Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams

L. A. Flores-Herrera, E. A. Merchán-Cruz, A. T. Velázquez-Sánchez, R. Rivera-Bias

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

The use in the past of mathematical techniques and methodologies to design macro-world structures in the past are now considered for designing micro-world structures. In this work, a computational algorithm for estimating natural frequencies and mode shapes of cantilever microbeams is presented. The methodology is based on the Rayleigh-Ritz method, which considers the potential and kinetic energies of the mechanical system. A proposed polynomial equation is first considered to establish the behavior of the microstructure. Together with the energy equations, an eigenvalue problem is constructed. The corresponding eigenvalues give an approximate estimation of the frequency values; the corresponding eigenvectors once substituted in the proposed polynomial describe the mode shapes of the microbeam for each frequency value. The results obtained with this methodology were compared with the finite element method. An interesting difference between the methodologies and the algorithm was found and the corresponding results are shown. © (2009) Trans Tech Publications.
Original languageAmerican English
Title of host publicationAlgorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams
Pages95-100
Number of pages84
ISBN (Electronic)0878493093, 9780878493098
DOIs
StatePublished - 1 Dec 2009
EventApplied Mechanics and Materials -
Duration: 1 Dec 2010 → …

Publication series

NameApplied Mechanics and Materials
Volume15
ISSN (Print)1660-9336

Conference

ConferenceApplied Mechanics and Materials
Period1/12/10 → …

Fingerprint

MEMS
Natural frequencies
Polynomials
Potential energy
Eigenvalues and eigenfunctions
Kinetic energy
Macros
Finite element method
Microstructure

Cite this

Flores-Herrera, L. A., Merchán-Cruz, E. A., Velázquez-Sánchez, A. T., & Rivera-Bias, R. (2009). Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams. In Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams (pp. 95-100). (Applied Mechanics and Materials; Vol. 15). https://doi.org/10.4028/www.scientific.net/AMM.15.95
Flores-Herrera, L. A. ; Merchán-Cruz, E. A. ; Velázquez-Sánchez, A. T. ; Rivera-Bias, R. / Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams. Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams. 2009. pp. 95-100 (Applied Mechanics and Materials).
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Flores-Herrera, LA, Merchán-Cruz, EA, Velázquez-Sánchez, AT & Rivera-Bias, R 2009, Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams. in Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams. Applied Mechanics and Materials, vol. 15, pp. 95-100, Applied Mechanics and Materials, 1/12/10. https://doi.org/10.4028/www.scientific.net/AMM.15.95

Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams. / Flores-Herrera, L. A.; Merchán-Cruz, E. A.; Velázquez-Sánchez, A. T.; Rivera-Bias, R.

Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams. 2009. p. 95-100 (Applied Mechanics and Materials; Vol. 15).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Flores-Herrera LA, Merchán-Cruz EA, Velázquez-Sánchez AT, Rivera-Bias R. Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams. In Algorithm for estimating natural frequencies and mode shapes of cantilever MEMS microbeams. 2009. p. 95-100. (Applied Mechanics and Materials). https://doi.org/10.4028/www.scientific.net/AMM.15.95