Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 149587

149587 - Nonlinearities and Linear Dynamic Range Across Multiple Modes in Nanomechanical Sensors 

A nanoelectromechanical systems (NEMS) resonator is a miniscule machine with feature sizes on the nanometer scale and has active mechanical and electrical components. NEMS are usually manufactured in simple geometries such as doubly clamped beams, cantilevers, or plates. Even a relatively weak drive force is enough to push a typical nanomechanical resonator into the nonlinear regime. Consequently, nonlinearities are widespread in nanomechanics and determine the critical characteristics of NEMS resonators. A thorough understanding of the nonlinear dynamics of higher eigenmodes of NEMS resonators would be beneficial for progress, given their use in applications and fundamental studies. As NEMS sensor work progresses, it has become more common to employ higher modes or multiple modes in applications, such as mass spectrometry of single molecules, viruses and bacteria. 

We characterize the nonlinearity and the linear dynamic range (LDR) of each eigenmode of two nanomechanical beam resonators with different intrinsic tension values up to eigenmode n = 11. On the experimental side, we use the electrothermal actuation technique to drive a NEMS beam into its nonlinear regime by gradually increasing the drive input power and sweeping the frequency near an eigenmode. We use optical interferometry to detect the vibrational amplitude of each eigenmode of the beam. We infer the modal nonlinear properties and critical parameters from the amplitude vs. frequency measurements. On the theoretical side, we analyze the Euler-Bernoulli beam equation with an intrinsic tension term that includes a nonlinear tension term resulting from the stretching of the beam at large amplitude oscillations. This nonlinear term gives rise to the geometric nonlinearity that is present in a typical NEMS resonator. We find that the intrinsic tension dominates the bending rigidity in all beams used in the study and simplify the tensioned beam equation to a string equation. Finally, using the hard clamp boundary conditions and string eigenmodes, we are able to solve the nonlinear dynamical equation to get an analytical expression for the nonlinear parameters of a NEMS beam under tension. We obtain excellent agreement between experimental and theoretical results.

We find that the modal Duffing constant increases as n⁴, while the critical amplitude for the onset of nonlinearity decreases as 1/n. The LDR, determined from the ratio of the critical amplitude to the thermal noise amplitude, increases weakly with n. Our findings are consistent with our theory treating the beam as a string, with the nonlinearity emerging from stretching at high amplitudes. These scaling laws, observed in experiments and validated theoretically, can be leveraged for pushing the limits of NEMS-based sensing even further.

 

Presenting Author: Monan Ma Boston University

Presenting Author Biography: Monan Ma is a PhD candidate in the department of Mechanical Engineering at Boston University.

Authors:

Monan Ma Boston University
Nathan Welles Virginia Tech
Mark Paul Virginia Tech
Kamil Ekinci Boston University