Theoretical and experimental investigation of mode localization in electrostatically and mechanically coupled microbeam resonators

The phenomenon of mode localization is explored theoretically and experimentally on two mechanically or electrostatically coupled beam resonators. Lumped parameter models are used to simulate the response of the systems. The eigenvalue problems are solved for both case studies under different stiffness perturbations and coupling strengths. The influence of the side electrode bias on the veering points is also explored. The dynamics of the systems are studied and compared using their frequency response curves under different perturbation and damping scenarios. The effect of damping for different elements of the coupled system is studied and proposed to improve sensitivity in high damping environments. It is observed that the exploitation of mode localization depends primarily on the choice of the resonator of the coupled system to be under direct excitation, its stiffness to be perturbed, and its response to be monitored. The revealed dynamic behaviors show great potential for applications in sensing and mechanical computing. The theoretical findings are validated using experimental case studies of two silicon doubly-clamped mechanically coupled microbeams and two electrostatically coupled microcantilevers. Electrothermal voltage is applied to the mechanically coupled resonators to introduce the stiffness perturbation in order to investigate mode localization. The theoretical and experimental results show good qualitative agreement.