An analytical approach to the analysis of an electrically permeable interface crack in a 1D piezoelectric quasicrystal

Лобода, В. В.; Komarov, Oleksandr; Bilyi, Dmytro; Lapusta, Yuri

doi:10.1007/s00707-020-02721-8

Cited by 21 publications

(9 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(3) In the absence of the phason field that means 𝑅 30 = 0, 𝐾 20 = 0, 𝑑 150 = 0, and in this case FG PQCs degenerated into FG piezoelectric materials (PEM), Equations (21)(22)(23)…”

Section: Case Studiesmentioning

confidence: 99%

“…Here, the Copson method is adopted to solve the dual integral Equations (21)(22)(23). The solution of Equations (21-23) can be written as…”

Section: Problem Description and Basic Formulationsmentioning

confidence: 99%

“…Lengthy literatures has been developed for fracture statics of QCs [16][17][18][19][20][21][22]. However, due to the coupled phonon field and phason field, the dynamic deformations of QCs structures are very complicated.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Scattering of SH wave by a crack in a functionally graded one dimensional hexagonal piezoelectric quasicrystals

et al. 2022

View full text Add to dashboard Cite

In this paper, the dynamic interaction between SH wave and a crack in functionally graded one‐dimensional hexagonal piezoelectric quasicrystals (PQCs) is studied by using integral transform technique. To make the analysis executable, the material properties are assumed to vary partially in the direction perpendicular to the crack face following an exponential function. The problem was transformed through Fourier transform into three pairs of dual integral equations, which are solved numerically by the Copson method. The explicit expressions of phonon field, phason field and electric field on crack surface are determined. The dynamic field intensity factors of crack tip are given and some special cases are discussed. Numerical examples are then conducted to reveal the influences of amplitude, incident angle and wave number of SH wave and crack length, gradient parameter on the normalized dynamic stress intensity factors (DSIFs). The results of this paper lay a theoretical foundation for the design and nondestructive testing of QCs structures.

show abstract

Section: Case Studiesmentioning

confidence: 99%

“…Here, the Copson method is adopted to solve the dual integral Equations (21)(22)(23). The solution of Equations (21-23) can be written as…”

Section: Problem Description and Basic Formulationsmentioning

confidence: 99%

See 1 more Smart Citation

Scattering of SH wave by a crack in a functionally graded one dimensional hexagonal piezoelectric quasicrystals

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Hu et al [30] studied the antiplane problem of an interface crack between dissimilar 1D hexagonal quasicrystals with piezoelectric effect, and obtained analytical full-field solution for the phonon and phason fields in the cracked bi-materials. Loboda et al [31] developed an exact analytical solution for an electrically permeable interface crack under in-plane deformation in a 1-D piezoelectric quasicrystal.…”

Section: Introductionmentioning

confidence: 99%

Interaction of collinear interface cracks between dissimilar one‐dimensional hexagonal piezoelectric quasicrystals

Gao

Zhong

et al. 2021

Z Angew Math Mech

View full text Add to dashboard Cite

In this paper, the interaction of collinear interface cracks between dissimilar onedimensional (1D) hexagonal quasicrystals with piezoelectric effect under antiplane shear and in-plane electric loading has been studied. By using complex variable method the mixed boundary value problem for the interface cracks was reduced to the solution of Riemann-Hilbert problem. Analytic full-field solution for phonon and phason stresses, electric fields, electric displacement in the cracked bi-materials has been obtained based on the electrically permeable crack model. The electric field and electric displacement inside the interface cracks are found to be nonlinearly distributed under line loadings. The field intensity factors of the interface cracks depend on both the mechanical and electric load for the line loading case, but the field intensity factors depend only on mechanical loading when the uniform loadings are applied at infinity. The investigation of the SIFs of neighboring interface cracks has been used to predict possible crack propagation. It is found that when the neighboring cracks are close enough, the inner crack tips are more likely to propagate and when the neighboring cracks are far away from each other, the outer crack tip of the bigger crack has more possibility to propagate.

show abstract

“…For the applications of piezoelectric quasi-crystal structures, it is necessary to investigate their mechanical behaviors in detail. For this reason, scholars have done a lot of work, including piezoelectric theory [8][9][10], static deformation [11][12][13], fracture mechanics [14][15][16], and contact problems [17]. However, these references are mainly focused on statics, because their dynamic deformations are extremely complicated owing to the coupled phonon, phason, and electric fields.…”

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

View full text Add to dashboard Cite

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.

show abstract

An analytical approach to the analysis of an electrically permeable interface crack in a 1D piezoelectric quasicrystal

Cited by 21 publications

References 37 publications

Scattering of SH wave by a crack in a functionally graded one dimensional hexagonal piezoelectric quasicrystals

Scattering of SH wave by a crack in a functionally graded one dimensional hexagonal piezoelectric quasicrystals

Interaction of collinear interface cracks between dissimilar one‐dimensional hexagonal piezoelectric quasicrystals

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

Contact Info

Product

Resources

About