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Crystals 2018, 8(9), 351; https://doi.org/10.3390/cryst8090351

Band Structures Analysis of Elastic Waves Propagating along Thickness Direction in Periodically Laminated Piezoelectric Composites

1
College of Urban and Rural Construction, Shanxi Agricultural University, Jinzhong 030801, China
2
School of Civil Engineering and Mechanics, Lanzhou University, and Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, Lanzhou 730000, China
*
Author to whom correspondence should be addressed.
Received: 18 July 2018 / Revised: 12 August 2018 / Accepted: 20 August 2018 / Published: 1 September 2018
(This article belongs to the Special Issue Phononics)
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Abstract

Existing studies on elastic waves in periodically laminated piezoelectric structures mainly concerned the passive band properties, since the electrical boundaries in the considered structures cannot vary. This paper investigates the tuning of band properties of uncoupled primary and shear (P- and S-) waves along the thickness direction by actively varying the electrical field in periodically multilayered piezoelectric structures consisting of orthotropic materials. The alteration of the electrical field is realized in the multilayered unit cell here by either applying or switching four kinds of electrical boundary conditions, including the electric-open, applied electric capacitance, electric-short, and applied feedback voltage, to the constituent piezoelectric layer via the constituent electrode layers covering both its surfaces. First, the state space formalism is introduced to obtain the partial wave solution of any constituent orthotropic layer in the unit cell. Second, the traditional transfer matrix method is adopted to derive the dispersion equation of general, periodically laminated piezoelectric composites with unit cells consisting of an arbitrary number of piezoelectric layers with various boundaries and of elastic layers. Third, numerical examples are provided to verify the proposed analysis method, and to study the influences of electrode thickness as well as four electrical boundaries on the band structures. All the frequency-related dispersion curves are also illustrated by numerical examples to summarize the general dispersion characteristics of uncoupled P- and S-waves in periodically laminated piezoelectric composites. The main finding is that the innovative dispersion characteristic resulting from the negative capacitance may also be achieved via feedback control. View Full-Text
Keywords: periodically laminates; piezoelectric composites; band structures; elastic waves; electrical boundaries; dispersion curves periodically laminates; piezoelectric composites; band structures; elastic waves; electrical boundaries; dispersion curves
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Li, Q.; Guo, Y.; Wang, J.; Chen, W. Band Structures Analysis of Elastic Waves Propagating along Thickness Direction in Periodically Laminated Piezoelectric Composites. Crystals 2018, 8, 351.

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