PIEZOTHERMOELASTIC COUPLING BEAM ELEMENT AND OPTIMAL VIBRATION CONTROL OF PIEZOELECTRIC FUNCTIONALLY GRADED BEAMS

A two-noded piezothermoelastic coupling beam element is presented for the dynamic analysis and optimal vibration control of piezoelectric functionally graded beams. The equivalent mechanical properties of functionally graded materials are modeled by Voigt model or Mori-Tanaka model. The kinematics of the beam is characterized by Shi's third-order shear deformation theory; whereas the electric potential function for piezoelectric laminae is modeled using layer-wise theory, and a piezoelectric layer can be divided into sublayers and modeled using discrete layers to characterize nonlinear voltage distribution. Hamilton’s principle is used to derive the piezothermoelastic finite element equations, and the quasi-conforming element technique is adopted to evaluate the explicit element stiffness matrix of the piezothermoelastic coupling beam element. Linear Quadratic Regulator (LQR) control scheme is employed for the optimal active vibration control. The proposed beam element and active control scheme are validated through static and dynamic analyses of piezoelectric functionally graded beams. The numerical results show that the present beam element is reliable, accurate and efficient, the optimal control voltage evaluated from LQR control scheme can efficiently control the vibration of functionally graded beams, and the LQR control scheme can optimize the energy input for vibration control.