Sensors 2011, 11(9), 8203-8226; doi:10.3390/s110908203
Article

Analytical Modeling for the Bending Resonant Frequency of Multilayered Microresonators with Variable Cross-Section

1 Centro de Investigación en Micro y Nanotecnología, Universidad Veracruzana, Calzada Ruiz Cortines 455, 94292, Boca del Río, Veracruz, Mexico 2 Depto. Ingeniería Mecánica, DICIS, Universidad de Guanajuato, Carr. Salamanca-Valle 3.5+1.8 km, Palo Blanco, 36885, Salamanca, Guanajuato, Mexico 3 Depto. Ingeniería Molecular de Materiales, Centro de Física Aplicada y Tecnología Aplicada, UNAM, Boulevard Juriquilla 3001, 76230, Juriquilla, Queretaro, Mexico 4 Research Center for Ubiquitous MEMS and Micro Engineering (UMEMSME), National Institute of Advanced Industrial Science and Technology (AIST), Namiki 1-2-1, 305-8564, Tsukuba, Ibaraki, Japan
* Author to whom correspondence should be addressed.
Received: 18 July 2011; in revised form: 9 August 2011 / Accepted: 16 August 2011 / Published: 25 August 2011
(This article belongs to the Special Issue Modeling, Testing and Reliability Issues in MEMS Engineering 2011)
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Abstract: Multilayered microresonators commonly use sensitive coating or piezoelectric layers for detection of mass and gas. Most of these microresonators have a variable cross-section that complicates the prediction of their fundamental resonant frequency (generally of the bending mode) through conventional analytical models. In this paper, we present an analytical model to estimate the first resonant frequency and deflection curve of single-clamped multilayered microresonators with variable cross-section. The analytical model is obtained using the Rayleigh and Macaulay methods, as well as the Euler-Bernoulli beam theory. Our model is applied to two multilayered microresonators with piezoelectric excitation reported in the literature. Both microresonators are composed by layers of seven different materials. The results of our analytical model agree very well with those obtained from finite element models (FEMs) and experimental data. Our analytical model can be used to determine the suitable dimensions of the microresonator’s layers in order to obtain a microresonator that operates at a resonant frequency necessary for a particular application.
Keywords: bending resonant frequency; Euler-Bernoulli beam theory; Macaulay method; multilayered microresonator; Rayleigh’s method

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MDPI and ACS Style

Herrera-May, A.L.; Aguilera-Cortés, L.A.; Plascencia-Mora, H.; Rodríguez-Morales, Á.L.; Lu, J. Analytical Modeling for the Bending Resonant Frequency of Multilayered Microresonators with Variable Cross-Section. Sensors 2011, 11, 8203-8226.

AMA Style

Herrera-May AL, Aguilera-Cortés LA, Plascencia-Mora H, Rodríguez-Morales ÁL, Lu J. Analytical Modeling for the Bending Resonant Frequency of Multilayered Microresonators with Variable Cross-Section. Sensors. 2011; 11(9):8203-8226.

Chicago/Turabian Style

Herrera-May, Agustín L.; Aguilera-Cortés, Luz A.; Plascencia-Mora, Hector; Rodríguez-Morales, Ángel L.; Lu, Jian. 2011. "Analytical Modeling for the Bending Resonant Frequency of Multilayered Microresonators with Variable Cross-Section." Sensors 11, no. 9: 8203-8226.

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