The scattering of the SH wave on a limited permeable crack in a functionally graded piezoelectric substrate bonded to a homogeneous piezoelectric strip

Yang, Junfeng; Xing, Li

doi:10.1007/s00707-015-1365-8

Cited by 7 publications

(11 citation statements)

References 24 publications

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“…In this section, we will present some numerical results to examine the effects of gradient parameter, electrical load, electric boundary condition, angle of incidence, crack length, and wave number on fracture characteristics of materials. The normalized wave number is determined as a ω / c sh [15], and the DSIFs of phonon and phason fields are normalized by K σ / σ 0 π a and K H / σ 0 π a [46]. The material constants are selected [33].…”

Section: Computation and Discussionmentioning

confidence: 99%

“…In the phonon field and the phason field, the crack surface is not tractive, that is, for the actual crack filled with air or vacuum, partially permeable or impermeable electrical boundary conditions are preferable because the dielectric constant of the air or vacuum inside the crack is much lower than that of the permeable air or vacuum. Therefore, similar to classical PEMs with an partially permeable [15,[42][43][44], this paper adopts the hypothesis of partially permeable crack mode, which are used below:…”

Section: Problem Description and Basic Formulationsmentioning

confidence: 99%

“…When the boundary conditions are fixed, u 1 (x, y, t), u 2 (x, y, t) and u 3 (x, y, t) can be determined by equation (15), and the stress component and the electric displacement component can be further determined.…”

Section: Problem Description and Basic Formulationsmentioning

confidence: 99%

“…The same problem was studied in document [15]. The authors used the Fourier transform instead of using the Fourier cosine transform in this paper.…”

Section: Case Studiesmentioning

confidence: 99%

“…The scattering of anti-plane stress waves by a crack in non-homogeneous orthotropic medium is analyzed by Ma et al [13]. Yang and Li [14,15] investigated the scattering of SH wave in an arbitrary direction by a crack in a semi-infinite magneto-electro-elastic material bonded to a half-space of PEM and in a functionally graded piezoelectric substrate bonded to a homogeneous piezoelectric strip. Deng and Luo [16] studied wave propagation in piezoelectric circular curved rods.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Computation and Discussionmentioning

confidence: 99%

Section: Problem Description and Basic Formulationsmentioning

confidence: 99%

Section: Problem Description and Basic Formulationsmentioning

confidence: 99%

“…The same problem was studied in document [15]. The authors used the Fourier transform instead of using the Fourier cosine transform in this paper.…”

Section: Case Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

et al. 2022

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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.

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Interaction of anti‐plane shear waves with two collinear cracks in 1D hexagonal piezoelectric quasicrystals

Panja,

Mandal

2023

Z Angew Math Mech

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The present article presents the interaction of anti‐plane shear waves by two collinear cracks in one dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs). With the aid of Fourier transform, the mixed boundary value problem (MBVP) is transformed into three pairs of dual integral equations, which are solved analytically by Hilbert transform. The explicit expressions for dynamic stress intensity factors (DSIFs) of phonon and phason fields, crack opening displacement (COD) and electric displacement (ED) are derived in closed form and some special cases are studied. Numerical values of DSIFs of phonon and phason fields, COD and ED are plotted to show the effect of crack length and electric boundary condition. Moreover, the DSIFs of phonon field and COD are represented graphically for single crack.

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The scattering of the SH wave on a limited permeable crack in a functionally graded piezoelectric substrate bonded to a homogeneous piezoelectric strip

Cited by 7 publications

References 24 publications

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

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

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

Interaction of anti‐plane shear waves with two collinear cracks in 1D hexagonal piezoelectric quasicrystals

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