Modares Mechanical Engineering

Modares Mechanical Engineering

Size-dependent analysis of micro-bridge gyroscopes under the combined effects of instantaneous DC voltage and harmonic base excitations

Authors
Mohammad Ali Mokhtari Amir Majdi 1
Masoud Tahani 2
1 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
2 Ferdowsi University of Mashhad
Abstract
The aim of the proposed study is to investigate the size dependent behavior of the micro-bridge gyroscopes under the combined effects of instantaneous DC voltage and harmonic base excitation. To do so, modified couple stress theory is utilized to model the size-dependent behavior of the micro-gyroscope. To avoid resonance, viscous damping is used. Hamilton’s principle is then employed to derive the governing equations of motion. Afterwards, to convert the partial differential equations of motion to ordinary differential equations of motion, a Galerkin based single mode approximation is made. Then fourth-order Range-Kutta method is used to solve the governing equations of motion. To check the accuracy of the present model, the results are then validated through comparison with the available results in the literature and the comparison shows good agreements. In addition to the previous comparison, the present results are the validated through comparison with the results of COMSOL simulation. Furthermore, the effects of different parameters on the dynamic pull-in instability and amplitude of the vibrations are investigated. The observation shows that for the case of the harmonic base excitation, the system will be excited on two frequencies.
Keywords
Micro-bridge gyroscopes
Pull-in instability
Modified couple stress theory
Harmonic base excitation
[1] S. D. Senturia, Microsystem Design, pp. 3-29, New York: Springer US, 2007.
[2] Z. Syed, P. Aggarwal, C. Goodall, X. Niu, N. El-Sheimy, A new multiposition calibration method for MEMS inertial navigation systems, Measurement Science and Technology, Vol. 18, No. 7, pp. 1897, 2007.
[3] H. A. Tilmans, W. De Raedt, E. Beyne, MEMS for wireless communications: from RF-MEMS components to RF-MEMS-SiP, Journal of Micromechanics and Microengineering, Vol. 13, No. 4, pp. S139, 2003.
[4] M. Mojahedi, M. T .Ahmadian, K. Firoozbakhsh, Static deflection and pullin instability analysis of an electrostatically actuated mirocantilever gyroscope considering geometric nonlinearities, Journal of Mechanical Science and Technology, Vol. 27, No. 8, pp. 2425-2434, 2013.
[5] K. Liu, W. Zhang, W. Chen, K. Li, F. Dai, F. Cui, X. Wu, G. Ma, Q. Xiao, The development of micro-gyroscope technology, Journal of Micromechanics and Microengineering, Vol. 19, No. 11, pp. 113001, 2009.
[6] M. Esmaeili, N. Jalili, M. Durali, Dynamic modeling and performance evaluation of a vibrating beam microgyroscope under general support motion, Journal of Sound and Vibration, Vol. 301, No. 1, pp. 146-164, 2007.
[7] M. Rasekh, S. 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.
[8] M. Ghommem, A. Nayfeh, S. Choura, F. Najar, E. Abdel-Rahman, Modeling and performance study of a beam microgyroscope, Journal of Sound and Vibration, Vol. 329, No. 23, pp. 4970-4979, 2010.
[9] S. Pamidighantam, R. Puers, K. Baert, H. A. Tilmans, Pull-in voltage analysis of electrostatically actuated beam structures with fixed–fixed and fixed–free end conditions, Journal of Micromechanics and Microengineering, Vol. 12, No. 4, pp. 458, 2002.
[10] M. Mojahedi, M. Ahmadian, K. Firoozbakhsh, Dynamic pull-in instability and vibration analysis of a nonlinear microcantilever gyroscope under step voltage considering squeeze film damping, International Journal of Applied Mechanics, Vol. 5, No. 03, pp. 1350032, 2013.
[11] X. Guo, D. Fang, X. Li, Measurement of deformation of pure Ni foils by speckle pattern interferometry, Mechanics and Engineering, Vol. 27, No. 2, pp. 21-25, 2005.
[12] A. W. McFarland, J. S. Colton, Role of material microstructure in plate stiffness with relevance to microcantilever sensors, Journal of Micromechanics and Microengineering, Vol. 15, No. 5, pp. 1060, 2005.
[13] R. A. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, Vol. 11, No. 1, pp. 385-414, 1962.
[14] W. Koiter, Couple-Stresses in the Theory of Elasticity, I & II, Proceedings of the Koninklijke Nederlandse Academie van Weteschappen, Vol. 67, pp. 17- 44 , 1969.
[15] F. Yang, A. Chong, D. C. C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, Vol. 39, No. 10, pp. 2731-2743, 2002.
[16] R. Mindlin, N. Eshel, On first strain-gradient theories in linear elasticity, International Journal of Solids and Structures, Vol. 4, No. 1, pp. 109-124, 1968.
[17] N. Fleck, J. Hutchinson, A phenomenological theory for strain gradient effects in plasticity, Journal of the Mechanics and Physics of Solids, Vol. 41, No. 12, pp. 1825-1857, 1993.
[18] D. C. Lam, F. Yang, A. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, Vol. 51, No. 8, pp. 1477-1508, 2003.
[19] M. Kahrobaiyan, M. Asghari, M. Ahmadian, Strain gradient beam element, Finite Elements in Analysis and Design, Vol. 68, pp. 63-75, 2013.
[20] M. H. Ghayesh, H. Farokhi, G. Alici, Size-dependent performance of microgyroscopes, International Journal of Engineering Science, Vol. 100, pp. 99-111, 2016.
[21] J. N. Reddy, Energy Principles and Variational Methods in Applied Mechanics, pp. 48-117, New York, John Wiley & Sons, 2017.
[22] M. Moghimi Zand, M. Ahmadian, Dynamic pull-in instability of electrostatically actuated beams incorporating Casimir and van der Waals forces, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 224, No. 9, pp. 2037-2047, 2010.
Modares Mechanical Engineering
Volume 18, Issue 1
March 2018
Pages 231-238