Dynamic Vibration Suppression of Smart Composite Plates via LQR and Finite Element Method

Abstract

In this paper, a comprehensive finite element (FE) formulation is developed for the dynamic analysis and active control of classical laminated composite plates with embedded piezoelectric layers. The model, based on the First-Order Shear Deformation Theory (FSDT) and Hamilton’s principle, accurately captures transverse shear effects and electromechanical coupling. Stiffness, mass, and piezoelectric contributions of actuator and sensor layers are explicitly included, providing a fully consistent multi-field representation of the intelligent structure. To enhance vibration performance, piezoelectric actuators are employed within an active vibration control (AVC) framework. A Linear Quadratic Regulator (LQR) controller is designed using the independent mode space approach, enabling efficient computation of optimal feedback gains for dominant vibration modes while keeping the control model reduced-order and computationally tractable. Numerical simulations on various laminated configurations show excellent agreement with ANSYS benchmark results in terms of natural frequencies and mode shapes. The LQR-based AVC strategy is shown to significantly reduce vibration amplitudes, with peak responses decreased by up to 92% within a few seconds and the damping ratio increased more than fivefold. Frequency-response analysis reveals up to 50% attenuation of resonance peaks, highlighting the synergistic effect of state-feedback control and piezoelectric coupling in increasing effective damping. These results confirm the effectiveness of the proposed FE-LQR approach in suppressing vibrations, accelerating structural stabilization, and enhancing the dynamic resilience of smart composite plates.