Nonlinear Analysis of Mechanical Behavior of Electrostatically Actuated Step Bilayer Cantilever Microbeam Considering Variable Width for Second Layer
Keywords:
Static Deflection, Natural Frequency, Electrostatic, Galerkin, Micro Electromechanical Systems
Abstract
The present paper is aimed to analyze static deformation, natural frequency and subharmonic resonance of a bilayer cantilever microbeam, the second layer of which has a variable width and is located on a point along the microbeam's length. Electrostatic actuation is induced by applying the voltage between the microbeam and its opposite electrode. The importance of such configuration is revealed particularly in mass and pollutants micro-sensors. First, the nonlinear equation of motion, which has been extracted in previous studies using Hamilton's principle and considering the bending neutral axis shortening assumption, was rewritten for a microbeam with variable-width second layer. Then differential equations governing the static deflection and free vibration equation around the stability point are solved using Galerkin method. Three mode shapes of a doubled stepped-microbeam are employed as the comparison function. The shapes such as triangular, parabolic, symmetric parabolic and hyperbolic are considered for the second layer. In order to find the optimal length and thickness for the selected form, the relevant diagrams were plotted for static deformation and natural frequency at constant volume and different lengths and thicknesses, and then were analyzed and investigated. The discretized equations are solved by the perturbation theory. The excitation frequency is tuned near twice the fundamental natural frequencies (subharmonic excitation). The results show that system behavior depends on the size, position and width of the coated layer. The results of this paper can be used for optimum design of microsystems such as microswitches and mass and pollutant microsensors.
References
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[31] Mahmoodi, S.N., Jalili, N. and Ahmadian, M. “Subharmonics analysis of nonlinear flexural vibrations of piezoelectrically actuated microcantilevers”, Nonlinear Dyn., Vol. 59(3), 397–409, 2010.
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[33] Mahmoodi, S.N. and Jalili, N. “Coupled Flexural-Torsional Nonlinear Vibrations of Piezoelectrically Actuated Microcantilevers With Application to Friction Force Microscopy”, J VIB ACOUST., Vol. 130 (6), 061003-1-10, 2008.
[34] Poloei, E., Zamanian, M., & Hosseini, S. A. A. “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(2), pp. 193-207, 2017.
[35] Zamanian, M., M. Hadilu, and B. Firouzi. “A study on the use of perturbation technique for analyzing the nonlinear forced response of piezoelectric microcantilevers” Journal of Computational & Applied Research in Mechanical Engineering (JCARME) 5, No. 2, pp. 161-172, 2016.
[36] Zamanian, M., Javadi, S., Firouzi, B., & Hosseini, S. A. A. “Modeling and analysis of power harvesting by a piezoelectric layer coated on an electrostatically actuated microcantilever” Materials Research Express, Vol. 5(12), 125502, 2018.
[37] Raeisifard, H., Zamanian, M., Bahrami, M. N., Yousefi-Koma, A., & Fard, H. R. “On the nonlinear primary resonances of a piezoelectric laminated micro system under electrostatic control voltage” Journal of Sound and Vibration, Vol. 333(21), pp. 5494-5510, 2014.
[38]Yin, T., Wang, B., Zhou, S., & Zhao, M. “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.
[39] A. H. Nayfeh, M. I. Younis, E. M. Abdel-Rahman, “Dynamic pull-in phenomenon in MEMS resonators” Nonlinear Dynamics, Vol. 48, No. 1-2, pp. 153-163, 2006.
[2] S. Chaterjee, G. A. Pohit, “Large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams,” Journal of sound and vibration, Vol. 322, No. 4-5, pp. 969-986, 2009.
[3] X. Lizhoung, J. Xiaoli, “Electromechanical coupled nonlinear dynamics for microbeams,” Arc. Appl. Mech, Vol. 77, No. 7, pp. 485-502, 2007.
[4] M. Rasekh, S. E. Khadem, “Pull-in analysis of an electrostatically actuated nano-cantilever beam with nonlinearity in curvature and inertia”, International journal of Mechanical Science, Vol. 53, No. 2, pp. 108-115, 2011.
[5] Y. Fang, P. Li, “A new approach and model for accurate determination of the dynamic pull-in parameters of microbeam actuated by a step voltage,” Micromechanics and Microengineering, Vol. 23, No. 4, pp. 045010-045021, 2013.
[6] M. Rahaeifard, M. T. Ahmadian, “On pull-in instabilities of microcantilevers,” International Journal of Engineering Science, Vol. 87, pp. 23-31, 2015.
[7] F. Najar, S. El-Borgi, J. N. Reddy, K. Mrabet, “Nonlinear nonlocal analysis of electrostatic nanoactuators,” Composite Structures, Vol. 120, pp. 117-128, 2015.
[8] Y. T. Huang, H. L. Chen, W. Hsu, “An analytical model for calculating the pull-in voltage of micro cantilever beams subjected to tilted and curled effects,” Microelectronic Engineering, Vol. 125, pp. 73-77, 2014.
[9] Y. Aboelkassem, A. H. Nayfeh, “M. Ghommem, Bio-mass sensor using an electrostatically actuated microcantilever in a vacuum microchannel” Microsyst Technol, Vol. 16, No. 10, pp. 1749-1755, 2010.
[10] M. Rasekh, S. E. Khadem, “Design and performance analysis of a nanogyroscope based on electrostatic actuation and capacitive sensing” Journal of Sound and Vibration, Vol. 332, No. 23, pp. 6155-6168, 2013.
[11] M. Mojahedia, M. T. Ahmadian, K. Firoozbakhsh, “The influence of the intermolecular surface forces on the static deflection and pull-in instability of the micro/nano cantilever gyroscopes” Composites Part B: Engineering, Vol. 56, pp. 336-343, 2014.
[12] Firouzi, B., Zamanian, M., & Hosseini, S. A. A. (2016). “Static and dynamic responses of a microcantilever with a T-shaped tip mass to an electrostatic actuation” Acta Mechanica Sinica, 32(6), 1104-1122.
[13] Firouzi, B., & Zamanian, M. (2019). “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, 71, 243-268.
[14] Mukherjee, B., & Sen, S. “Generalized closed form solutions for feasible dimension limit and pull-in characteristics of nanocantilever under the Influences of van der Waals and Casimir forces” Materials Research Express, Vol. 5(4), 045028, 2018.
[15] Hu, Y. C., Chang, C. M., & Huang, S. C. “Some design considerations on the electrostatically actuated microstructures” Sensors and Actuators A: Physical, Vol. 112(1), pp. 155-161, 2004.
[16] Bhojawala, V. M., & Vakharia, D. P. (2017) “Closed-form solution for static pull-in voltage of electrostatically actuated clamped–clamped micro/nano beams under the effect of fringing field and van der Waals force” Materials Research Express, Vol. 4(12), 126306.
[17] M. M. Joglekar · D. N. Pawaskar, “Shape optimization of electrostatically actuated microbeams for extending static and dynamic operating ranges” Structural and Multidisciplinary Optimization, Vol. 46, pp. 871–890, December 2012.
[18] M. Nie, Q. Huang, W. Li, “Measurement of materialproperties of individual layers for composite films by apull-in method” Journal of Physics, Vol. 34, No. 34, pp. 516–521, 2006.
[19] Pamidighantam S, Puers R, Baert K, Tilmans H, “Pull-in voltage analysis of electrostatically actuated beam structures with fixed–fixed and fixed-free end conditions” J Micromech Microeng, Vol. 12(4), pp. 458–464, 2002.
[20] Michael Raulli, “Prediction and optimization of pull-in voltage for arbitrarily complex electro-mechanical systems” Coll. of technic, Vol 2, pp 899–911, 2006.
[21] Esfahani, S., Khadem, S. E., & Mamaghani, A. E. “Nonlinear vibration analysis of an electrostatic functionally graded nano-resonator with surface effects based on nonlocal strain gradient theory” International Journal of Mechanical Sciences, Sciences, Vol. 151, pp. 508-522, 2019.
[22] Qiao, Y., Xu, W., Sun, J., & Zhang, H. “Reliability of electrostatically actuated MEMS resonators to random mass disturbance” Mechanical Systems and Signal Processing, Vol. 121, pp. 711-724, 2019.
[23] Ilyas, S., Alfosail, F. K., & Younis, M. I. “On the Application of the Multiple Scales Method on Electrostatically Actuated Resonators” Journal of Computational and Nonlinear Dynamics, Vol. 14(4), 041006, 2019.
[24] Chen, D., Wang, Y., Chen, X., Yang, L., & Xie, J. “Temperature-frequency drift suppression via electrostatic stiffness softening in MEMS resonator with weakened duffing nonlinearity” Applied Physics Letters, Vol. 114(2), 023502, 2019.
[25] Caruntu, D. I., Botello, M. A., Reyes, C. A., & Beatriz, J. S. “Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators” Journal of Computational and Nonlinear Dynamics, Vol. 14(3), 031005, 2019.
[26] Li, L., Han, J., Zhang, Q., Liu, C., & Guo, Z. “Nonlinear dynamics and parameter identification of electrostatically coupled resonators” International Journal of Non-Linear Mechanics, Vol. 110, pp. 104-114, 2019.
[27] G. Rezazadeh, “A comprehensive model to study nonlinearbehavior of multilayered micro beam switchesMicrosyst” Microsyst Technol, Vol. 14, No. 1, pp. 135–141, 2007.
[28] H. L. Dai, L. Wang, “Size-dependent pull-in voltage and nonlinear dynamics of electrically actuated microcantilever-based MEMS: A full nonlinear analysis” Communications in Nonlinear Science and Numerical Simulation, Vol. 46, pp. 116-125, May 2017.
[29] Enrico Radi, Giovanni Bianchi, Lorenzo di Ruvo, “Upper and lower bounds for the pull-in parameters of a micro- or nanocantilever on a flexible support” International Journal of Non-Linear Mechanics, Vol. 92, pp. 176-186, June 2017.
[30] Mahmoodi, S.N. and Jalili, N. “Non-linear vibrations and frequency response analysis of piezoelectricallydriven microcantilevers”, Int. J. Nonlinear Mech., Vol. 42 (4), pp. 577 – 587, 2007.
[31] Mahmoodi, S.N., Jalili, N. and Ahmadian, M. “Subharmonics analysis of nonlinear flexural vibrations of piezoelectrically actuated microcantilevers”, Nonlinear Dyn., Vol. 59(3), 397–409, 2010.
[32] Mahmoodi, S.N., Afshari, M. and Jalili, N. “Nonlinear vibrations of piezoelectric microcantilevers for biologically-induced surface stress sensing”, Commun Nonlinear Sci Numer Simul., Vol. 13 (9), pp. 1964-1977, 2007.
[33] Mahmoodi, S.N. and Jalili, N. “Coupled Flexural-Torsional Nonlinear Vibrations of Piezoelectrically Actuated Microcantilevers With Application to Friction Force Microscopy”, J VIB ACOUST., Vol. 130 (6), 061003-1-10, 2008.
[34] Poloei, E., Zamanian, M., & Hosseini, S. A. A. “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(2), pp. 193-207, 2017.
[35] Zamanian, M., M. Hadilu, and B. Firouzi. “A study on the use of perturbation technique for analyzing the nonlinear forced response of piezoelectric microcantilevers” Journal of Computational & Applied Research in Mechanical Engineering (JCARME) 5, No. 2, pp. 161-172, 2016.
[36] Zamanian, M., Javadi, S., Firouzi, B., & Hosseini, S. A. A. “Modeling and analysis of power harvesting by a piezoelectric layer coated on an electrostatically actuated microcantilever” Materials Research Express, Vol. 5(12), 125502, 2018.
[37] Raeisifard, H., Zamanian, M., Bahrami, M. N., Yousefi-Koma, A., & Fard, H. R. “On the nonlinear primary resonances of a piezoelectric laminated micro system under electrostatic control voltage” Journal of Sound and Vibration, Vol. 333(21), pp. 5494-5510, 2014.
[38]Yin, T., Wang, B., Zhou, S., & Zhao, M. “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.
[39] A. H. Nayfeh, M. I. Younis, E. M. Abdel-Rahman, “Dynamic pull-in phenomenon in MEMS resonators” Nonlinear Dynamics, Vol. 48, No. 1-2, pp. 153-163, 2006.
Published
2020-12-01
How to Cite
Habibikhah, M., Zamanian, M., Firouzi, B., & Hosseini, S. A. A. (2020). Nonlinear Analysis of Mechanical Behavior of Electrostatically Actuated Step Bilayer Cantilever Microbeam Considering Variable Width for Second Layer. Majlesi Journal of Mechatronic Systems, 9(4), 35-50. Retrieved from https://ms.majlesi.info/index.php/ms/article/view/463
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Articles
