Axial guided wave characteristics in functionally graded one-dimensional hexagonal piezoelectric quasi-crystal cylinders

2021 ◽  
pp. 108128652110134
Author(s):  
B. Zhang ◽  
X.H. Wang ◽  
L. Elmaimouni ◽  
J.G. Yu ◽  
X.M. Zhang
Keyword(s):  
Coupling Effect ◽  
Energy Conversion Efficiency ◽  
Guided Wave ◽  
Functionally Graded ◽  
Phonon Modes ◽  
One Dimensional ◽  
Longitudinal Modes ◽  
Wave Characteristics ◽  
Piezoelectric Effects ◽  
Hollow Cylinders

In one-dimensional hexagonal piezoelectric quasi-crystals, there exist the phonon–phason, electro–phonon, and electro–phason couplings. Therefore, the phonon–phason coupling and piezoelectric effects on axial guided wave characteristics in one-dimensional hexagonal functionally graded piezoelectric quasi-crystal (FGPQC) cylinders are investigated by utilizing the Legendre polynomial series method. The dispersion curves and cut-off frequencies are illustrated. Wave characteristics in three hollow cylinders with different quasi-periodic directions are comparatively studied. Some new wave phenomena are revealed: the phonon–phason coupling and piezoelectric effects on the longitudinal and torsional phonon modes ( N = 0) vary as the quasi-periodic direction changes; the phonon–phason coupling effect on flexural–torsional modes in the r-, z-FGPQC hollow cylinders, and on flexural–longitudinal modes in ϑ-FGPQC hollow cylinders increases as N increases. The corresponding results obtained in this work lay the theoretical foundation for the design and manufacture of piezoelectric transducers with high resolution and energy-conversion efficiency.

Guided Wave Propagation in Functionally Graded One-Dimensional Hexagonal Quasi-Crystal Plates

2020 ◽  
Vol 36 (6) ◽  
pp. 773-788
Author(s):  
B. Zhang ◽  
J.G. Yu ◽  
X.M. Zhang
Keyword(s):  
Coupling Effect ◽  
Guided Wave ◽  
Functionally Graded ◽  
Polynomial Method ◽  
Coupling Coefficients ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Sh Waves ◽  
One Dimensional ◽  
Non Destructive

ABSTRACTDue to the high brittleness, cracks, holes, and other defects that are easily generated in quasi-crystal structures can affect safe applications in serious cases. For guided wave non-destructive testing, the propagation of Lamb and SH waves in functionally graded one-dimensional hexagonal quasi-crystal plates are investigated. Governing equations of wave motion in the context of Bak’s model are deduced and solved by the Legendre orthogonal polynomial method. Dispersion curves, phonon and phason displacement, and stress distributions are illustrated. The convergence of the present method applied to functionally graded quasi-crystal plates is verified. Moreover, the influences of the phonon-phason coupling effect and graded fields on wave characteristics are analyzed. Some new results are obtained: angular frequencies of phason modes always decrease as phonon-phason coupling coefficients, Ri, increase; and phonon and phason displacements of Lamb and SH waves at high frequencies are mainly distributed in the region that contains more quasi-crystal material with a smaller elasticity modulus and less rigidity. The obtained results establish the theoretical foundation of guided wave non-destructive testing for functionally graded quasi-crystal plates.

One-Dimensional Solutions for Transient Thermal Stresses in Functionally Graded Hollow Cylinders and Hollow Spheres

2008 ◽  
Author(s):  
Yoshihiro Ootao ◽  
Yoshinobu Tanigawa ◽  
Glaucio H. Paulino ◽  
Marek-Jerzy Pindera ◽  
Robert H. Dodds ◽  
...  
Keyword(s):  
Thermal Stresses ◽  
Hollow Spheres ◽  
Functionally Graded ◽  
One Dimensional ◽  
Hollow Cylinders ◽  
Transient Thermal

Guided waves in a functionally graded 1-D hexagonal quasi-crystal plate with piezoelectric effect

2021 ◽  
pp. 1045389X2110639
Author(s):  
Bo Zhang ◽  
Jiangong Yu ◽  
Hongmei Zhou ◽  
Xiaoming Zhang ◽  
Lahoucine Elmaimouni
Keyword(s):  
Significant Influence ◽  
Guided Waves ◽  
Coupling Effect ◽  
Functionally Graded ◽  
Crystal Plate ◽  
Polynomial Method ◽  
Coupling Coefficients ◽  
Governing Equations ◽  
Phonon Modes ◽  
Sh Waves

For the purpose of design and optimization for piezoelectric quasi-crystal transducers, guided waves in a functionally graded 1-D hexagonal piezoelectric quasi-crystal plate are investigated. In this paper, a model combined with the Bak’s and elastohydrodynamic models is utilized to derive governing equations of wave motion, and real, pure imaginary, and complex roots of governing equations are calculated by using the modified Legendre polynomial method. Subsequently, dispersion curves and displacements of phonon and phason modes are illustrated. Then, guided waves in functionally graded 1-D hexagonal piezoelectric quasi-crystal plates with different quasi-periodic directions are studied. And the phonon-phason coupling effect on Lamb and SH waves are analyzed. Accordingly, some interesting results are obtained: The phonon-phason coupling just affects Lamb waves in the x- and z-direction quasi-crystal plates, and SH waves in the y-direction quasi-crystal plate. Besides, frequencies of propagative phason modes decrease as phonon-phason coupling coefficients Ri increase. Furthermore, a variation in the polarization has a more significant influence on phonon modes, and a variation in the quasi-periodic direction has a more significant influence on phason modes.

Guided wave propagation in functionally graded cylindrical structures with sector cross-sections

2017 ◽  
Vol 24 (2) ◽  
pp. 434-447 ◽  
Author(s):  
Zhang Bo ◽  
Yu Jiangong ◽  
Jean-Etienne Lefebvre ◽  
Xu Weijiang ◽  
Zhang Xiaoming ◽  
...  
Keyword(s):  
Cross Sections ◽  
Guided Waves ◽  
Guided Wave ◽  
Functionally Graded ◽  
Destructive Testing ◽  
Cylindrical Structures ◽  
Angular Measure ◽  
Wave Characteristics ◽  
Ultrasonic Guided Wave ◽  
Phase Velocity Dispersion

The differential equations governing guided waves in functionally graded cylindrical structures with sector cross-sections are solved by introducing the double orthogonal polynomial series method into the cylindrical coordinate system, and the wave characteristics are subsequently investigated. The validity of the present method is confirmed by way of the comparison with available references, and the convergence is discussed. The corresponding phase velocity dispersion curves, displacement distributions and Poynting vectors are illustrated. The influences of the variation in the radius to thickness ratio, angular measure and gradient index on the guided wave characteristics are discussed, which can be used as significant guidance on ultrasonic guided wave non-destructive testing for functionally graded cylindrical structures with sector cross-sections.

The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited

2003 ◽  
Vol 70 (3) ◽  
pp. 359-363 ◽  
Author(s):  
S. Mukherjee ◽  
Glaucio H. Paulino
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Graded Materials ◽  
One Dimensional ◽  
Space And Time ◽  
Graded Material ◽  
Nonhomogeneous Materials ◽  
Exponentially Graded

Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.

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