30. Resonance vibration of an optical fiber micro‑cantilever using electro-thermal actuation

Mojtaba Komeili1, Aydin Ahrabi2, Carlo Menon3

MENRVA Research Group, School of Engineering Science, Simon Fraser University,
Metro Vancouver, Canada

3Corresponding author

E-mail: 1mojtaba.komeili@gmail.com, 2aaa91@sfu.ca, 3cmenon@sfu.ca

Received 4 February 2017; received in revised form 19 February 2017; accepted 23 February 2017

DOI https://doi.org/10.21595/mme.2017.18228


Abstract. The resonance excitation of an optical fiber actuated by a conductive wire is studied in this paper. A novel approach based on exciting the micro-cantilever fiber at a location close to its base is proposed for this purpose. Analytical modeling is conducted on the mechanical models of this system in order to predict its behavior. The continuous Euler‑Bernoulli beam equation with the effect of surrounding fluid medium is formulated as a boundary value problem. The natural frequencies of the system and its harmonic response are expanded analytically, and results are verified using Finite Element analysis. The obtained analytical solutions are used to draw conclusions on the response of the system and suggestions to optimize its performance are presented. In order to verify the idea in practice, an experimental setup that can closely resemble the system under consideration is made in the laboratory and its response to a periodic input with different frequencies are recorded. Comparison between the results of analytical formulation and experimental observations highlights the effectiveness of suggested technique in resonance vibration of optical fibers.

Keywords: micro-electro-mechanical systems (MEMS), micro-cantilever beam, thermal excitation, harmonic response, resonance vibration.


[1]        Seibel E., Smithwick Q. Unique features of optical scanning, single fiber endoscopy. Lasers in Surgery and Medicine, Vol. 183, 2002, p. 177‑183.

[2]        Liu X., Chen Y., Cobb M., Li X. Rapid-scanning miniature endoscope for real-time forward-imaging optical coherence tomography. Conference on Lasers and Electro-Optics, San Francisco, 2004, p. 3‑4.

[3]        Lee C., Engelbrecht C., Soper T., Helmchen F., Seibel E. Scanning fiber endoscopy with highly flexible, 1 mm catheterscopes for wide-field, full-color imaging. Journal of Biophotonics, Vol. 3, Issues 5‑6, 2010, p. 385‑407.

[4]        Munce N., Wright G., Mariampillai A., Standish B., Leung M., Tan L., Lee K., Courtney K., Teitelbaum A., Strauss B., Vitkin A., Yang V. Doppler optical coherence tomography for interventional cardiovascular guidance: in vivo feasibility and forward-viewing probe flow phantom demonstration. Journal of Biomedical Optics, Vol. 15, Issue 1, 2010, p. 011103‑1.

[5]        Munce N., Mariampillai A., Standish B., Pop M., Anderson K., Liu G., Luk T., Courtney B., Wright G., Vitkin I., Yang V. Electrostatic forward-viewing scanning probe for Doppler optical coherence tomography using a dissipative polymer catheter. Optics Letters, Vol. 33, Issue 7, 2008, p. 657.

[6]        Joos K., Shen J. Miniature real-time intraoperative forward-imaging optical coherence tomography probe. Biomedical Optics Express, Vol. 4, Issue 8, 2013, p. 1342‑1350.

[7]        Maluf N., Williams K. Introduction to Microelectromechanical Systems Engineering. Artech House Inc., Boston, 2004.

[8]        Jiang L., Cheung R., Hedley J., Hassan M., Harris J., Burdess J., Mehregany M., Zorman C. SiC cantilever resonators with electrothermal actuation. Sensors and Actuators A: Physical, Vol. 128, Issue 2, 2006, p. 376‑386.

[9]        Mestrom R., Fey R., Beek J., Phan K., Nijmeijer H. Modelling the dynamics of a MEMS resonator: simulations and experiments. Sensors and Actuators A: Physical, Vol. 142, Issue 2, 2008, p. 306‑315.

[10]     Rezazadeh G., Fathalilou M., Shabani R., Tarverdilou S., Talebian S. Dynamic characteristics and forced response of an electrostatically-actuated microbeam subjected to fluid loading. Microsystem Technologies, Vol. 15, Issue 9, 2009, p. 1355‑1363.

[11]     Ouakad H., Younis M. The dynamic behavior of MEMS arch resonators actuated electrically. International Journal of Non-Linear Mechanics, Vol. 45, Issue 7, 2010, p. 704‑713.

[12]     Iloh T., Ohashi T., Siiga T. Piezoelectric cantilever array for multi-probe scanning force microscopy. 9th Annual International Workshop on Micro Electro Mechanical Systems, 1996, p. 451‑455.

[13]     Zhang W., Meng G., Li H. Adaptive vibration control of micro-cantilever beam with piezoelectric actuator in MEMS. The International Journal of Advanced Manufacturing Technology, Vol. 28, Issues 3‑4, 2005, p. 321‑327.

[14]     Blom F. Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry. Journal of Vacuum Science and Technology B: Microelectronics and Nanometer Structures, Vol. 10, Issue 1, 1992, p. 19.

[15]     Chen W., Chu C., Hsieh J., Fang W. A reliable single-layer out-of-plane micromachined thermal actuator. Sensors and Actuators A: Physical, Vol. 103, Issues 1‑2, 2003, p. 48‑58.

[16]     Lobontiu N., Garcia E. Mechanics of Microelectromechanical Systems. Kluwer Academic Publishers, New York, 2005.

[17]     Jianqiang H., Changchun Z., Junhua L., Yongning H. Dependence of the resonance frequency of thermally excited microcantilever resonators on temperature. Sensors and Actuators A: Physical, Vol. 101, Issues 1‑2, 2002, p. 37‑41.

[18]     Rahafrooz A., Pourkamali S. High-frequency thermally actuated electromechanical resonators with piezoresistive readout. IEEE Transactions on Electron Devices, Vol. 58, Issue 4, 2011, p. 1205‑1214.

[19]     Sinclair M. A high frequency resonant scanner using thermal actuation. 15th IEEE International Conference on Micro Electro Mechanical Systems, 2002, p. 698‑701.

[20]     Comtois J., Michalicek M., Barron C. Electrothermal actuators fabricated in four-level planarized surface micromachined polycrystalline silicon. Sensors and Actuators A: Physical, Vol. 70, Issues 1‑2, 1998, p. 23‑31.

[21]     Komeili M., Menon C. Analysis and design of thermally actuated micro-cantilevers for high frequency vibrations using finite element method. World Journal of Mechanics, Vol. 6, Issue 3, 2016, p. 94‑107.

[22]     Komeili M., Menon C. Robust design of thermally actuated micro-cantilever using numerical simulations. International Journal of Simulation Modelling, Vol. 15, Issue 3, 2016.

[23]     Komeili M., Menon C. Modelling a micro-cantilever vibrating in vacuum, gas or liquid under thermal base excitation. Mechanics Research Communications, Vol. 73, 2016, p. 39‑46.

[24]     Grigorov A. A longitudinal thermal actuation principle for mass detection using a resonant micro‑cantilever in a fluid medium. Microelectronic Engineering, Vols. 73‑74, 2004, p. 881‑886.

[25]     Thomson W. Theory of Vibration with Applications. CRC Press, New York, 1996.

[26]     Beer F., Johnston R. DeWolf J., Mazurek D. Mechanics of Materials. McGraw-Hill, Boston, 2011.

[27]     Asmar N. Partial Differential Equations and Boundary Value Problems with Fourier Series. Boston, 2004.

[28]     Sader J. Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. Journal of Applied Physics, Vol. 84, Issue 1, 1998, p. 64.

[29]     Rosenhead L. Laminar Boundary Layers. Clarendon Press, Oxford, 1963.

[30]     Ogata K. Modern Control Engineering. Toronto, 2012.

[31]     Norton M., Karczub D. Fundamentals of Noise and Vibration Analysis for Engineers. Cambridge University Press, Cambridge, 2003.

[32]     Lobontiu N. Dynamics of Microelectromechanical Systems. Springer US, Boston, MA, 2007.

[33]     Van Eysden C., Sader J. Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: arbitrary mode order. Journal of Applied Physics, Vol. 101, Issue 15, 2007, p. 44908-0-11.

[34]     Sader J., Lee J., Manalis S. Energy dissipation in microfluidic beam resonators: dependence on mode number. Journal of Applied Physics, Vol. 108, Issue 11, 2010, p. 114507.

Cite this article

Komeili Mojtaba, Ahrabi Aydin, Menon Carlo Resonance vibration of an optical fiber micro‑cantilever using electro‑thermal actuation. Mathematical Models in Engineering, Vol. 3, Issue 1, 2017, p. 1‑16.


Mathematical Models in Engineering. June 2017, Volume 3, Issue 1

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