Shunted piezoelectric patches on auxetic microstructures for the enhancement of band gaps
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O R I G I NA L
Panagiotis I. Koutsianitis · Georgios K. Tairidis Georgios E. Stavroulakis
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Shunted piezoelectric patches on auxetic microstructures for the enhancement of band gaps
Received: 17 March 2020 / Accepted: 1 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Certain frequency ranges where waves do not propagate, and thus, vibrations are suppressed, are called band gaps. In the present paper, the appearance and the behavior of such areas are investigated on star-shaped auxetic microstructures, which are equipped with shunted piezoelectric elements. The optimal position of the piezoelectric patches is found using genetic algorithms, considering the maximization of the electromechanical coupling coefficient. A genetic algorithm is also used for the calculation of the values of the electrical parameters of the resonant shunt circuit, with objective the maximization of certain band gaps. The results indicate that the proposed technique can be used for the maximization of band gaps at certain frequency ranges, as well as at frequency bands which have not been considered in the optimization problem of the mechanical microstructure. Keywords Auxetic material · Band gaps · Vibration · Shunts · Piezoelectrics 1 Introduction For the study of the mechanical and/or electromechanical behavior of a smart composite structure, homogenization techniques can be used. In this case, the structural behavior of the medium is derived from the detailed study of representative unit elements in periodic forms, creating the final structures in form of lattices according to Bloch theory [1]. The periodic boundary conditions are obtained according the Floquet’s theorem [2,3] for the study of the propagation of the waves to the whole structure. The unit elements, which are also called unit cells, can exhibit frequency zones free of vibrations, that is band gaps, if designed properly. Unit cells can be for example phononic crystals, made by two or more different media with divergent material properties (density, elasticity, etc.). These crystals are also known for their ability to exhibit these isolated frequency zones, especially in areas where propagation of waves, either acoustic or elastic, is limited in every direction. Thus, in certain frequency ranges, the band gaps appear, creating an environment which is mainly free of vibrations [4]. Discrete and continuous aspects of metamaterial elastic 1D and 2D continuous structures with band gaps are studied in [5]. It is shown by the authors that the rigidity of the hosting structure does not affect the P. I. Koutsianitis · G. K. Tairidis · G. E. Stavroulakis (B) Institute of Computational Mechanics and Optimization, School of Production Engineering and Management, Technical University of Crete, University Campus, Kounoupidiana, 73100 Chania, Greece E-mail: [email protected] P. I. Koutsianitis E-mail: [email protected] G. K. Tairidis E-mail: [email protected]
P. I. Koutsianitis et al.
frequency values of the band gap; however, the distance
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