Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published December 1, 2023 | v1
Journal Article Open

Effect of intramodal and intermodal nonlinearities on the flexural resonant frequencies of cantilevered beams

  • 1. ROR icon California Institute of Technology

Abstract

Sensing applications that utilize nanomechanical resonators require careful control of nonlinear effects in their eigenmodes to ensure robust measurement. While the effect of intra- and intermodal nonlinearities on the resonant frequencies of doubly clamped elastic beams have been widely studied using theory and experiment, commensurate studies on cantilevered beams are limited in comparison. Here, we present such a detailed study that includes an explicit and simple formula for the flexural resonant frequencies of slender cantilevered beams that accounts for intra- and intermodal nonlinearities. Using this general theory, numerical results for the modal nonlinear coefficients are tabulated for the first 20 flexural eigenmodes of cantilevered beams possessing uniform cross sections. The accuracy of this theory, and the effect of cantilever aspect ratio (length/width) on these nonlinear coefficients, is explored using high-accuracy laser Doppler vibrometry experiments. We anticipate that these results will find utility in single- and multimode applications, where the effect of finite oscillation amplitude on the cantilever resonant frequencies can significantly impact measurement design and interpretation.

Copyright and License

© 2023 American Physical Society.

Acknowledgement

The authors thank M. Matheny for useful discussions. J.E.S. and M.L.R. acknowledge support from the Kavli Nanoscience Institute at Caltech. This research was partly supported by the Ministero dell'Istruzione, dell'Università e della ricerca (MIUR), through the PRIN2017–Prot.20172TZHYX grant.

Files

PhysRevB.108.224303.pdf
Files (882.3 kB)
Name Size Download all
md5:2872e3e2bdd58afd965f5c3016fffa0a
882.3 kB Preview Download

Additional details

Created:
December 6, 2023
Modified:
January 9, 2024