Nonlinearity in nanomechanical cantilevers

• Published in: Physical review. B, Condensed matter and materials physics Vol. 87; no. 2
• Main Authors: Villanueva, L. G., Karabalin, R. B., Matheny, M. H., Chi, D., Sader, J. E., Roukes, M. L.
• Format: Journal Article
• Language: English
• Published: 28-01-2013
• Subjects: Approximation; Condensed matter; Devices; Dynamical systems; Mathematical analysis; Nanostructure; Nonlinear dynamics; Nonlinearity
• ISSN: 1098-0121; 1550-235X
• DOI: 10.1103/PhysRevB.87.024304

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.