This work aims to investigate experimentally and analytically the linear coupling between the two first symmetric and anti-symmetric modes of an electrothermally heated V-shaped based micro-resonator. The doubly-clamped micro-beam is fabricated from highly doped silicon and is sandwiched between four electrodes to activate electrostatically both modes of vibrations.&nbsp; Also, these electrodes offer a partial electrostatic actuation option. Applying a DC voltage between the resonator and one of the lower electrodes results into an attractive electrostatic force. This force causes the movable electrode (resonator) to move toward the actuating electrode, thereby decreasing its effective stiffness. When tuning the micro-beam with electrothermal voltage, the first symmetric frequency increases while the first anti-symmetric frequency decreases until they cross. As increasing the electrothermal voltage further, these two frequencies depart away from each other. Upon actuating the V-shaped micro-beam electrostatically (using half electrode arrangement) and electrothermally, avoided-crossover phenomenon (veering) is realized.Experimentally, we demonstrate that the DC load can induce symmetry breaking in the actuation, &nbsp;which is shown to change the mode-crossing phenomenon into mode-veering. Then, an analytical study is presented based on a modal-expansion Galerkin reduced-order modelling of a nonlinear Euler–Bernoulli shallow arch beam equation. The analytical solutions are then compared against the experimental data and excellent agreement is obtained.Static results are first obtained using the reduced order model showing the deflection of the device. Then, dynamic results for the variation of the natural frequencies as the DC voltage is swept for various values of electrothermal loads. Experimental data are obtained based on Silicon beams placed in vacuum chambers and the frequency responses are detected using optical laser Doppler vibrometers.We show that as the DC load is increased near mode crossing; veering is created with strong coupling effect, which is then gets weaker as the DC load is further increased. The obtained results can be potentially influential in the design of MEMS sensors through sensitivity enhancement of the system, which is not only away from pull-in but also can simply perform in broader range of actuating forces. Likewise, results show possibility of deploying both the thermal loads and the DC loads at certain values to tune the first two natural frequencies of the V-shaped structures, such that the strength of linear coupling and veering is tuned, when used as resonators. Various results for the change of the mode shapes as varying the voltage parameters are shown. This offers various possibilities to optimize the geometry of this micro-structure for specific applications, which require high sensitivity, and also is promising for mode localization applications.

Investigations Into the Linear Coupling Between Symmetric and Anti-Symmetric Modes of V-Shaped MEMS Resonators Under Electrostatic Perturbation

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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