Laminated piezoelectric beam element for dynamic analysis of piezolaminated smart beams and GA-based LQR active vibration control

摘要

This paper presents an accurate two-noded laminated piezoelectric beam element for the dynamic analysis and active vibration control of laminated composite beams with piezoelectric layers. A refined third-order shear deformation plate theory is used to model the kinematics, and a piecewise linear interpolation is used to char-acterize the electrical potential. The equations of motion are derived from Hamilton's principle. The quasi-conforming element technique is adopted to evaluate the explicit element stiffness matrix. The resulting two-noded piezolaminated beam element is free from shear locking and the numerical integration. Linear Quadratic Regulator (LQR) control scheme is used for the active vibration control and Genetic Algorism (QA) is employed to determine the optimal weighting matrix used in the control performance index. The laminated piezoelectric beam element is validated by numerical examples. The numerical results show that present laminated piezoelectric beam element is very accurate in dynamic analysis of laminated piezoelectric beams and it is an effective strategy to use QA to merely evaluate the optimal weighting matrix for the vibration con-trol performance by fixing the weighting matrix for the control input cost as an identity matrix in the LQR-based active vibration control.