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    Frequency Shifts of Micro and Nano Cantilever Beam Resonators Due to Added Masses

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    Type
    Article
    Authors
    Bouchaala, Adam M.
    Nayfeh, Ali H.
    Younis, Mohammad I. cc
    KAUST Department
    Mechanical Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2016-03-21
    Online Publication Date
    2016-03-21
    Print Publication Date
    2016-05-25
    Permanent link to this record
    http://hdl.handle.net/10754/621548
    
    Metadata
    Show full item record
    Abstract
    We present analytical and numerical techniques to accurately calculate the shifts in the natural frequencies of electrically actuated micro and nano (carbon nanotubes (CNTs)) cantilever beams implemented as resonant sensors for mass detection of biological entities, particularly Escherichia coli (E. coli) and prostate specific antigen (PSA) cells. The beams are modeled as Euler-Bernoulli beams, including the nonlinear electrostatic forces and the added biological cells, which are modeled as discrete point masses. The frequency shifts due to the added masses of the cells are calculated for the fundamental and higher-order modes of vibrations. Analytical expressions of the natural frequency shifts under a direct current (DC) voltage and an added mass have been developed using perturbation techniques and the Galerkin approximation. Numerical techniques are also used to calculate the frequency shifts and compared with the analytical technique. We found that a hybrid approach that relies on the analytical perturbation expression and the Galerkin procedure for calculating accurately the static behavior presents the most computationally efficient approach. We found that using higher-order modes of vibration of micro-electro-mechanical-system (MEMS) beams or miniaturizing the sizes of the beams to nanoscale leads to significant improved frequency shifts, and thus increased sensitivities. © 2016 by ASME.
    Citation
    Bouchaala A, Nayfeh AH, Younis MI (2016) Frequency Shifts of Micro and Nano Cantilever Beam Resonators Due to Added Masses. Journal of Dynamic Systems, Measurement, and Control 138: 091002. Available: http://dx.doi.org/10.1115/1.4033075.
    Publisher
    ASME International
    Journal
    Journal of Dynamic Systems, Measurement, and Control
    DOI
    10.1115/1.4033075
    ae974a485f413a2113503eed53cd6c53
    10.1115/1.4033075
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Mechanical Engineering Program

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