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Analytical Modeling for the Bending Resonant Frequency of Multilayered Microresonators with Variable Cross-Section
Centro de Investigación en Micro y Nanotecnología, Universidad Veracruzana, Calzada Ruiz Cortines 455, 94292, Boca del Río, Veracruz, Mexico
Depto. Ingeniería Mecánica, DICIS, Universidad de Guanajuato, Carr. Salamanca-Valle 3.5+1.8 km, Palo Blanco, 36885, Salamanca, Guanajuato, Mexico
Depto. Ingeniería Molecular de Materiales, Centro de Física Aplicada y Tecnología Aplicada, UNAM, Boulevard Juriquilla 3001, 76230, Juriquilla, Queretaro, Mexico
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
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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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.
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.
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.