Nonlinear Coupled Vibration of Electrically Actuated Arch with Flexible Supports

Area of Science:

• Nonlinear dynamics
• Micro-electromechanical systems (MEMS)
• Vibrational analysis

Background:

• Electrically actuated arch microbeams exhibit complex nonlinear coupled vibrations.
• Understanding these dynamics is crucial for micro-device design and applications.
• Flexible supports introduce additional complexities to microbeam behavior.

Purpose of the Study:

• To investigate the nonlinear dynamics of electrically actuated arch microbeams with flexible supports.
• To analyze the effects of two-to-one internal resonance between the first and second modes.
• To determine equilibrium solutions, stability, and various dynamic phenomena.

Main Methods:

• Utilized the multiple scales method to derive approximate analytical solutions.
• Formulated four first-order ordinary differential equations for amplitude and phase modulation.
• Employed numerical simulations to validate analytical findings.

Main Results:

• Identified stable periodic and modulated motions under primary resonance of the first mode.
• Observed the double-jumping phenomenon.
• Found single-mode and two-mode solutions for primary resonance of the second mode, including double-jumping, hysteresis, and saturation.

Conclusions:

• The multiple scales method effectively captures the complex nonlinear dynamics of arch microbeams.
• Flexible supports and internal resonance significantly influence microbeam vibrational behavior.
• Analytical and numerical results confirm the occurrence of diverse nonlinear phenomena.