Nonlinearity in nanomechanical cantilevers

Luis Guillermo Villanueva Torrijo, R. B. Karabalin, M. H. Matheny, D. Chi, J. E. Sader, M. L. Roukes

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development. In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory. These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304
    Original languageEnglish
    JournalPhysical Review B Condensed Matter
    Volume87
    Issue number2
    Pages (from-to)-
    ISSN0163-1829
    DOIs
    Publication statusPublished - 2013

    Keywords

    • PHYSICS,
    • ATOMIC-FORCE MICROSCOPE
    • BOUNDARY-CONDITIONS
    • RECTANGULAR-PLATES
    • BEAM
    • RESONATORS
    • VIBRATIONS
    • FREQUENCY
    • MASS

    Cite this

    Villanueva Torrijo, L. G., Karabalin, R. B., Matheny, M. H., Chi, D., Sader, J. E., & Roukes, M. L. (2013). Nonlinearity in nanomechanical cantilevers. Physical Review B Condensed Matter, 87(2), -. https://doi.org/10.1103/PhysRevB.87.024304