MechE PhD Final Oral Defense: Monan Ma

TITLE: FUNDAMENTALS OF NONLINEAR NANOMECHANICAL RESONATORS: ACTUATION, SCALING, AND FLUCTATION-DRIVEN DYNAMICS

ABSTRACT:Nanoelectromechanical systems (NEMS), which consist of nanomechanical resonators with integrated transducers, are highly precise sensing devices because even small changes in their environment (e.g., force, viscosity, or electric field) produce measurable shifts in resonance frequency and amplitude in one or multiple eigenmodes. In a typical linear operation, the NEMS response scales linearly with the applied stimulus. However, continued device miniaturization and operation at higher signal levels drive NEMS beyond the linear regime, where both extrinsic nonlinearities from transducers and intrinsic nonlinearities from the mechanical structure significantly change the device behavior. A quantitative understanding of how these nonlinearities emerge under deterministic and stochastic forces, scale across modes, and how they affect sensing has remained incomplete. This dissertation addresses this gap through extensive experiments on nonlinear NEMS dynamics under deterministic and stochastic forces. First, we develop and experimentally validate a numerical model for electrothermal transducers in NEMS. By coupling time-domain heat transport with frequency-domain structural response in COMSOL, the model predicts temperature oscillations, bending moments, and mode-dependent displacements over a broad range of operating conditions. The model determines thermodynamic temperature and quantifies transducer-related extrinsic nonlinearities, as well as transduction efficiency and bandwidth in vacuum, air, and water. Second, we measure intrinsic nonlinearity across 11 eigenmodes of NEMS devices and establish mode-dependent scaling laws. The results show that the stiffening nonlinearity originates from the device geometry and increases rapidly with mode number, whereas sensitivity gains from higher modes remain subtle due to dissipation dilution. The findings provide quantitative guidance for choosing operating modes and geometries for NEMSbased sensing applications. Third, we investigate fluctuation-driven nonlinear dynamics by applying Gaussian force noise to induce nonlinear NEMS fluctuations at high effective temperatures. From the measured response statistics, we reconstruct the emergence of nonlinear potential energy and higher-order moments of the probability distribution, achieving excellent agreement with theory. This study provides an experimental method for mapping nonlinear physical properties to the statistics of a nonlinear fluctuating system.

COMMITTEE: ADVISOR Professor Kamil Ekinici, ME/MSE; CHAIR Professor James Chapman, ME/MSE; Professor Scott Bunch, ME/MSE; Professor Greg McDaniel, ME/MSE; Professor Mark Paul, ME