Nonlinear Dynamics

, Volume 92, Issue 2, pp 287–304 | Cite as

A micromechanical mass sensing method based on amplitude tracking within an ultra-wide broadband resonance

  • Randi Potekin
  • Seok Kim
  • D. Michael McFarland
  • Lawrence A. Bergman
  • Hanna Cho
  • Alexander F. Vakakis
Original Paper


We propose a mass sensing scheme in which amplitude shifts within a nonlinear ultra-wide broadband resonance serve as indicators for mass detection. To achieve the broad resonance bandwidth, we considered a nonlinear design of the resonator comprised of a doubly clamped beam with a concentrated mass at its center. A reduced-order model of the beam system was constructed in the form of a discrete spring-mass system that contains cubic stiffness due to axial stretching of the beam in addition to linear stiffness (Duffing equation). The cubic nonlinearity has a stiffening effect on the frequency response causing nonlinear bending of the frequency response toward higher frequencies. Interestingly, we found that the presence of the concentrated mass broadens the resonant bandwidth significantly, allowing for an ultra-wide operational range of frequencies and response amplitudes in the proposed mass sensing scheme. A secondary effect of the cubic nonlinearity is strong amplification of the third harmonic in the beam’s response. We computationally study the sensitivity of the first and third harmonic amplitudes to mass addition and find that both metrics are more sensitive than the linearized natural frequency and that in particular, the third harmonic amplitude is most sensitive. This type of open-loop mass sensing avoids complex feedback control and time-consuming frequency sweeping. Moreover, the mass resolution is within a functional range, and the design parameters of the resonator are reasonable from a manufacturing perspective.


Broadband nonlinear resonator Mass sensor Third harmonic 



This work was financially supported in part by the National Science Foundation, Grant NSF CMMI 14-638558 at the University of Illinois at Urbana-Champaign, and Grants CMMI-1619801 at The Ohio State University. This support is gratefully acknowledged.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Randi Potekin
    • 1
  • Seok Kim
    • 1
  • D. Michael McFarland
    • 2
  • Lawrence A. Bergman
    • 2
  • Hanna Cho
    • 3
  • Alexander F. Vakakis
    • 1
  1. 1.Department of Mechanical Science and EngineeringUniversity of IllinoisUrbanaUSA
  2. 2.Department of Aerospace EngineeringUniversity of IllinoisUrbanaUSA
  3. 3.Department of Mechanical and Aerospace EngineeringOhio State UniversityColumbusUSA

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