Macro fiber composite-based active control of nonlinear forced vibration of functionally graded plate

• Published in: Applied mathematics and mechanics Vol. 46; no. 5; pp. 869 - 884
• Main Authors: Zhang, Peiliang, Wang, Jianfei
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2025; Springer Nature B.V
• Edition: English ed.
• Subjects: Active control; Actuation; Actuator position; Algorithms; Applications of Mathematics; Carbon nanotubes; Classical Mechanics; Control algorithms; Control theory; Effectiveness; Feedback control; Fiber composites; Finite element method; Flexible structures; Fluid- and Aerodynamics; Forced vibration; Functionally gradient materials; Hamilton's principle; Iterative methods; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nonlinear control; Partial Differential Equations; Shear deformation; Thin wall structures; Vibration; Vibration analysis; Vibration control; O322; nonlinear resonance; geometrically nonlinearity; 70K30; macro fiber composite (MFC); active vibration control; amplitude-frequency response
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-025-3250-9

Owing to their high flexibility and directional actuation capabilities, macro fiber composites (MFCs) have attracted significant attention for the active control of structures, especially in the nonlinear vibration suppression applications for large-scale flexible structures. In this paper, an MFC-based self-feedback system is introduced for the active control of geometrically nonlinear steady-state forced vibrations in functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates subject to transverse mechanical loads. Based on the first-order shear deformation theory and the von Kármán nonlinear strain-displacement relationship, the nonlinear vibration control equations of the plate with MFC sensor and actuator layers are derived by Hamilton’s principle. These equations are discretized by the finite element method (FEM), and solved by the Newton-Raphson and direct iterative methods. A velocity feedback control algorithm is introduced, and the effects of the control gain and the MFC actuator position on the nonlinear vibration active control effectiveness are analyzed. Additionally, a nonlinear resonance analysis is carried out, considering the effects of carbon nanotube (CNT) volume fraction and distribution type. The results indicate that the intrinsic characteristics of the structures significantly influence the vibration behavior. Furthermore, the appropriate selections of control gain and MFC position are crucial for the effective active control of the structures. The present work provides a promising route of the active and efficient nonlinear vibration suppression for various thin-walled structures.