Abstract
We investigate the response of an electrically actuated clamped circular plate to a primary resonance excitation of its first axisymmetric mode using an analytical reduced-order model (macromodel). We discuss the inf luence of the number of modes retained in the discretization on the predicted solutions. The reduced-order model, which is a system of coupled nonlinear ordinary-dif ferential equations, accounts for general residual stress and strain hardening and allows for general material and geometric design variables. Our reduced-order model is robust up to the pull-in instability and is general enough to be an ef fective design tool for capacitive micromachined ultrasonic transducers.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Haller, M.I., Khuri-Yakub, B.T.: A surface micromachined electrostatic ultrasonic air transducer. In: Proc. of IEEE Ultrasonics Symp. Cannes, France, Vol. 2, pp. 1241–1244 (1994)
Ladabaum, I., Khuri-Yakub, B.T., Spoliansky, D., Haller, M.I.: Micromachined ultrasonic tranducers (MUTs). In: Proc. of IEEE Ultrasonics Symp, Seattle, WA Vol. 1, pp. 501–504 (1995)
Haller, M.I., Khuri-Yakub, B.T.: A surface micromachined electrostatic ultrasonic air transducer. IEEE Trans. Ultrason., Ferroelectr. Freq. Control 43, 1–6 (1996)
Jin, X., Ladabaum, I., Khuri-Yakub, B.T.: The microfabrication of capacitive ultrasonic transducers. J. Microelectromech. Syst. 7, 295–302 (1998)
Hansen, S.T., Turo, A., Degertekin, F.L., Khuri-Yakub, B.T.: Characterization of capacitive micromachined ultrasonic transducers in air using optical measurements. In: Proc. of IEEE Ultrasonics Symp. San Juan, Puerto Rico Vol. 1, pp. 947–950 (2000)
Yaralioglu, G.G., Ergun, A.S., Bayram, B., Marentis, T., Khuri-Yakub, B.T.: Residual stress and young's modulus measurement of capacitive micromachined ultrasonic transducer membranes. In: Proc. of IEEE Ultrasonics Symp., Atlanta, GA, Vol. 2, pp. 953–956 (2001)
Caronti, A., Majjad, H., Ballandras, S., Caliano, G., Carotenuto, R., Iula, A., Foglietti, V., Pappalardo, M.: Vibration maps of capacitive micromachined ultrasonic transducers by laser interferometry. IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control 49, 289–292 (2002)
Huang, Y., Ergun, A.S., Hæ ggström, E., Badi, M.H., Khuri-Yakub, B.T.: Fabricating capacitive micromachined ultrasonic transducers with wafer-bonding technology. J. Microelectromech. Syst. 12, 128–137 (2003)
Yaralioglu, G.G., Ergun, A.S., Bayram, B., Hæ ggström, E., Khuri-Yakub, B.T.: Calculation and measurement of electromechanical coupling coefficient of capacitive micromachined ultrasonic transducers. IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control 50, 449–456 (2003)
Ladabaum, I., Jin, X., Soh, H.T., Pierre, F., Atalar, A., Khuri-Yakub, B.T.: Microfabricated ultrasonic transducers: towards robust models and immersion devices. In: Proc. of IEEE Ultrasonics Symp., San Antonio, TX Vol. 1, pp. 335–338 (1996)
Jin, X., Oralkan, Ö., Degertekin, F.L., Khuri-Yakub, B.T.: Characterization of one-dimensional capacitive micromachined ultrasonic immersion transducer arrays. IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control 48, 750–760 (2001)
Ergun, A.S., Cheng, C-H., Demirci, U., Khuri-Yakub, B.T.: Fabrication and characterization of 1-dimensional and 2-dimensional capacitive Micromachined ultrasonic transducer (CMUT) arrays for 2-dimensional and volumetric ultrasonic imaging. In: Proc. of Oceans '02 MTS/IEEE, Biloxi, MS Vol. 4, pp. 2361–2367 (2002)
Bozkurt, A., Degertekin, F.L., Atalar, A., Khuri-Yakub, B.T.: Analytic modeling of loss and cross-coupling in capacitive micromachined ultrasonic transducers. In: Proc. of IEEE Ultrasonics Symp., Sendai, Japan, Vol. 2, pp. 1025–1028 (1998)
Bozkurt, A., Ladabaum, I., Atalar, A., Khuri-Yakub, B.T.: Theory and analysis of electrode size optimization for capacitive microfabricated ultrasonic transducers. IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control. 46, 1364–1374 (1999)
Bayram, B., Yaralioglu, G.G., Ergun, A.S., Khuri-Yakub, B.T.: Influence of the electrode size and location on the performance of a CMUT. In: Proc. of IEEE Ultrasonics Symp., Atlanta, GA Vol. 2, pp. 949–952 (2001)
Buhrdorf, A., Ahrens, O., Binder, J.: Capacitive micromachined ultrasonic transducers and their application. In: Proc. of IEEE Ultrasonics Symp., Atlanta, GA Vol. 2, pp. 933–940 (2001)
Pelesko, J.A., Chen, X.Y.: Electrostatic deflections of circular elastic membranes. J. Electrostatics Vol. 57, 1–12 (2003)
Yu, M., Balachandran, B.: Sensor diaphragm under initial tension: linear analysis. Exp. Mech. Vol. 45, 123–129 (2005)
Li, G., Aluru, N.R.: Linear, nonlinear, and mixed-regime analysis of electrostatic MEMS. Sensors and Actuators A Vol. 91, 278–291 (2001)
Vogl, G.W., Nayfeh, A.H.: A reduced-order model for electrically actuated clamped circular plates. In: Proc. of ASME Design Engineering Technical Conf., Chicago, IL, DETC VIB-48530 (2003)
Vogl, G.W., Nayfeh, A.H.: A reduced-order model for electrically actuated clamped circular plates. J. Micromech. and Microeng. 15, 684–690 (2005)
Nayfeh, A.H.: Perturbation Methods, Wiley, New York, pp. 228–236 (1973)
Nayfeh, A.H.: Introduction to Perturbation Techniques, Wiley, New York, pp. 122–127 (1981)
Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations, Wiley, New York, pp. 366–367 (1979)
Nayfeh, A.H.: Nonlinear Interactions: Analytical, Computational, and Experimental Methods, Wiley, New York, p. xvi (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vogl, G.W., Nayfeh, A.H. Primary resonance excitation of electrically actuated clamped circular plates. Nonlinear Dyn 47, 181–192 (2007). https://doi.org/10.1007/s11071-006-9064-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-006-9064-6