Nonlinear Dynamics of Electrically Actuated Micro Beams for Improved Sensing and Actuation

  • Wen Zhao

Student thesis: Doctoral Thesis


In this dissertation, we present analytical and experimental investigations of the electrically actuated micro resonators, when using multi-frequency and/or multi-mode excitation, combined with partial electrodes. We aim to understand their interesting frequency performance and use it to improve the sensing and actuation in microelectromechanical systems (MEMS) and explore their potential applications, such as amplification, gas sensing, magnetometer, multi-physical sensors, and digital-to-analog converters. In the first part, we propose a method of the multi-mode excitation (MME). The concept of the multi-mode excitation is demonstrated by utilizing the superposition principle of two vibration modes in the same phase. To fully understand the difference between the single source excitation (SSE) and multi-mode excitation, we derive the dynamic equations of motions of the electrically-actuated micro cantilever beam and clamped-clamped beam actuated by single/multi-mode excitation. Then, we analytically solve the equations based on the procedure of the Galerkin method with five modes. The simulated results indicate that the MME is clearly superior to that of the SSE, as it can amplify the amplitude performance and signal-to-noise ratio of micro resonators. In the second part, we aim to experimentally prove the concept of the multi-mode excitation and explore its use for gas sensing applications. First, we experimentally investigate the performance of MEMS resonators by single source excitation and multi-mode excitation. We prove the feasibility of the MME approach in enhancing the higher-order mode response for both cantilever and clamped-clamped beams, respectively. We prove that the multi-mode excitation approach provides a better way to activate the higher-order modes with an improved amplitude under a small actuation compared to using a single-source excitation. We then show an improved performance for gas detection. In the third and fourth parts, we propose a technique based on multi-mode excitation for simultaneous sensing for two physical parameters: magnetic field and gas concentration. We respectively investigate a single out-of-plane/in-plane device for in-plane/out-of-plane magnetic field and gas concentration sensing based on tracking the first two vibration modes of a heated buckled micro-beam. We found that operating the resonator at the post-buckling regime, the magnetometer is gas-independent since the first antisymmetric mode (f2) is unaffected by the thermal axial load. Based on it, we utilized the first resonance frequency f1 to detect the gas based on the cooling/heating effects while the second resonance frequency f2 to sense the in-plane/out-of-plane magnetic field. The obtained results demonstrated the sensor acts as a magnetometer and gas sensor, showing good sensitivity, linearity and repeatability. Thus, this technique provides a good candidate for multi-environment monitoring applications. In the last part, we aim to investigate the effects of partial electrodes actuation on the micro resonator and explore its application on the digital-to-analog converter. We analytically and experimentally present modeling, investigation, validation, and optimization of the MEMS resonator-based 3-bit digital to analog converter (DAC) consisting of an in-plane clamped-clamped beam actuated by partial electrodes with different air gaps. The results suggest that the proposed modeling, simulations, and optimization analysis could be successfully implemented in the design of the DAC under various digital combinations. The rich nonlinear behavior with low energy consumption could provide some high potential applications in IoT, such as logic, computation, sensing, and actuation.
Date of AwardOct 1 2022
Original languageEnglish (US)
Awarding Institution
  • Physical Sciences and Engineering
SupervisorMohammad Younis (Supervisor)


  • MEMS
  • Sensor
  • multi-mode excitation
  • signal-to-noise ratio
  • response Amplification
  • Sensing and actuation
  • dynamic amplification

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