Static and Dynamic Mechanical Behaviors of Electrostatic MEMS Resonator with Surface Processing Error.

Area of Science:

• * Micro-electro-mechanical systems (MEMS)
• * Nonlinear dynamics and vibrations
• * Surface processing and fabrication

Background:

• * Surface processing in MEMS fabrication can lead to unintended changes in microbeam cross-sectional shape.
• * These geometric variations can significantly impact the mechanical properties and performance of MEMS resonators.
• * Existing models often neglect the effects of neutral plane stretching and electrostatic nonlinearities in microbeam resonators.

Purpose of the Study:

• * To introduce a section parameter for quantifying microbeam shape changes in MEMS resonators.
• * To analytically investigate the influence of section shape variations on mechanical properties and static pull-in behavior.
• * To explore the dynamic analysis and frequency response of microbeam resonators considering nonlinearities and shape changes.

Main Methods:

• * Development of a higher-order analytical model for doubly-clamped microbeams, incorporating neutral plane stretching and electrostatic nonlinearity.
• * Application of the Galerkin and Newton-Cotes methods for model order reduction.
• * Utilizing the Method of Multiple Scales (MMS) for analyzing small amplitude vibrations and frequency response.
• * Finite element analysis (FEA) using COMSOL for validation.

Main Results:

• * Section shape and gap variations demonstrably influence static pull-in instability.
• * Microbeam shape changes can induce softening or hardening nonlinear frequency response behaviors.
• * The Method of Multiple Scales (MMS) shows that softening effects are weakened at large amplitudes.
• * Large amplitude motions reveal transitions between hardening and softening behaviors.
• * FEA results closely match theoretical predictions in stable regions.

Conclusions:

• * A novel section parameter effectively describes microbeam shape changes and their impact on MEMS resonator mechanics.
• * Microbeam geometry is a critical factor in tailoring the nonlinear frequency response of resonators.
• * The developed analytical model and validation methods provide accurate predictions for MEMS resonator behavior under various conditions.