Global Bifurcation Behaviors and Control in a Class of Bilateral MEMS Resonators

• Published in: Fractal and fractional Vol. 6; no. 10; p. 538
• Main Authors: Zhu, Yijun, Shang, Huilin
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-10-2022
• Subjects: Behavior; Bifurcation theory; chaos; Control algorithms; Eigenvalues; Electrodes; Equilibrium; Feedback; fractal; global bifurcation; heteroclinic orbit; homoclinic orbit; Mathematical analysis; MEMS resonator; Microelectromechanical systems; Resonators; Stability; Stability analysis
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract6100538

The investigation of global bifurcation behaviors the vibrating structures of micro-electromechanical systems (MEMS) has received substantial attention. This paper considers the vibrating system of a typical bilateral MEMS resonator containing fractional functions and multiple potential wells. By introducing new variations, the Melnikov method is applied to derive the critical conditions for global bifurcations. By engaging in the fractal erosion of safe basin to depict the phenomenon pull-in instability intuitively, the point-mapping approach is used to present numerical simulations which are in close agreement with the analytical prediction, showing the validity of the analysis. It is found that chaos and pull-in instability, two initial-sensitive phenomena of MEMS resonators, can be due to homoclinic bifurcation and heteroclinic bifurcation, respectively. On this basis, two types of delayed feedback are proposed to control the complex dynamics successively. Their control mechanisms and effect are then studied. It follows that under a positive gain coefficient, delayed position feedback and delayed velocity feedback can both reduce pull-in instability; nevertheless, to suppress chaos, only the former can be effective. The results may have some potential value in broadening the application fields of global bifurcation theory and improving the performance reliability of capacitive MEMS devices.