Nonlinear Behavior of Electrostatically Actuated Microbeams with Coupled Longitudinal⁻Transversal Vibration

Area of Science:

• * Mechanical Engineering
• * Applied Physics
• * Microelectromechanical Systems (MEMS)

Background:

• * Microelectromechanical switches are crucial in diverse fields like consumer electronics, biomechanics, and aerospace.
• * Electrostatically actuated microbeams and microplates are fundamental components in MEMS devices.
• * Understanding nonlinear dynamics is essential for optimizing MEMS performance and reliability.

Purpose of the Study:

• * To investigate the nonlinear characteristics of coupled longitudinal-transversal vibrations in an electrostatically actuated microbeam.
• * To analyze the internal resonance phenomenon with a 2:1 frequency ratio between longitudinal and transversal vibrations.
• * To explore the influence of bias voltage, longitudinal excitation, and frequency detuning on the system's dynamics.

Main Methods:

• * Nonlinear governing equations derived and truncated using the Galerkin method.
• * Solution of coupled ordinary differential equations via the multiple-scales method.
• * Analysis of nonlinear dynamics and amplitude-response curves using the pseudo-arclength continuation method.

Main Results:

• * Bias voltage and detuning frequency significantly impact saturation and jump phenomena.
• * Energy transfer from longitudinal to transversal motion observed beyond a critical excitation amplitude.
• * Nonlinear amplitude-response curves plotted continuously, revealing complex dynamic behaviors.

Conclusions:

• * The study elucidates the complex nonlinear dynamics of electrostatically actuated microbeams with internal resonance.
• * Observed energy transfer and jump phenomena offer potential for novel sensing applications in MEMS.
• * Large-amplitude jumps in low-order modes can be leveraged for precise detection of parameter variations, improving MEMS switch accuracy.