Mechanical behavior analysis of a clamped-clamped micro-beam with stepped viscoelastic layer under electrostatic excitation
Document Type : Research Paper
Authors
Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Mofatteh Avenue, P.O. Box 15719-14911, Tehran, Iran
Abstract
In this study, static deflection, natural frequency and nonlinear vibration in bi-layer clamped-clamped microbeam are investigated. In this configuration, the second layer is the viscoelastic layer which covers a part of the microbeam length. This model is the main element of many chemical microsensors. The governing equations of motion for the system are obtained by Lagrange method and discretized using the assumed mode method. The non-uniform micro-beam modes shape are used as the comparison function in the assumed mode method. Initially, considering the DC voltage, system static response and natural frequency around the static position are obtained. Then, considering the AC voltage, the dynamic response around the dynamic position is calculated by both analytical (perturbation method) and numerical methods (Rung-kutta) and compared for validation purposes. The effect of different geometrical parameters of the viscoelastic layer on the static and dynamic behaviors of the system is also analyzed. The results indicate that the dimensions and location of the viscoelastic layer significantly affect the static and dynamic behavior of the system. Therefore, by using this property and considering the application of microsensors, their behaviors can be made efficient. For sensors operating based on resonance frequency shift, the optimum shift of frequency state can be obtained by varying the dimensions and position of the viscoelastic layer. Moreover, time of response can be optimized when the system is operating based on changes in the capacity of a capacitor. The results also represent that convergence in the assumed mode method used in this paper is feasible even using a single mode, whereas in previous works and using the Galerkin method, convergence was fulfilled in the presence of 3 modes.
Keywords
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[28] M. Shaat, A. Abdelkefi, Modeling of mechanical resonators used for nanocrystalline materials characterization and disease diagnosis of HIVs, Microsystem Technologies, Vol. 22, No. 2, pp. 305-318, 2016.
[29] M. Khater, M. Al-Ghamdi, S. Park, K. M. Stewart, E. Abdel-Rahman, A. Penlidis, A. Nayfeh, A. Abdel-Aziz, M. Basha, Binary MEMS gas sensors, Journal of Micromechanics and Microengineering, Vol. 24, No. 6, pp. 065007, 2014.
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[34] H. Raeisifard, M. Zamanian, M. N. Bahrami, A. Yousefi-Koma, H. R. Fard, On the nonlinear primary resonances of a piezoelectric laminated micro system under electrostatic control voltage, Journal of Sound and Vibration, Vol. 333, No. 21, pp. 5494-5510, 2014.
[35] I. Dufour, F. Lochon, S. M. Heinrich, F. Josse, D. Rebière, Effect of coating viscoelasticity on quality factor and limit of detection of microcantilever chemical sensors, IEEE Sensors Journal, Vol. 7, No. 2, pp. 230-236, 2007.
[36] E. Poloei, M. Zamanian, S. Hosseini, Nonlinear vibration analysis of an electrostatically excited micro cantilever beam coated by viscoelastic layer with the aim of finding the modified configuration, Structural Engineering and Mechanics, Vol. 61, No. 2, pp. 193-207, 2017.
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[40] M. I. Younis, A. Nayfeh, A study of the nonlinear response of a resonant microbeam to an electric actuation, Nonlinear Dynamics, Vol. 31, No. 1, pp. 91-117, 2003.
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[2] M. I. Younis, 2011, MEMS linear and nonlinear statics and dynamics, Springer Science & Business Media,
[3] Y. Zhang, Y.-p. Zhao, Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading, Sensors and Actuators A: Physical, Vol. 127, No. 2, pp. 366-380, 2006.
[4] D. Chen, Y. Wang, X. Chen, L. Yang, J. Xie, Temperature-frequency drift suppression via electrostatic stiffness softening in MEMS resonator with weakened duffing nonlinearity, Applied Physics Letters, Vol. 114, No. 2, pp. 023502, 2019.
[5] L. Xu, X. Jia, Electromechanical coupled nonlinear dynamics for microbeams, Archive of Applied Mechanics, Vol. 77, No. 7, pp. 485-502, 2007.
[6] N. Jaber, A. Ramini, M. I. Younis, Multifrequency excitation of a clamped–clamped microbeam: Analytical and experimental investigation, Microsystems & nanoengineering, Vol. 2, No. 1, pp. 1-6, 2016.
[7] J. Duan, Z. Li, J. Liu, Pull-in instability analyses for NEMS actuators with quartic shape approximation, Applied Mathematics and Mechanics, Vol. 37, No. 3, pp. 303-314, 2016.
[8] D. Younesian, M. Sadri, E. Esmailzadeh, Primary and secondary resonance analyses of clamped–clamped micro-beams, Nonlinear dynamics, Vol. 76, No. 4, pp. 1867-1884, 2014.
[9] M. Zamanzadeh, H. M. Ouakad, S. Azizi, Theoretical and experimental investigations of the primary and parametric resonances in repulsive force based MEMS actuators, Sensors and Actuators A: Physical, Vol. 303, pp. 111635, 2020.
[10] S. Ilyas, F. K. Alfosail, M. I. Younis, On the application of the multiple scales method on electrostatically actuated resonators, Journal of Computational and Nonlinear Dynamics, Vol. 14, No. 4, 2019.
[11] M. Uncuer, B. Marinkovic, H. Koser, Simulation of clamped-free and clamped-clamped microbeams dynamics for nonlinear mechanical switch applications, in Proceeding of, 439.
[12] H. Farokhi, M. H. Ghayesh, Viscoelasticity effects on resonant response of a shear deformable extensible microbeam, Nonlinear Dynamics, Vol. 87, No. 1, pp. 391-406, 2017.
[13] H. Farokhi, M. H. Ghayesh, Electrically actuated MEMS resonators: Effects of fringing field and viscoelasticity, Mechanical Systems and Signal Processing, Vol. 95, pp. 345-362, 2017.
[14] Y. Zhang, Y. Liu, K. D. Murphy, Nonlinear dynamic response of beam and its application in nanomechanical resonator, Acta Mechanica Sinica, Vol. 28, No. 1, pp. 190-200, 2012.
[15] M. Mohammadi, M. Ghayour, A. Farajpour, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B: Engineering, Vol. 45, No. 1, pp. 32-42, 2013.
[16] M. Mohammadi, M. Hosseini, M. Shishesaz, A. Hadi, A. Rastgoo, Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads, European Journal of Mechanics-A/Solids, Vol. 77, pp. 103793, 2019.
[17] R. Sepahvandi, M. Zamanian, B. Firouzi, S. Hosseini, Nonlinear vibration analysis of a partially coated circular microplate under electrostatic actuationpartially coated circular microplate under electrostatic actuation, Scientia Iranica, Vol. 27, No. 2, pp. 715-729, 2020.
[18] M. R. Farajpour, A. Rastgoo, A. Farajpour, M. Mohammadi, Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory, Micro & Nano Letters, Vol. 11, No. 6, pp. 302-307, 2016.
[19] A. Barati, M.M. Adeli, A.. Hadi, Static torsion of bi-directional functionally graded microtube based on the couple stress theory under magnetic field, International Journal of Applied Mechanics, Vol. 12, No 2, pp. 2050021, 2020.
[20] M. Mohammadi, A. Rastgoo, Nonlinear vibration analysis of the viscoelastic composite nanoplate with three directionally imperfect porous FG core, Structural Engineering and Mechanics, Vol. 69, No. 2, pp. 131, 2019.
[21] M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco-Pasternak foundation, 2014.
[22] S. Asemi, A. Farajpour, M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Composite Structures, Vol. 116, pp. 703-712, 2014.
[23] A. Bouchaala, A. H. Nayfeh, M. I. Younis, Analytical study of the frequency shifts of micro and nano clamped–clamped beam resonators due to an added mass, Meccanica, Vol. 52, No. 1-2, pp. 333-348, 2017.
[24] H. M. Ouakad, Nonlinear structural behavior of a size-dependent MEMS gyroscope assuming a non-trivial shaped proof mass, Microsystem Technologies, Vol. 26, No. 2, pp. 573-582, 2020.
[25] M. Zamanian, A. Karimiyan, S. Hosseini, H. Tourajizadeh, Nonlinear vibration analysis of a┴-shaped mass attached to a clamped–clamped microbeam under electrostatic actuation, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 231, No. 11, pp. 2147-2158, 2017.
[26] B. Firouzi, M. Zamanian, S. Hosseini, Static and dynamic responses of a microcantilever with a T-shaped tip mass to an electrostatic actuation, Acta Mechanica Sinica, Vol. 32, No. 6, pp. 1104-1122, 2016.
[27] B. Firouzi, M. Zamanian, The effect of capillary and intermolecular forces on instability of the electrostatically actuated microbeam with T-shaped paddle in the presence of fringing field, Applied Mathematical Modelling, Vol. 71, pp. 243-268, 2019.
[28] M. Shaat, A. Abdelkefi, Modeling of mechanical resonators used for nanocrystalline materials characterization and disease diagnosis of HIVs, Microsystem Technologies, Vol. 22, No. 2, pp. 305-318, 2016.
[29] M. Khater, M. Al-Ghamdi, S. Park, K. M. Stewart, E. Abdel-Rahman, A. Penlidis, A. Nayfeh, A. Abdel-Aziz, M. Basha, Binary MEMS gas sensors, Journal of Micromechanics and Microengineering, Vol. 24, No. 6, pp. 065007, 2014.
[30] G. Rezazadeh, A comprehensive model to study nonlinear behavior of multilayered micro beam switches, Microsystem Technologies, Vol. 14, No. 1, pp. 135-141, 2008.
[31] S. Rahmanian, S. Hosseini-Hashemi, Size-dependent resonant response of a double-layered viscoelastic nanoresonator under electrostatic and piezoelectric actuations incorporating surface effects and Casimir regime, International Journal of Non-Linear Mechanics, Vol. 109, pp. 118-131, 2019.
[32] S. N. Mahmoodi, N. Jalili, Non-linear vibrations and frequency response analysis of piezoelectrically driven microcantilevers, International Journal of Non-Linear Mechanics, Vol. 42, No. 4, pp. 577-587, 2007.
[33] T. Yin, B. Wang, S. Zhou, M. Zhao, A size-dependent model for beam-like MEMS driven by electrostatic and piezoelectric forces: A variational approach, Physica E: Low-dimensional Systems and Nanostructures, Vol. 84, pp. 46-54, 2016.
[34] H. Raeisifard, M. Zamanian, M. N. Bahrami, A. Yousefi-Koma, H. R. Fard, On the nonlinear primary resonances of a piezoelectric laminated micro system under electrostatic control voltage, Journal of Sound and Vibration, Vol. 333, No. 21, pp. 5494-5510, 2014.
[35] I. Dufour, F. Lochon, S. M. Heinrich, F. Josse, D. Rebière, Effect of coating viscoelasticity on quality factor and limit of detection of microcantilever chemical sensors, IEEE Sensors Journal, Vol. 7, No. 2, pp. 230-236, 2007.
[36] E. Poloei, M. Zamanian, S. Hosseini, Nonlinear vibration analysis of an electrostatically excited micro cantilever beam coated by viscoelastic layer with the aim of finding the modified configuration, Structural Engineering and Mechanics, Vol. 61, No. 2, pp. 193-207, 2017.
[37] M. Zamanian, S. Javadi, B. Firouzi, S. Hosseini, Modeling and analysis of power harvesting by a piezoelectric layer coated on an electrostatically actuated microcantilever, Materials Research Express, Vol. 5, No. 12, pp. 125502, 2018.
[38] A. F. Marques, R. C. Castelló, A. Shkel, Modelling the electrostatic actuation of MEMS: state of the art 2005, 2005.
[39] E. M. Abdel-Rahman, M. I. Younis, A. H. Nayfeh, Characterization of the mechanical behavior of an electrically actuated microbeam, Journal of Micromechanics and Microengineering, Vol. 12, No. 6, pp. 759, 2002.
[40] M. I. Younis, A. Nayfeh, A study of the nonlinear response of a resonant microbeam to an electric actuation, Nonlinear Dynamics, Vol. 31, No. 1, pp. 91-117, 2003.
[41] A. H. Nayfeh, M. I. Younis, A new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping, Journal of Micromechanics and Microengineering, Vol. 14, No. 2, pp. 170, 2003.
)
Volume 51, Issue 2
December 2020Pages 486-497
- Receive Date: 31 August 2020
- Revise Date: 11 October 2020
- Accept Date: 15 October 2020