An efficient modelling method for laminated composite plates with piezoelectric sensors and actuators

Finite element formulations for the modelling of a laminated composite plate with distributed piezoelectric sensors/actuators are presented. The formulation is based on the first-order shear deformation laminated plate theory. The stiffness and mass effects of the piezoelectric sensors and actuators are also considered in the formulation. The closed loop of the negative velocity feedback control through the piezoelectric sensors and actuators is expressed as an active damping matrix. No additional degree of freedom (DOF) for the voltage is introduced in this formation. After the global finite element model is formulated, the total DOFs of the structure are divided into the kept and deleted sets. An efficient method is presented to condense the deleted DOFs from the global model while the accuracy is kept as high as required. The effects of the active damping, Rayleigh damping, and the external loads on the deleted DOFs are also discussed in this paper. Natural frequencies as well as the responses in frequency and time domains are applied to demonstrate the accuracy of the reduced model. Numerical results show that the present modelling method is very efficient. Usually, only two or three iterations are enough for the accuracy of the responses in the frequency and time domains. The proposed approach is also compared with the conventional condensation method, Guyan condensation, in the derivation and numerical example.

[1]  Singiresu S. Rao,et al.  Piezoelectricity and Its Use in Disturbance Sensing and Control of Flexible Structures: A Survey , 1994 .

[2]  R. Guyan.  Reduction of stiffness and mass matrices , 1965 .

[3]  Jaroslav Mackerle,et al.  Smart materials and structures: FEM and BEM simulations a bibliography (1997-1999) , 2001 .

[4]  K. Chandrashekhara,et al.  Thermally induced vibration suppression of laminated plates with piezoelectric sensors and actuators , 1995 .

[5]  K. Chandrashekhara,et al.  Active Vibration Control of Laminated Composite Plates Using Piezoelectric Devices: A Finite Element Approach , 1993 .

[6]  W. Hwang,et al.  Vibration Control of a Laminated Plate with Piezoelectric Sensor/Actuator: Finite Element Formulation and Modal Analysis , 1993 .

[7]  Ayech Benjeddou,et al.  Advances in piezoelectric finite element modeling of adaptive structural elements: a survey , 2000 .

[8]  B. Irons.  Structural eigenvalue problems - elimination of unwanted variables , 1965 .

[9]  C. K. Lee.  Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part I: Governing equations and reciprocal relationships , 1990 .

[10]  Z. Qu,et al.  Iterative methods for dynamic condensation of structural matrices , 2000 .

[11]  D. Owen,et al.  Finite elements in plasticity : theory and practice , 1980 .

[12]  Z. Qu,et al.  New Structural Dynamic Condensation Method for Finite Element Models , 1998 .

[13]  Zu-Qing Qu,et al.  Accurate methods for frequency responses and their sensitivities of proportionally damped systems , 2001 .

[14]  H. S. Tzou,et al.  Integrated distributed sensing and active vibration suppression of flexible manipulators using distributed piezoelectrics , 1989, J. Field Robotics.

[15]  Grant P. Steven,et al.  A Review on the Modelling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures , 1998 .