Rahmanian, Sasan2024-05-312024-05-312024-05-15http://hdl.handle.net/10012/20636The impetus of this work is to introduce nonlinear modal interactions as novel actuation mechanism for electrostatic MEMS-based scanning micromirrors. Modal interactions refer to the engagement of two or more modes of vibration in a system, creating a bridge to channel vibration energy from a directly excited mode to one or more of the coupled modes. In chapter two, this report carries out a comprehensive literature review of the different types of mode coupling in nonlinear resonators. First, internal resonance in general nonlinear oscillators are addressed. Second, we limit our focus to mode coupling in electrostatic MEMS. As an initial test-bed, we examine in chapter three the modulation equations governing a system of two nonlinearly coupled 1-DOF oscillators involved in a 2:1 parametric modal interaction. Simulations show that as the excitation frequency varies in the vicinity of the directly excited higher-frequency oscillator, the amplitude of its motions saturate. Meanwhile, the amplitude of the lower-frequency oscillator undergoes large motions under the influence of a parametric ‘energy pump’. The fourth chapter reports on nonlinear modal interaction in a MEMS made of an electrostatically actuated curved-beam. We characterize the first few in-plane and out-of-plane bending modes of the beam. Thermal noise excitation is utilized to extract the out-of-plane natural frequencies, whereas the in-plane natural frequencies are captured using pulse excitation. Then, the frequency response of the MEMS in the neighbor of the first symmetric and second symmetric in-plane modes. Characterization results discloses a 2:1 ratio between the second symmetric and the first anti-symmetric in-plane modes. We show that this anti-symmetric mode can be effectively excited via the energy channel between it and the second symmetric mode when the latter is driven directly by external electrostatic forcing. In the fifth chapter, we establish bending-torsional equations of motion for a symmetric electrostatic MEMS actuator that can capture the 2:1 modal interaction between its in-plane bending and out-of-plane rotational motions. Our approach demonstrates that incorporating the linear slopes into the cross-sectional shear strains efficiently originates quadratic couplings between the bending and torsional motions whose existence depends on non-vanishing first moments of area of the microbeam's cross-section. According to imperfections in microdevice fabrication, we assumed a minuscule offset in positions between the centroid of the as-fabricated and as-designed cross-sections of the microbeams. Energy approach is exploited to derive the equations of motion (EoM). The static response of the MEMS actuator together with its tuned eigenmodes are examined in this chapter. Chapter six reports the frequency- and voltage-displacement behaviors of the mirror addressing the 2:1 and 3:1 flexural torsional internal resonance experimentally and numerically. The numerical simulation results indicate that the in-plane motion, which is the directly excited mode, saturates upon the initiation of a 2:1 energy pathway between the bending and torsional motions. Through suitable tuning of the AC frequency, the amplitude of the in-plane motion is minimized, while the amplitude of the torsional motion, an indirectly excited mode, is maximized. The numerical simulation results demonstrate that the actuator's torsional motion, when subjected to a 1:2:1 electro-flexural-torsional modal interactions, is triggered by applying a maximum voltage of 10 V, resulting in about 15 degrees rotational angle. Further, prolific frequency combs are generated as a result of secondary Hopf bifurcations along the large-amplitude response branches, capturing quasi-periodicity in the MEMS dynamics. The experimental results demonstrate the mirror's dynamics exhibiting 3:1 flexural-torsional modal interaction that provides an efficient out-of-plane rotation drive through in-plane excitation. The present study is a platform for the implementation of a novel actuation mechanism of MEMS scanning micromirrors using parametric modal interaction. Conclusion remarks and propose future work with the are presented seven chapter.enMEMS scanning mirrorFlexural-torsional modal interactionAuto-parametric modal interactionSaturationCross-sectional imperfectionDoctoral Thesis