Two-to-one internal resonance of MEMS arch resonators

We investigate experimentally and theoretically the two-to-one internal resonance between the first two symmetric vibrational modes of a micromachined arch resonator, which is electrothermally tuned and electrostatically driven. An electrothermal voltage is applied across the beam anchors, which controls its stiffness, and hence, tunes the ratio between the first two symmetric frequencies close to two. The dynamic behavior of the arch beam is examined when excited using large harmonic AC voltages, which leads to direct simultaneous excitation of the first two symmetric vibrational modes, in addition to the activation of the internal resonance. Varieties of complex behaviors are demonstrated including quasi-periodic and aperiodic motion leading to potential chaotic motion. A reduced order model based on the Galerkin procedure and the Euler–Bernoulli beam theory is utilized to analyze the dynamic response of the structure. Poincare sections, power spectra, and time histories are used to analyze the dynamic responses. A good agreement is shown among the experimental and theoretical results.