Analysis of Static Pull-in Instability and Nonlinear Vibrations of an Functionally Graded Micro-Resonator Beam

Document Type : Research Article

Authors

Department of Mechanical Engineering, Shiraz University, Shiraz, Iran

Abstract

In This paper, the behavior of a functionally graded micro-resonator that is excited by thecombination of DC electrostatic force and AC harmonic force, Casimir force, the uniform temperaturechange is investigated based on the Euler-Bernoulli beam theory and the nonlinear von-Karman strain. Itis assumed that material properties follow exponential law distributions through the thickness direction.The principle of minimum total potential energy and the modified couple stress theory are used to derivethe nonlinear governing differential equation of micro-beam. Static differential equations are solvedby using the differential quadrature method. The effects of temperature change, material length scaleparameter and power distributions model on pull-in voltage are investigated. Applying perturbationmethod with multiple scales technique and numerical integration of the second order nonlinear ordinarydifferential equation, an approximation for the response of the micro-beam to the primary-resonanceexcitation is obtained.

Keywords

Main Subjects

References

[1] M. I. Younis, E. M. Abdel-Rahman, and A. H. Nayfeh, Static and dynamic behavior of an electrically excited resonant microbeam, in 43 rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, CO, 2002.
[2] H. M. Ouakad, A. M. Alofi, and A. H. Nayfeh, Dynamic Analysis of Multilayers Based MEMS Resonators, Mathematical Problems in Engineering, 2017.
[3] A. H. Nayfeh and D. T. Mook, Nonlinear oscillations: John Wiley & Sons, 2008.
[4] S. Azizi, M. R. Ghazavi, G. Rezazadeh, I. Ahmadian, and C. Cetinkaya, Tuning the primary resonances of a micro resonator, using piezoelectric actuation, Nonlinear dynamics, 76, (2014) 839-852.
[5] F. Najar, S. Choura, E. Abdel-Rahman, S. El-Borgi, and A. Nayfeh, Dynamics of Variable-Geometry Electrostatic Microactuators, in ASME 2006 International Mechanical Engineering Congress and Exposition, (2006) 273-281.
[6] X. Jia, J. Yang, S. Kitipornchai, and C. W. Lim, Pull-in instability and free vibration of electrically actuated poly-SiGe graded micro-beams with a curved ground electrode, Applied Mathematical Modelling, 36 (2012) 1875-1884.
[7] A. Witvrouw and A. Mehta, The use of functionally graded poly-SiGe layers for MEMS applications, in Materials science forum, (2005) 255-260.
[8] M. Gromova, A. Mehta, K. Baert, and A. Witvrouw, Characterization and strain gradient optimization of PECVD poly-SiGe layers for MEMS applications, Sensors and Actuators A: Physical, 130 (2006) 403-410.
[9] D. Hasanyan, R. Batra, and S. Harutyunyan, Pull-in instabilities in functionally graded microthermoelectromechanical systems, Journal of Thermal Stresses, 31(2008) 1006-1021.
[10] M. Asghari, M. Ahmadian, M. Kahrobaiyan, and M. Rahaeifard, On the size-dependent behavior of functionally graded micro-beams, Materials & Design (1980-2015), 31 (2010) 2324-2329.
[11] X. Jia, J. Yang, S. Kitipornchai, and C. Lim, Forced vibration of electrically actuated FGM micro-switches, Procedia Engineering, 14 (2011) 280-287.
[12] B. Mohammadi-Alasti, G. Rezazadeh, A.-M. Borgheei, S. Minaei, and R. Habibifar, On the mechanical behavior of a functionally graded micro-beam subjected to a thermal moment and nonlinear electrostatic pressure, Composite Structures, 93 (2011) 1516-1525.
[13] M. Rezaee, N. Sharafkhani, and A. Chitsaz, Electrostatically actuated FGM micro-tweezer under the thermal moment, Microsystem technologies, 19 (2013) 1829-1837.
[14] X. Jia, L. Ke, C. Feng, J. Yang, and S. Kitipornchai, Size effect on the free vibration of geometrically nonlinear functionally graded micro-beams under electrical actuation and temperature change, Composite Structures, 133 (2015) 1137-1148.
[15] R. Gholami, R. Ansari, and H. Rouhi, Studying the effects of small scale and Casimir force on the non-linear pull-in instability and vibrations of FGM microswitches under electrostatic actuation, International Journal of Non-Linear Mechanics, 77 (2015) 193-207.
[16] L. C. Trinh, H. X. Nguyen, T. P. Vo, and T.-K. Nguyen, Size-dependent behaviour of functionally graded microbeams using various shear deformation theories based on the modified couple stress theory, Composite Structures, 154 (2016) 556-572.
[17] X. Xie, H. Zheng, and H. Yang, Indirect radial basis function approach for bending, free vibration and buckling analyses of functionally graded microbeams, Composite Structures, 131 (2015) 606-615.
[18] N. Fleck, G. Muller, M. Ashby, and J. Hutchinson, Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia, 42 (1994) 475-487.
[19] J. Stölken and A. Evans, A microbend test method for measuring the plasticity length scale, Acta Materialia, 46 (1998) 5109-5115.
[20] M. Attia and S. Mohamed, Nonlinear modeling and analysis of electrically actuated viscoelastic microbeams based on the modified couple stress theory, Applied Mathematical Modelling, 41 (2017) 195-222.
[21] S. K. Lamoreaux, The Casimir force: background, experiments, and applications, Reports on progress in Physics, 68 (2004). 201.
[22] P. Ganguly and G. R. Desiraju, Van der Waals and polar intermolecular contact distances: Quantifying supramolecular synthons, Chemistry–An Asian Journal, 3 (2008) 868-880.
[23] B. D. Agarwal, L. J. Broutman, and K. Chandrashekhara, Analysis and performance of fiber composites: John Wiley & Sons, 2006.
[24] H.-S. Shen, Functionally graded materials: nonlinear analysis of plates and shells: CRC press, 2016.
[25] K. B. Lee, Principles of microelectromechanical systems: John Wiley & Sons, 2011.
[26] M. Eltaher, A. Alshorbagy, and F. Mahmoud, Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams, Composite Structures, 99, (2013) 193-201.
[27] F. Najar, S. Choura, E. M. Abdel-Rahman, S. El-Borgi, and A. Nayfeh, Dynamic analysis of variable-geometry electrostatic microactuators, Journal of micromechanics and microengineering, 16(2006) 2449.
[28] R. Legtenberg and H. A. Tilmans, Electrostatically driven vacuum-encapsulated polysilicon resonators Part I. Design and fabrication, Sensors and Actuators A: Physical, 45 (1994) 57-66.
[29] G. Kerschen, M. Peeters, J.-C. Golinval, and A. F. Vakakis, Nonlinear normal modes, Part I: A useful framework for the structural dynamicist, Mechanical Systems and Signal Processing, 23 (2009) 170-194.
Amirkabir Journal of Mechanical Engineering
Volume 51, Issue 1
March and April 2019
Pages 119-132

Files

Share

How to cite

Statistics