  Euler-Bernoulli beam theory is widely used to successfully predict the linear
dynamics of micro- and nano-cantilever 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
ultra-linear 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.
