MS10.4: Micro- and Nano-Electro-Mechanical Systems

The study of the nonlinear behavior of a pre-shaped Micro-ElectroMechanical (MEMS) resonator is numerically investigated. The studied microresonator consists of a clamped-clamped (cc-) beam modeled as an Euler-Bernoulli beam accounting for mid-plane stretching in the in- and out-of-plane vibrations (Y- and Z- directions). The cc-beam is pre-shaped in the XY-plane (in-plane) placed on both edges to mimic springs clamped to their ends, while it is excited in the Z-direction. The tunability of the slope of the nonlinear behavior and the maintenance of the out-of-plane resonance frequencies are observed, which can be beneficial for applications operating at large vibrations.

In this paper, we experimentally observe, for the first time, the coexistence of two phononic frequency comb (PFC) branches emerging in the excitation-frequency sweeps. The experiments were conducted on an electrostatically actuated curved microbeam exhibiting a 1:2 internal resonance. Through the examination of the time history, spectra, phase portraits, and Poincaré sections of these results, we unravel that these two branches originate at different secondary Hopf bifurcation points and terminate in a chaotic attractor.

Force reconstruction in Atomic Force Microscopy (AFM) data represents a significant challenge due to the complex dynamic interactions between the AFM tip and the sample, which are both highly nonlinear and non-smooth. Various methods have been proposed to retrieve this information, yet traditional approaches often fail to accurately represent these non-smooth interactions. Recent advancements demonstrate that machine learning could be an influential factor in extracting detailed information from data. However, conventional machine learning methods tend to smooth the force-distance curves, which misrepresents the tip-sample interactions. This study employs recent advancements in machine learning to preserve and retrieve the non-smooth characteristics of these dynamics. To achieve this, we combine nearest neighbor data-clustering machine learning and Sparse Identification of Nonlinear Dynamics (SINDy) to accurately reconstruct the force-distance relations from synthetic data. This methodology allows for the recovery of the non-smooth equations of motion for cantilever beams in various AFM models, such as DMT and JKR. Furthermore, the algorithm precisely estimates intermolecular distances, demonstrating its effectiveness in predicting the transition between attractive and repulsive forces. The results highlight the potential of this method to significantly improve force reconstruction fidelity, offering a robust tool for advanced nanomechanical studies.

In this study, we investigate the nonlinear dynamics of an in-plane rotational disc mass sensor. The proposed structure not only benefits from the low damping ratio thanks to the in-plane motion, but also tackles the position dependency of the added mass due to the ring structure of the central disc. The sensor is supported by fully clamped cantilever beams and is subjected to harmonic base excitation. The governing equations of motion are derived using the Lagrangian method. The resulting reduced-order model manifests as a nonlinear Duffing-type equation, incorporating a non-homogeneous term arising from the base excitation. Subsequently, we numerically integrate the equation of motion over time to analyse the impact of added mass on the central disc. The results show that the sensor offers 4 Hz resolution of mass detection for an added mass of 500 fg.