” Int. J. Solids Struct., 43(3–4), 675–685.
Gupta, R. K., Hung, E. S., Yang, Y. J., Ananthasuresh, G., and Senturia, S. D. (1996). “Pull-in dynamics of electrostatically-actuated beams.” Proc., Solid-State Sensor and Actuator Workshop, IEEE, Piscataway, NJ.
Han, Y., and, Elliott, J. (2007). “Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites.” Comput. Mater. Sci., 39(2), 315–323.
He, J. H. (2003). “Homotopy perturbation method: A new nonlinear analytical technique.” Appl. Math. Comput., 135(1), 73–79.
He, J. H. (2006). “Homotopy perturbation method for solving boundary value problems.” Phys. Lett. A, 350(1), 87–88.
Kacem, N., Hentz, S., Pinto, D., Reig, B., and Nguyen, V. (2009). “Nonlinear dynamics of nanomechanical beam resonators: Improving the performance of NEMS-based sensors.” Nanotechnology, 20(27), 275501.
Ke, L. L., Yang, J., and Kitipornchai, S. (2010). “Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams.” Compos. Struct., 92(3), 676–683.
Liew, K., Lei, Z., and Zhang, L. (2015). “Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review.” Compos. Struct., 120, 90–97.
Lin, W. H., and Zhao, Y. P. (2005). “Casimir effect on the pull-in parameters of nanometer switches.” Microsyst. Technol., 11(2–3), 80–85.
Liu, C. C., and Liu, C. H. (2014). “Analysis of nonlinear dynamic behavior of electrically actuated micro-beam with piezoelectric layers and squeeze-film damping effect.” Nonlinear Dyn., 77(4), 1349–1361.
Lu, P., Lee, H. P., and Lu, C. (2007). “Application of nonlocal beam models for carbon nanotubes.” Int. J. Solids Struct., 44(16), 5289–5300.
Mobki, H., Sadeghi, M. H., Rezazadeh, G., Fathalilou, M., and keyvani-janbahan, A. A. (2014). “Nonlinear behavior of a nano-scale beam considering length scale-parameter.” Appl. Math. Model., 38(5–6), 1881–1895.
Mojahedi, M., Ahmadian, M. T., and Firoozbakhsh, K. (2013). “Dynamic pull-in instability and vibration analysis of a nonlinear microcantilever gyroscope under step voltage considering squeeze film damping.” Int. J. Appl. Mech., 5(3), 1350032.
Mojahedi, M., Ahmadian, M. T., and Firoozbakhsh, K. (2014). “Effects of Casimir and van der Waals forces on the pull-in instability of the nonlinear micro and nano-bridge gyroscopes.” Int. J. Struct. Stab. Dyn., 14(2), 1350059.
Mousavi, T., Bornassi, S., and Haddadpour, H. (2013). “The effect of small scale on the pull-in instability of nano-switches using DQM.” Int. J. Solids Struct., 50(9), 1193–1202.
Murmu, T., and Adhikari, S. (2012). “Nonlocal frequency analysis of nanoscale biosensors.” Sens. Actuators A, 173(1), 41–48.
Najar, F., El-Borgi, S., Reddy, J. N., and Mrabet, K. (2015). “Nonlinear nonlocal analysis of electrostatic nanoactuators.” Compos. Struct., 120, 117–128.
Nayfeh, A. H., Younis, M. I., and Abdel-Rahman, E. M. (2007). “Dynamic pull-in phenomenon in MEMS resonators.” Nonlinear Dyn., 48(1–2), 153–163.
Nielson, G. N., and Barbastathis, G. (2006). “Dynamic pull-in of parallel-plate and torsional electrostatic MEMS actuators.” J. Microelectromech. Syst., 15(4), 811–821.
Okada, Y., and Tokumaru, Y. (1984). “Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1,500 K.” J. Appl. Phys., 56(2), 314–320.
Pournaki, I. J., Zamanzadeh, M., Madinei, H., Rezazadeh, G. (2014). “Static pull-in analysis of capacitive FGM nanocantilevers subjected to thermal moment using Eringen’s nonlocal elasticity.” Int. J. Eng. Trans. A, 27(4), 633–642.
Raeisifard, H., Bahrami, M. N., Yousefi-Koma, A., and Fard, H. R. (2014). “Static characterization and pull-in voltage of a micro-switch under both electrostatic and piezoelectric excitations.” Eur. J. Mech. A. Solids, 44, 116–124.
Rafiee, M., Yang, J., and Kitipornchai, S. (2013). “Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers.” Compos. Struct., 96, 716–725.
Ramezani, A., and Alasty, A. (2009). “Instability of nanocantilever arrays in electrostatic and van der Waals interactions.” J. Phys. D, 42(22), 225506.
Ramezani, A., Alasty, A., and Akbari, J. (2006). “Influence of van der Waals force on the pull-in parameters of cantilever type nanoscale electrostatic actuators.” Microsyst. Technol., 12(12), 1153–1161.
Ramezani, A., Alasty, A., and Akbari, J. (2007a). “Closed-form solutions of the pull-in instability in nano-cantilevers under electrostatic and intermolecular surface forces.” Int. J. Solids Struct., 44(14–15), 4925–4941.
Ramezani, A., Alasty, A., and Akbari, J. (2007b). “Pull-in parameters of cantilever type nanomechanical switches in presence of Casimir force.” Nonlinear Anal. Hybrid Syst., 1(3), 364–382.
Reddy, J. N. (2007). “Nonlocal theories for bending, buckling and vibration of beams.” Int. J. Eng. Sci., 45(2–8), 288–307.
Rodriguez, A. W., Capasso, F., and Johnson, S. G. (2011). “The Casimir effect in microstructured geometries.” Nat. photonics, 5(4), 211–221.
Sedighi, H. M. (2014a). “Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory.” Acta Astronaut., 95, 111–123.
Sedighi, H. M. (2014b). “The influence of small scale on the pull-in behavior of nonlocal nanobridges considering surface effect, Casimir and van der Waals attractions.” Int. J. Appl. Mech., 6(3), 1450030.
Sedighi, H. M. (2015). “Modeling of surface stress effects on the dynamic behavior of actuated non-classical nano-bridges.” Trans. Can. Soc. Mech. Eng., 39(2), 137–151.
Sedighi, H. M., Daneshmand, F., and Abadyan, M. (2015). “Dynamic instability analysis of electrostatic functionally graded doubly-clamped nano-actuators.” Compos. Struct., 124, 55–64.
Sedighi, H. M., Daneshmand, F., and Abadyan, M. (2016). “Modeling the effects of material properties on the pull-in instability of nonlocal functionally graded nano-actuators.” ZAMM J. Appl. Math. Mech., 96(3), 385–400.
Sedighi, H. M., Keivani, M., and Abadyan, M. (2015c). “Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect.” Compos. Part B, 83, 117–133.
Sedighi, H. M., Koochi, A., Daneshmand, F., and Abadyan, M. (2015d). “Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow.” Int. J. Non Linear Mech., 77, 96–106.
Shen, H. S. (2009). “Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments.” Compos. Struct., 91(1), 9–19.
Shen, H. S. (2012). “Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells.” Compos. Part B, 43(3), 1030–1038.
Shen, H. S., and Xiang, Y. (2013). “Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments.” Eng. Struct., 56, 698–708.
Shen, H. S., and Zhang, C. L., (2011). “Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates.” Comput. Mater. Sci., 50(3), 1022–1029.
Soroush, R., Koochi, A., Kazemi, A. S., Noghrehabadi, A., Haddadpour, H., and Abadyan, M. (2010). “Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano-actuators.” Phys. Scr., 82(4), 045801.
Wattanasakulpong, N., and Ungbhakorn, V. (2013). “Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation.” Comput. Mater. Sci., 71, 201–208.
Yang, J., Jia, X. L., and Kitipornchai, S. (2008). “Pull-in instability of nano-switches using nonlocal elasticity theory.” J. Phys. D, 41(3), 035103.
Yang, W., and Wang, X. (2016). “Nonlinear pull-in instability of carbon nanotubes reinforced nano-actuator with thermally corrected Casimir force and surface effect.” Int. J. Mech. Sci., 107, 34–42.
Yang, W., Wang, X., and Fang, C. (2015). “Pull-in instability of carbon nanotube-reinforced nano-switches considering scale, surface and thermal effects.” Compos. Part B, 82, 143–151.
Yang, W. D., Wang, X., Fang, C. Q., and Lu, G. (2014). “Electromechanical coupling characteristics of carbon nanotube reinforced cantilever nano-actuator.” Sens. Actuators A, 220, 178–187.
Yas, M. H., and Heshmati, M. (2012). “Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load.” Appl. Math. Modell., 36(4), 1371–1394.
Zhang, L. X., and Zhao, Y. P. (2003). “Electromechanical model of RF MEMS switches.” Microsyst. Technol., 9(6–7), 420–426.
Zhang, W. M., Yan, H., Peng, Z. K., and Meng, G. (2014). “Electrostatic pull-in instability in MEMS/NEMS: A review.” Sens. Actuators A., 214, 187–218.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 30 • Issue 3 • May 2017
Copyright
©2016 American Society of Civil Engineers.
History
Received: Mar 2, 2016
Accepted: Aug 11, 2016
Published online: Oct 27, 2016
Discussion open until: Mar 27, 2017
Published in print: May 1, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.