Investigation of instability and vibration behavior of microbeam-gyroscope with considering distribution of proof mass

Authors

1 Assis. Prof., Mech. Eng., Golpayegan Univ. of Tech., Golpayegan, Iran.

2 MSc., Mech. Eng., Golpayegan Univ. of Tech., Golpayegan, Iran.

Abstract

In this research, vibration behavior of a microgyroscope including beam structure is investigated. microgyroscope consists of a microcantilever beam and distributed proof mass that is actuated by electrostatic force. A developed model and formulation based on the distributed assumption for proof mass are presented to investigate the instability and vibration behavior of beam microgyroscope. Considering distributed assumption for proof mass, electrostatic force changes from concentrated force to distributed force and produces a moment that is effective on the mechanical behavior of the gyroscope.The equations of motion are reduced by Galerkin’s method and solved via numerical and analytical techniques. An important nondimensional parameter named as nondimensional length parameter is presented which it is the ratio of the proof mass length to beam length. Effects of the nondimensional length parameter on the static, dynamic, vibration behaviors and natural frequency of the microsyetem are investigated. Results show that by increasing the nondimensional parameter, the differences between the results of concentration and distribution hypothesizes for proof mass increase.

Keywords

Main Subjects

References

[1] Acar C, Shkel A (2008) MEMS vibratory gyroscopes: structural approaches to improve robustness. Springer, US.
[2] Armenise MN (2011) Advances in Gyroscope Technologies. Springer, Berlin Heidelberg.
[3] Mohite S, Patil N, Pratap R (2006) Design, modelling and simulation of vibratory micromachined gyroscopes. J Phys Conf Ser 34: 757-763.
[4] Hong YS, Lee JH, Kim SH (2000) A laterally driven symmetric micro-resonator for gyroscopic applications. J Micromech Microengineering 10: 452.
[5] Mojahedi M, Ahmadian M, Firoozbakhsh K (2014) The influence of the intermolecular surface forces on the static deflection and pull-in instability of the micro/nano cantilever gyroscopes. Compos Part B:Eng 56: 336-343.
[6] Mojahedi M, Ahmadian MT, Firoozbakhsh K (2013) Oscillatory behavior of an electrostatically actuated microcantilever gyroscope Int J Struct Stab Dy 13: 24.
[7] Mojahedi M, Ahmadian MT, 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: 1350032 (26 page).
[8] Ghommem M, Nayfeh AH, Choura S, Najar F, Abdel-Rahman EM (2010) Modeling and performance study of a beam microgyroscope. J Sound Vib 329: 4970-4979.
[9] Ansari M (2008) Modeling and vibration analysis of a rocking–mass gyroscope system. MASc Thesis. Canada University of Ontario Institute of Technology.
[10] Bhadbhade V, Jalili N, Nima Mahmoodi S (2008) A novel piezoelectrically actuated flexural/torsional vibrating beam gyroscope J Sound Vib 311: 1305-1324.
[11] Jeong C, Seok S, Lee B, Kim H, Chun K (2004) A study on resonant frequency and Q factor tunings for MEMS vibratory gyroscopes. J Micromech Microengineering 14: 1530.
[12] Ghommem M, Abdelkefi A (2017) Performance analysis of differential-frequency microgyroscopes made of nanocrystalline material. Int J Mech Sci 133: 495-503.
[13] Mojahedi M, Ahmadian M, Firoozbakhsh K (2014) The oscillatory behavior, static and dynamic analyses of a micro/nano gyroscope considering geometric nonlinearities and intermolecular forces. Acta Mechanica Sinica.
[14] Sharifinsab E, Mojahedi M (2018) Nonlinear Vibration of Size Dependent Microresonators with an Electrostatically Actuated Proof Mass. Int J Struct Stab Dy 1850057.
[15] Bina R, Mojahedi M (2017) Static Deflection, Pull-in Instability and Oscillatory Behavior of the Electrostatically Actuated Microresonator with a Distributed Proof Mass Considering Non-Classical Theory. Int J Appl Mech 1750023.
[16] Nayfeh AH, Pai PF (2004) Linear and nonlinear structural mechanics. Wiley-VCH, Strauss GmbH Morlenbach, Germany.
[17] Batra R, Porfiri M, Spinello D (2008) Vibrations and pull-in instabilities of microelectromechanical von Kármán elliptic plates incorporating the Casimir force. J Sound Vib 315: 939-960.
[18] Batra RC, Pofiri M, Spinello D (2007) Capacitance estimate for electrostatically actuated narrow microbeams. Micro Nano 1: 71-73.
[19] Thomson W, Dahleh M (1998) Theory of vibration with applications. Prentice Hall, New Jersey.
[20] Fazel R, Jalili MM, Abootorabi MM (2017) Determination of Stability Regions of Wheel and Workpiece in Plunge Grinding Process Using a 3-D Workpiece Model. Journal of Solid and Fluid Mechanics 7: 67-82.
[21] Ghazi R, Payghaneh G, Shahgholi M (2017) Resonance analysis and free nonlinear vibrations of a nanocomposite with internal damping. Modares Mechanical Engineering 17: 98-104.
[22] Pirmoradian M, Karimpour H (2017) Nonlinear Effects on Parametric Resonance of a Beam Subjected to Periodic Mass Transition. Modares Mechanical Engineering 17: 284-292.
[23] Nayfeh AH, Mook DT (2008) Nonlinear oscillations. Wiley-VCH, US.
Journal of Solid and Fluid Mechanics
Volume 8, Issue 2
July 2018
Pages 93-106

Files

Share

How to cite

Statistics