M. Pietrzakowski
Institute of Machine Design Fundamentals, Warsaw University of Technology, Poland
Keywords: laminated plate, piezoelectric control, functionally graded actuator.
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Piezoelectric composites show great potential for vibration control of thin-walled flexible structures. A promising class for actuating purposes are functionally graded piezoelectric materials (FGPMs). Their effective electromechanical properties can be tailored varying the piezoelectric phase volume fraction across the layer thickness. The appropriate compositional gradient improves the reliability and lifetime of active piezoelectric composites by minimizing interlaminar shear stresses and keeps a satisfactory level of control efficiency.
The objective of the study presented in this paper is to develop models of active laminated plates with FGPM actuator layers characterized by almost continuous gradation of elastic and piezoelectric properties. In the earlier study by the author [1] a two-phase functionally graded composite being a mixture of piezoceramic inclusions and matrix material was analysed. Now, the considered representation is a multi-layer structure consisted of the composite laminae with piezoceramic (PZT) fibres arranged in-plane according to a rectangular packing pattern and polarized longitudinally. Modification of the electromechanical properties is achieved by changing the PZT material volume fraction (number of PZT fibres), which is constant for each lamina and graded through the total thickness of the actuator. The inter-digitated electrodes are used to direct the electric field along the fibres. The effective properties of particular laminae are obtained based on the periodic unit cell model and the uniform field method. In the study the actuator material compositional gradient is approximated according to the power and parabolic functions.
The dynamic analysis concerns steady-state vibration of a simply supported plate with piezopolymer sensor layers and FGPM actuator layers. A constant-gain velocity feedback control is used to realize the transverse vibration suppression. The interaction between the FGPM actuator layers and the host structure is reduced to the equivalent moment resultant distributed along the activated area.
The calculations based on the formulated mathematical model of the system are performed to recognize the influence of the applied PZT distribution pattern on the gradient of elastic and piezoelectric properties within the FGPM actuator and the active plate amplitude-frequency characteristics. The results are presented in diagrams, which demonstrate changes in the natural frequencies and the resonant amplitudes depending on the gradient function and its parameters defined as the material inhomogeneity and the maximal PZT volume fraction.
It is observed that for the considered gradations the control system effectiveness becomes lower with increasing the inhomogeneity parameter value and the natural frequencies slightly change. For the same distribution parameters the parabolic type actuators show better control effectiveness because of a greater amount of the PZT component.
Generally, the results presented proved that the FGPM actuators offer a satisfactory operational effectiveness. Thus, the FGPM actuator layers produce sufficient control forces and by applying a suitable distribution of material properties may also reduce interlayer stresses and in consequence a damage hazard in comparison with traditional piezoelectric actuators.
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- 1
- M. Pietrzakowski, "Vibration control of functionally graded piezoelectric plates", Mechanics Quarterly AGH, 26(4), 187-192, 2007.
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