Guided wave propagating in a 1-D hexagonal piezoelectric quasi-crystal plate
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O R I G I NA L PA P E R
B. Zhang · J. G. Yu · X. M Zhang · L. Elmaimouni
Guided wave propagating in a 1-D hexagonal piezoelectric quasi-crystal plate
Received: 15 July 2019 / Revised: 17 August 2020 / Accepted: 5 September 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract In the context of Bak’s model, guided waves in a 1-D hexagonal piezoelectric quasi-crystal plate are investigated by applying the Legendre polynomial method. Three cases of quasi-periodic directions are discussed. The dispersion curves, phonon, and phason displacement distributions are illustrated. Some new wave phenomena are revealed: The phase velocity of Lamb wave phason modes decreases as the phonon– phason coupling parameters, Ri , increase. Phason displacements and the electric potential have consistent distributions with those of phonon displacement components in the quasi-periodic direction. These obtained results lay the theoretical basis for the design and optimization of piezoelectric devices.
1 Introduction There existed an accepted fact that solid matters were either crystals or amorphous materials until 1980s. However, it was broken down by the discovery of a novel kind of material, i.e., quasi-crystals (QCs) with long-range orientational and quasi-periodic translational orders [1]. Due to their unique arrangement of atoms, quasi-crystals are of some desirable material properties. For example, their frictional and adhesion coefficients are quite low, but their electric resistivity, abrasion and thermal resistances are very high [2–4]. Accordingly, they have promising applications in the coating surface of engines, thin films, thermoelectric converters, electronics, communication, and so on [5,6]. As one of the important properties, the piezoelectricity of QCs has been paid increasing attention. The governing equations of piezoelectric quasi-crystal media were described by Altay et al. [7]. The piezoelasticity theory of 1-D QCs was investigated by using the operator and complex variable function methods [8]. The axial shear fracture of a transversely isotropic piezoelectric quasi-crystal cylinder was studied by Li et al. [9]. A generally loaded strip crack in a half-space of a 1-D hexagonal piezoelectric quasi-crystal was investigated by Tupholme [10]. The closed-form solutions were obtained for wedges in 1-D piezoelectric QCs by Zhang et al. [11]. Two collinear permeable anti-plane shear or mode-III cracks in a 1-D piezoelectric quasi-crystal structure were studied by Zhou and Li [12]. The mechanical and electric behaviors of 1-D piezoelectric QCs subjected to different loads were studied by Wu et al. [13]. The above references were mainly focused on static investigations. To our best knowledge, kinetic investigations are relatively rare owing to the complexity of the dynamic deformation in QCs. However, they have drawn increasing attention with increasing actual application needs. Actually, there are different opinions about the role of the phason field played in the dynamic deformation. And there exist
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