Multi-Modal Nonlinear Response of an Electrically Actuated Microelectromechanical System Resonator

Microelectromechanical systems (MEMS) have a widespread use in several applications such as signal filtering, time referencing, and sensing. This paper explores the nonlinear dynamic behavior of a MEMS resonator using a reduced-order modeling approach. The study focuses on how multi-modal formulation and detuning affect the system’s response under primary resonance. Using the method of multiple scales, amplitude–phase response equations are derived, and time-domain simulations are generated with the Runge–Kutta method. Two mode combinations are examined: the first mode combined with the second mode and the first mode with the third mode for multi-modal influence evaluation. Results indicate that the first mode provides the dominant behavior to MEMS response, while the second and third modes exhibit minimal participation despite the nonlinearities retained in the presented multi-modal model. Additionally, a detuning study reveals that the geometric and forcing nonlinear effects are stronger near resonance and diminish as the system moves away from it. The analysis suggests that the significant features of the response can be captured in the case of primary resonance using only the first mode, which offers an effective modeling approach. From a design perspective, finding that the first mode alone is sufficient means that the essential dynamic behavior of the MEMS resonator can be predicted and controlled by focusing on its first mode of vibration. In practical terms, this greatly allows engineers to optimize geometry, driving voltage, or control parameters to target the first mode natural frequency without accounting for higher modes, which reduces computational cost and design complexity.