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| Nonlinear Dynamics and Pull-In Phenomena in a Magneto-Electro MEMS Actuator with Hardening Spring |
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| KeyWord:MEMS, magneto-electro actuator, nonlinear hardening spring, pull-in instability, bifurcation and qualitative analysis |
| Author Name | Affiliation | | Lijun Zhang | School of Science, Zhejiang University of Science and Technology, Liuhe Road, 310023 Hangzhou, China
Material Science, Innovation and Modelling Research Focus Area, North-West University, Mafikeng Campus, 2735 Mmabatho, South Africa | | Jun Ma | College of Mathematics and Systems Science, Shandong University of Science and Technology, 266590 Qingdao, China |
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| Abstract: |
| This paper investigates the dynamic behavior and pull-in instability of a magneto-electro Micro-Electro-Mechanical System (MEMS) actuator, focusing on the nonlinear effects arising from magnetic forces and spring stiffness. The system consists of a movable wire attracted toward a stationary wire due to magnetic forces generated by applied currents. A critical equilibrium, known as the pull-in point, is reached when the currents exceed a threshold, leading to instability. We consider the governing equation based on Newton's Second Law, incorporating a nonlinear restoring force for the spring, which exhibits hardening behavior. The resulting second-order differential equation is analyzed using qualitative and bifurcation theories, revealing the critical bifurcation values determined by the currents and spring stiffness. Through a dynamical systems approach, we characterize the phase portraits and solutions, identifying distinct dynamical behaviors and the conditions for pull-in instability. Numerical simulations are performed to validate the analytical predictions, demonstrating excellent agreement with the theoretically derived threshold. |
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