Nonlinear dynamics and chaos in micro/nanoelectromechanical beam resonators actuated by two-sided electrodes

• Published in: Chaos, solitons and fractals solitons and fractals, 2019-05, Vol.122, p.6-16
• Main Authors: Gusso, André, Viana, Ricardo L., Mathias, Amanda C., Caldas, Iberê L.
• Format: Article
• Language: English
• Subjects: Basin entropy; Chaos; Microelectromechanical systems; Nanoelectromechanical systems; Nonlinear dynamics
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2019.03.004

•The nonlinear and chaotic dynamics of a realistic MEMS/NEMS beam resonator is investigated.•We determine the regions in the parameter space with periodic and chaotic dynamics, and pull-in.•Multistability is found on significant portions of the parameter space where attractors are mixed.•Basins of attraction are also investigated and fractal basins are found and analyzed.•The basin entropy method is used to calculate the uncertainty exponent. We investigate theoretically the nonlinear dynamics and the emergence of chaos in suspended beam micro/nanoelectromechanical (MEMS/NEMS) resonators actuated by two-sided electrodes. Through the analysis of phase diagrams we have found that the system presents a rich and complex nonlinear behavior. Multistability is observed in a significant region of the relevant parameter space, involving periodic and chaotic attractors. Complex and varied routes to chaos were also found. Basins of attraction with strongly intermingled attractors provide further evidence of multistability. The basins are analyzed in greater detail. Their fractal dimensions and uncertainty exponent are calculated using the well known box counting and uncertainty methods. The results for the uncertainty exponent are compared with those obtained with yet another approach, based on the recently proposed basin entropy method. The comparison provides a test for the new approach, which we conclude that is a reliable alternative method of calculation. Very low uncertainty exponents have been obtained, indicating that some basins have extremely intermingled attractors, what may have significant influence in the experimental investigation and practical applications of the resonators. We also conclude that the observation of chaos in this system is favored by lower frequencies of excitation and comparatively small quality factors (larger dissipation).