Nonlinearity in nanomechanical cantilevers

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

Damage precursor detection for structures subjected to rotational base vibration

This paper presents a nonlinear dynamic methodology for monitoring precursors of fatigue damage in metallic structures under variable rotational base excitation. The methodology accounts for important nonlinearities due to the complex loading generated by variable rotation and structural degradation. The sources of the nonlinearities include: structural stiffening due to gyroscopic motion and high-response amplitude at the fundamental mode, softening due to inertial forces and gyroscopic loads, and localized microscopic material damage and micro-plasticity. The loading intensity and number of vibration cycles increase the influence of these effects. The change in the dynamic response due to fatigue damage accumulation is experimentally investigated by exciting a cantilever beam at variable rotational base motions. The observed fatigue evolution in the material microstructure at regions of large stresses (and the resulting progressive structural softening) is tracked by quantifying the growth in the tip response, the change in the fundamental natural frequency of the beam and the skewedness of the stepped-sine response curve. Previous understanding of the structural dynamic behavior is necessary to ascertain the damage precursor location and evolution. Nanoindentation studies near the beam clamped boundary are conducted to confirm the gradual progression in the local mechanical properties as a function of loading cycles, and microstructural studies are conducted to obtain qualitative preliminary insights into the microstructure evolution. This study demonstrates that careful monitoring of the nonlinearities in the structural dynamic response can be a sensitive parameter for detection of damage precursors