Multiple internal resonances in MEMS arch resonators

Abstract

Micromachined shallow arch resonant beams have attracted significant attention thanks to their rich dynamical behavior, inherent nonlinearities, and the potential to excite various internal resonances. Currently, there is a lack of comprehensive experimental studies for the various types of internal resonances in arches and particularly at the micro and nano scales. Here, we aim to investigate and identify different types of internal resonances of an initially curved beam, electrothermally actuated and electrostatically driven, by electrical characterization techniques. Upon changing the electrothermal voltage of silicon micromachined arches, the second symmetric natural frequency of an arch is adjusted to near twice, three times, and four times the fundamental natural frequency, which gives rise to 2:1, 3:1, and 4:1 autoparametric resonances between the two modes. These resonances are demonstrated experimentally. We show various frequency-response curves of the total response around the excitation frequency and highlight the contribution of each mode before, during, and after the internal resonances. Allandeviation results are also shown indicating enhanced frequency stabilization of the arch oscillation when experiencing internal resonances. These studies motivate further research in this direction to exploit internal resonances of micromachined resonators for practical applications, such as sensors and mechanical amplifier.

Theoretical and experimental investigations of the crossover phenomenon in micromachined arch resonator: part II—simultaneous 1:1 and 2:1 internal resonances

“…Energy transfer via internal resonance among various modes of vibration of micro and nano-electromechanical structures (MEMS and NEMS) has been explored for several potential applications, such as timing/synchronization [1,2], energy harvesting [3,4], mass sensing [5], and frequency stabilization [6,7]. Internal resonance, also called auto-parametric resonance, represents a nonlinear 2 mechanism for energy leakage from the targeted vibration mode to another mode.…”

“…One necessary condition to activate internal resonance is to have an integer ratio between the involved modes. Commonly, the 1:1 [8,9], 2:1 [10,11,7,12,13], 3:1 [11,9,7,6], and 4:1 [7] internal resonance types are investigated.…”

“…The same group [1] has recently shown a novel technique to realize a self-sustained oscillation, via internal resonance, to compensate for energy losses. In electrothermally tuned MEMS arch resonator [23,12,7,9,11], 2:1 and 3:1 internal resonances were explored experimentally and theoretically among the first two symmetric vibrational modes. Rich complex dynamics were shown, such as Hopf bifurcation, limit cycle instabilities, and chaotic behavior.…”

Theoretical and experimental investigations of the crossover phenomenon in micromachined arch resonator: part I—linear problem

“…The coupling between different modes can be linear or nonlinear. The nonlinear coupling can be through a mechanical coupler within the involved structures [7,8] or via internal resonance [1,2,4,5,[9][10][11]. The majority of the reported nonlinear coupling studies are based on internal resonance [1,2,4,5,[9][10][11].…”

“…Since curved beams inherit cubic and quadratic nonlinearities, they have been widely reported to have different types of couplings either linear, via veering and crossover phenomena [3,14,15], or nonlinear through several types of internal resonances, 1:1, 2:1, 3:1 and 4:1 [10,23,24], resulting from interactions among different vibrational modes. With increasing their curvature, the fundamental frequency rises rapidly due to the stiffening stretching mechanism, while the antisymmetric frequency does not experience any alteration since it is not affected by stretching [27].…”