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Nonlinearity in nanomechanical cantilevers

Villanueva, L. G. and Karabalin, R. B. and Matheny, M. H. and Chi, D. and Sader, J. E. and Roukes, M. L. (2013) Nonlinearity in nanomechanical cantilevers. Physical Review B, 87 (2). Art. No. 024304. ISSN 1098-0121. doi:10.1103/PhysRevB.87.024304.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription DOIArticle
Matheny, M. H.0000-0002-3488-1083
Sader, J. E.0000-0002-7096-0627
Roukes, M. L.0000-0002-2916-6026
Additional Information:© 2013 American Physical Society. Received 27 March 2012; revised manuscript received 8 June 2012; published 28 January 2013. We would like to thank I. Bargatin and E. Myers for useful suggestions and discussions. L.G.V. acknowledges financial support from the European Commission (PIOF-GA-2008- 220682) and A. Boisen. J.E.S. acknowledges support from the Australian Research Council grants scheme.
Funding AgencyGrant Number
Marie Curie FellowshipPIOF-GA-2008-220682
Australian Research CouncilUNSPECIFIED
Issue or Number:2
Classification Code:PACS: 85.85.+j, 05.45.-a, 62.25.-g
Record Number:CaltechAUTHORS:20130221-084718989
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37040
Deposited By: Tony Diaz
Deposited On:22 Feb 2013 23:48
Last Modified:09 Nov 2021 23:26

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