Nonlinear Oscillations of CNT Nano-resonator Based on Nonlocal Elasticity: The Energy Balance Method
This paper deals with investigating the nonlinear oscillation of carbon nanotube manufactured nano-resonator. The governing equation of the nano-resonator is extracted in the context of the nonlocal elasticity. The impact of the Casimir force is also incorporated in the developed model. A closed-form solution based on the energy balance method is presented for investigating the oscillations of the nano-resonator. The proposed closed-form solution is compared with the numerical solution. The impact of influential parameters including applied voltage, Casimir force, geometrical and nonlocal parameters on the nano resonator’s vibration and frequency are investigated. The obtained results demonstrated that the Casimir force reduces the nano-resonator frequency. However, the nonlocal parameter has a hardening effect and enhances the system’s frequency.
Ali-Akbari, H., Ceballes, S., & Abdelkefi, A. (2019). Nonlinear performance analysis of forced carbon nanotube-based bio-mass sensors. International Journal of Mechanics and Materials in Design, 15(2), 291-315.
Amorim, T. D., Dantas, W. G., & Gusso, A. (2015). Analysis of the chaotic regime of MEMS/NEMS fixed–fixed beam resonators using an improved 1DOF model. Nonlinear Dynamics, 79(2), 967-981.
Besley, N. A. (2020). Vibrational Analysis of Carbon Nanotube Based Nanomechanical Resonators. The Journal of Physical Chemistry C.
Dantas, W. G., & Gusso, A. (2018). Analysis of the chaotic dynamics of MEMS/NEMS doubly clamped beam resonators with two-sided electrodes. International Journal of Bifurcation and Chaos, 28(10), 1850122.
Dequesnes, M., Tang, Z., & Aluru, N. R. (2004). Static and dynamic analysis of carbon nanotube-based switches. J. Eng. Mater. Technol., 126(3), 230-237.
Eringen, A. C., & Edelen, D. (1972). On nonlocal elasticity. International Journal of Engineering Science, 10(3), 233-248.
Farrokhabadi, A., Koochi, A., & Abadyan, M. (2014). Modeling the instability of CNT tweezers using a continuum model. Microsystem Technologies, 20(2), 291-302.
Fu, Y., Zhang, J., & Wan, L. (2011). Application of the energy balance method to a nonlinear oscillator arising in the microelectromechanical system (MEMS). Current Applied Physics, 11(3), 482-485.
Ganji, S., Ganji, D., & Karimpour, S. (2009). He’s energy balance and He’s variational methods for nonlinear oscillations in engineering. International Journal of Modern Physics B, 23(03), 461-471.
Ghalambaz, M., Ghalambaz, M., & Edalatifar, M. (2015). Buckling Analysis of Cantilever Nanoactuators Immersed in an Electrolyte: A Close Form Solution Using Duan-Rach Modified Adomian Decomposition Method. Journal of Applied and Computational Mechanics, 1(4), 207-219.
Hajjam, A., & Pourkamali, S. (2011). Fabrication and characterization of MEMS-based resonant organic gas sensors. IEEE Sensors Journal, 12(6), 1958-1964.
Hosseini, S. M. (2018). Analytical solution for nonlocal coupled thermoelasticity analysis in a heat-affected MEMS/NEMS beam resonator based on Green–Naghdi theory. Applied Mathematical Modelling, 57, 21-36.
Jamshidi, N., & Ganji, D. (2010). Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire. Current Applied Physics, 10(2), 484-486.
Kang, D.-K., Kim, C.-W., & Yang, H.-I. (2017). Thermal effects on nonlinear vibration of a carbon nanotube-based mass sensor using finite element analysis. Physica E: Low-dimensional Systems and Nanostructures, 85, 125-136.
Khosravi, F., Hosseini, S. A., & Hayati, H. (2020). Free and forced axial vibration of single walled carbon nanotube under linear and harmonic concentrated forces based on nonlocal theory. International Journal of Modern Physics B, 34(08), 2050067.
Kim, P., & Lieber, C. M. (1999). Nanotube nanotweezers. Science, 286(5447), 2148-2150.
Koochi, A., Farrokhabadi, A., & Abadyan, M. (2015). Modeling the size dependent instability of NEMS sensor/actuator made of nano-wire with circular cross-section. Microsystem Technologies, 21(2), 355-364.
Liu, H., Li, B., & Liu, Y. (2019). The inconsistency of nonlocal effect on carbon nanotube conveying fluid and a proposed solution based on local/nonlocal model. European Journal of Mechanics-A/Solids, 78, 103837.
Liu, Y., Song, T., Jia, X., Meng, L., & Mao, X. (2017). Gold nanoparticles decorated carbon nanotube probe based immunochromatographic assay on cotton thread. Sensors and Actuators B: Chemical, 251, 1112-1118.
Mahmoud, F., Eltaher, M., Alshorbagy, A., & Meletis, E. (2012). Static analysis of nanobeams including surface effects by nonlocal finite element. Journal of mechanical science and technology, 26(11), 3555-3563.
Mehdipour, I., Ganji, D., & Mozaffari, M. (2010). Application of the energy balance method to nonlinear vibrating equations. Current Applied Physics, 10(1), 104-112.
Mestrom, R., Fey, R., Van Beek, J., Phan, K., & Nijmeijer, H. (2008). Modelling the dynamics of a MEMS resonator: simulations and experiments. Sensors and Actuators A: Physical, 142(1), 306-315.
Miandoab, E. M., Yousefi-Koma, A., Pishkenari, H. N., & Fathi, M. (2014). Nano-resonator frequency response based on strain gradient theory. Journal of Physics D: Applied Physics, 47(36), 365303.
Miandoab, E. M., Yousefi-Koma, A., Pishkenari, H. N., & Tajaddodianfar, F. (2015). Study of nonlinear dynamics and chaos in MEMS/NEMS resonators. Communications in Nonlinear Science and Numerical Simulation, 22(1-3), 611-622.
Ouakad, H. M., & Younis, M. I. (2010). Nonlinear dynamics of electrically actuated carbon nanotube resonators. Journal of computational and nonlinear dynamics, 5(1).
Pashaki, P. V., & Ji, J.-C. (2020). Nonlocal nonlinear vibration of an embedded carbon nanotube conveying viscous fluid by introducing a modified variational iteration method. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42(4), 1-13.
Qian, Z., Hui, Y., Liu, F., Kang, S., Kar, S., & Rinaldi, M. (2016). Graphene–aluminum nitride NEMS resonant infrared detector. Microsystems & nanoengineering, 2(1), 1-7.
Rahmani, O., Shokrnia, M., Golmohammadi, H., & Hosseini, S. (2018). Dynamic response of a single-walled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory. The European Physical Journal Plus, 133(2), 1-13.
Sedighi, H. M., & Farjam, N. (2017). A modified model for dynamic instability of CNT based actuators by considering rippling deformation, tip-charge concentration and Casimir attraction. Microsystem Technologies, 23(6), 2175-2191.
Tajaddodianfar, F., Yazdi, M. R. H., & Pishkenari, H. N. (2017). Nonlinear dynamics of MEMS/NEMS resonators: analytical solution by the homotopy analysis method. Microsystem Technologies, 23(6), 1913-1926.
Tocchio, A., Caspani, A., & Langfelder, G. (2011). Mechanical and electronic amplitude-limiting techniques in a MEMS resonant accelerometer. IEEE Sensors Journal, 12(6), 1719-1725.
Yang, Y., Wang, J., & Yu, Y. (2018). Wave propagation in fluid-filled single-walled carbon nanotube based on the nonlocal strain gradient theory. Acta Mechanica Solida Sinica, 31(4), 484-492.
Zeighampour, H., Beni, Y. T., & Karimipour, I. (2017). Wave propagation in double-walled carbon nanotube conveying fluid considering slip boundary condition and shell model based on nonlocal strain gradient theory. Microfluidics and Nanofluidics, 21(5), 85.