Electromechanical Coupling Modeling and LQG Active Vibration Control of CFRP Cantilever Plates Using MFCs

This study addresses the inherently low damping and vibration susceptibility of carbon fiber reinforced polymer (CFRP) laminated cantilever plates by developing a comprehensive dynamic modeling and active vibration control framework. An electromechanical coupling model incorporating macro-fiber composite (MFC) actuators and sensors is established using the first-order shear deformation theory (FSDT) and the assumed mode method, with virtual springs introduced to account for non-ideal clamped boundary conditions. A reduced-order state-space model is then derived through model reduction, and a linear quadratic Gaussian (LQG) controller is designed for optimal state estimation and feedback control. The theoretical model is systematically validated via convergence analysis, ANSYS finite element simulations, and LMS impact hammer testing. The results demonstrate that, with the relative errors of the first four natural frequencies controlled within 2%, the theoretical mode shapes are highly consistent with those obtained from ANSYS simulations. An active vibration control experimental platform is established, and the effectiveness of the control strategy is verified under dual-spectrum harmonic and impact excitations. The results show that the designed LQG controller can effectively suppress multi-modal vibrations, substantially attenuating the response amplitudes of dominant modes and significantly accelerating the transient vibration convergence. This study addresses the challenge of precisely characterizing actual non-ideal clamped boundary conditions. Through model order reduction and closed-loop LQG control experiments, it provides a comprehensive set of theoretical methodologies, numerical solution strategies, and engineering-oriented experimental schemes for the electromechanical coupling dynamic modeling and optimal vibration suppression of CFRP thin-walled composite structures.