Guided wave characteristics in the functionally graded two‐dimensional hexagonal quasi‐crystal plate

Zhang, Bo; Yu, Jiangong; Zhang, Xiaoming; Elmaimouni, L.

doi:10.1002/zamm.201900210

Cited by 5 publications

(4 citation statements)

References 30 publications

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“…Second, the phonon-phason coupling effect on wave characteristics is investigated. It can be observed from Figure 3 that the phonon-phason coupling effect has no influence on torsional modes as N = 0, which can be confirmed by equation (23). Furthermore, the phonon-phason coupling effect on flexural and longitudinal phonon modes is weak.…”

Section: Dispersion Curvessupporting

confidence: 52%

“…Buckling and vibration of the two-dimensional quasi-crystal cylindrical shells under axial compression were investigated by Li et al [22]. Guided wave propagation in a functionally graded two-dimensional hexagonal quasi-crystal plate was studied by Zhang et al [23]. From the above review, few references about guided waves in functionally graded piezoelectric quasi-crystal (FGPQC) hollow cylinders are available.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang¹,

Wang

Elmaimouni

et al. 2021

Mathematics and Mechanics of Solids

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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.

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Section: Dispersion Curvessupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

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

Zhang¹,

Wang

Elmaimouni

et al. 2021

Mathematics and Mechanics of Solids

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“…Recently, more and more attention has been paid to the mechanical research of functional hierarchical quality control structures [36][37][38]. Zhang et al [39,40] studied guided wave characteristics in the functionally graded 1D and 2D hexagonal QCs plate. However, to the best of the authors' knowledge, for the partially permeable electrical boundary conditions, the scattering of cracks by elastic wave in functionally graded PEQCs has not been carried out yet in any open literature.…”

Section: Introductionmentioning

confidence: 99%

Dynamic fracture of a partially permeable crack in a functionally graded one-dimensional hexagonal piezoelectric quasicrystal under a time-harmonic elastic SH-wave

Yang

Ding

et al. 2023

Mathematics and Mechanics of Solids

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The dynamic fracture of a crack in a functionally graded one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs) subjected to a time-harmonic elastic SH-wave is studied by using integral transform technique and Copson method. It is assumed that the crack surface is a partially permeable boundary condition and the material properties vary continuously as an exponential function. With the help of the Fourier transform, the boundary value problem of partial differential equation describing fracture problem is formulated to three pairs of dual integral equations, which are numerically solved by Copson method. Explicit expressions for the electroelastic field including phonon and phason stresses and electric field on the crack face are determined. The dynamic intensity factors of the electroelastic field are obtained in closed form, and some special cases of obtained results are discussed. On the basis of theoretical analysis and numerical simulation of the established models, numerical analysis was then conducted to discuss crack length, gradient parameter, electric boundary condition, electric loading, incident angle, amplitude, and wave number on the fracture characteristics of material. The research of this paper will provide a theoretical basis for nondestructive testing, optimal design, and reliability analysis of materials and will enrich the research content of fracture mechanics of multi-field coupling materials.

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“…Based on Legendre polynomial series approach (LPSA), circumferential Lamb wave characteristics in orthotropic fractional order thermoelastic cylindrical plates are studied in this paper. The Legendre polynomial approach has been widely used in a variety of waveguide structures [16][17][18][19]. Nevertheless, in the solving process, the integral kernel functions, including the Legendre polynomials, the Heaviside functions and their derivatives, lead to a large amount of integral calculation and long solving time.…”

Section: Introductionmentioning

confidence: 99%

Circumferential thermoelastic Lamb wave in fractional order cylindrical plates

Wang

et al. 2020

Z Angew Math Mech

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An improved Legendre polynomial series approach (AILPSA) is presented to investigate the circumferential thermoelastic Lamb wave in a fractional order orthotropic cylindrical plate. In the AILPSA, the analytical integration is developed based on the orthogonality and recursive properties of the Legendre polynomial to simplify the integral computation involved in the solving progress. As a consequence, the computational efficiency is improved significantly. Results are compared with those from the previous article to confirm the validity of the introduced method. Using the AILPSA, guided wave characteristics in various fractional order orthotropic cylindrical plates are investigated by solving the eigenvalues and eigenvectors of the system of algebraic equations. The influences of fractional order and radius‐thickness ratio on dispersion curve and displacement, temperature amplitudes are illustrated. The results show that the fractional order almost has no effect on the phase velocities of quasi‐elastic wave modes, but has notable effect on their attenuations. A smaller fractional order means a smaller temperature amplitude for the quasi‐elastic wave mode, but means a larger temperature amplitude for the thermal wave mode. A smaller radius thickness ratio indicates a smaller attenuation and a larger temperature amplitude.

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Guided wave characteristics in the functionally graded two‐dimensional hexagonal quasi‐crystal plate

Cited by 5 publications

References 30 publications

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

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

Dynamic fracture of a partially permeable crack in a functionally graded one-dimensional hexagonal piezoelectric quasicrystal under a time-harmonic elastic SH-wave

Circumferential thermoelastic Lamb wave in fractional order cylindrical plates

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