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CONTENTS
Volume 12, Number 5, November 2013
 

Abstract
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Key Words
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Address
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Abstract
new piezoceramic d15 shear-induced torsion actuation mechanism representative benchmark is proposed and its experimentations and corresponding 3D finite element (FE) simulations are conducted. For this purpose, a long and thin smart sandwich cantilever beam is dimensioned and built so that it can be used later for either validating analytical Saint Venant-type solutions or for analyzing arm or blade-based smart structures and systems applications. The sandwich beam core is formed by two adjacent rows of 8 oppositely axially polarized d15 shear piezoceramic patches, and its faces are dimensionally identical and made of the same glass fiber reinforced polymer composite material. Quasi-static and static experimentations were made using a point laser sensor and a scanning laser vibrometer, while the 3D FE simulations were conducted using the commercial software ABAQUS R The measured transverse deflection by both sensors showed strong nonlinear and hysteretic (static only) variation with the actuation voltage, which cannot be caught by the linear 3D FE simulations.

Key Words
piezoceramic d15 shear actuation; direct torsion actuation mechanism; piezoelectric composite beam; quasi–static and static experiments; finite element simulation

Address
Pelin Berik and Michael Krommer : Institute for Technical Mechanics, Johannes Kepler University, 4040 Linz, Austria
Ayech Benjeddou : Structures, Institut Superieur de Mecanique de Paris, 93400 Saint Ouen, France

Abstract
This paper is concerned with static and dynamic shape control of a laminated Bernoulli-Euler beam hosting a uniformly distributed array of resistively interconnected piezoelectric patches. We present an analytical one-dimensional model for a laminated piezoelectric beam with material discontinuities within the framework of Bernoulli-Euler and extent the model by a network of resistors which are connected to several piezoelectric patch actuators. The voltage of only one piezoelectric patch is prescribed: we answer the question how to design the interconnected resistive electric network in order to annihilate lateral vibrations of a cantilever. As a practical example, a cantilever with eight patch actuators under the influence of a tip-force is studied. It is found that the deflection at eight arbitrary points along the beam axis may be controlled independently, if the local action of the piezoelectric patches is equal in magnitude, but opposite in sign, to the external load. This is achieved by the proper design of the resistive network and a suitable choice of the input voltage signal. The validity of our method is exact in the static case for a Bernoulli-Euler beam, but it also gives satisfactory results at higher frequencies and for transient excitations. As long as a certain non-dimensional parameter, involving the number of the piezoelectric patches, the sum of the resistances in the electric network and the excitation frequency, is small, the proposed shape control method is approximately fulfilled for dynamic load excitations. We evaluate the feasibility of the proposed shape control method with a more refined model, by comparing the results of our one-dimensional calculations based on the extended Bernoulli-Euler equations to three-dimensional electromechanically coupled finite element results in ANSYS 12.0. The results with the simple Bernoulli-Euler model agree well with the three-dimensional finite element results.

Key Words
piezoelastic modeling of a beam; static shape control; dynamic shape control; patch actuators; resistive network; feed-forward control of piezoelastic beam-structures

Address
J. Schoeftner: Institute of Technical Mechanics, Johannes Kepler University Linz, A-4040 Linz, Altenberger Str.69, Austria
G. Buchberger: Institute for Microelectronics and Microsensors, Johannes Kepler University Linz, A-4040 Linz,
Altenberger Str.69, Austria

Abstract
Piezoelectric and dielectric behaviors of a piezoceramic patch adhesively centered on a carbon composite plate are identified using a robust multi–objective optimization procedure. For this purpose, the patch piezoelectric stress coupling and blocked dielectric constants are automatically evaluated for a wide frequency range and for the different identifiable behaviors. Latters\' symmetry conditions are coded in the design plans serving for response surface methodology–based sensitivity analysis and meta-modeling. The identified constants result from the measured and computed open-circuit frequencies deviations minimization by a genetic algorithm that uses meta-model estimated frequencies. Present investigations show that the bonded piezoceramic patch has effective three-dimensional (3D) orthotropic piezoelectric and dielectric behaviors. Besides, the sensitivity analysis indicates that four constants, from eight, dominate the 3D orthotropic behavior, and that the analyses can be reduced to the electromechanically coupled modes only; therefore, in this case, and if only the dominated parameters are optimized while the others keep their nominal values, the resulting piezoelectric and dielectric behaviors are found to be transverse–isotropic. These results can help designing piezoceramics smart composites for various applications like noise, vibration, shape, and health control.

Key Words
finite element–experimental vibration–based mixed inverse identification; multi–objective optimization; piezoelectric effective behavior; dielectric effective behavior; piezoceramic patch; CFRP composite plate

Address
Ayech Benjeddou : Institut Superieur de Mecanique de Paris, 93400 Saint-Ouen, France
Mohsen Hamdi and Samir Ghanmi :Institut Preparatoire aux Etudes d\'Ingenieurs de Nabeul, 8000 Nabeul, Tunisia

Abstract
To suppress vibration and noise of mechanical structures piezoelectric ceramics play an increasing role as effective, simple and light-weighted damping devices as they are suitable for sensing and actuating. Out of the various piezoelectric damping methods this paper compares mode based active control strategies to passive shunt damping for thin plates. Therefore, a new approach for the optimal placement of the piezoelectric sensors/actuators, or more general transducers, is proposed after intense theoretical investigations based on the Kirchhoff kinematical hypotheses of plates; in particular, modal and nilpotent transducers are discussed in detail. Based on the proposed distribution a discrete design for modal transducers is implemented, tested and verified on an experimental setup. For active control the modal sensors clearly identify the eigenmodes, whereas the modal actuators impose distributed eigenstrains in order to reduce the transverse plate vibrations. In contrast to the modal control, passive shunt damping works without requiring additional actuators or auxiliary power and can therefore act as an autonomous system, but it is less effective compensating the flexible vibrations. Exemplarily, an acryl glass plate disturbed by an arbitrary force initialized by a loudspeaker is investigated. Comparing the different methods their specific advantages are highlighted and a significant broadband reduction of the vibrations of up to -20dB is obtained.

Key Words
smart structures; plate vibrations; piezoelectric transducers; modal transducers; nilpotent transducer; shunt damping, modal control

Address
Georg Zenz, Wolfgang Berger, Johannes Gerstmayr and Manfred Nader : Linz Center of Mechatronics (LCM), Altenbergerstr.69, A-4040 Linz, Austria
Michael Krommer : Institute of Technical Mechanics, Johannes Kepler University Linz, Altenbergerstr.69, A-4040 Linz, Austria

Abstract
new enthalpy – based procedure for the homogenization of the electromechanical material parameters of composite piezoelectric modules with integrated electrodes is presented. It is based on a finite element (FE) modeling of the latter\'s representative volume element (RVE). In contrast to most previously published homogenization approaches that are based on averaged quantities, the presented method uses a direct evaluation of the electromechanical enthalpy. Hence, for the linear orthotropic piezoelectric composite behavior full set of elastic, piezoelectric, and dielectric material parameters, 17 load cases (LC) are used where each load case leads directly to one material parameter. This gives the possibility to elaborate a very strict and easy to program processing. In conjunction with the 17 LC, the enthalpy – based homogenization is particularly suitable for laminated composite piezoelectric modules with integrated electrodes. In this case, the electric load has to be given at the electrodes rather than at the RVE FE model boundaries. The proposed procedure is validated through its comparison to literature available results on a classical 1-3 piezoelectric micro fiber (longitudinally polarized) reinforced composite and a shear piezoelectric macro-fiber (transversely polarized) composite module.

Key Words
electromechanical enthalpy; finite element homogenization; piezoelectric composite modules; integrated electrodes

Address
Burkhard Kranz : Fraunhofer Institute for Machine Tools and Forming Technology, 01187 Dresden, Germany
Ayech Benjeddou : Institut Superieur de Mecanique de Paris, 93400 Saint-Ouen, France
Welf-Guntram Drossel: Institute for Machine Tools and Production Processes, Chemnitz University of Technology, 09107 Chemnitz, Germany


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