Dynamic anti-plane analysis for two symmetrically interfacial cracks near circular cavity in piezoelectric bi-materials

Hassan, Ahmed; Song, Tianshu

doi:10.1007/s10483-014-1891-9

Cited by 32 publications

(9 citation statements)

References 10 publications

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“…The magnetization direction is along the 𝑧-axis, and the time harmonic factor 𝑒 −𝑖𝜔𝑡 is omitted. Taking into account the absence of body forces and free magnetic charge, the steady state equilibrium equations are expressed as follows [11]:…”

Section: Governing Equation and Boundary Conditionsmentioning

confidence: 99%

“…A large number of scholars use the characteristics of wave to establish nondestructive testing method to study the defects of materials, and have achieved a lot of results [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Since Pao and Mow [1] used analyzed elastic wave in the whole space by separating time variable, elastic wave theory has been gradually improved and widely used in engineering.…”

Section: Introductionmentioning

confidence: 99%

“…Zhang et al [9] examined the two-dimensional (2D) scattering and diffraction of plane SH waves induced by a non-symmetrical V-shaped canyon is examined by using the wavefunction expansion method. Song et al [10,11] investigated the dynamic problem of cavity near the horizontal boundary, and Hui et al [12][13][14] studied the dynamic stress around cavity in a piezoelectric bi-material media.…”

Section: Introductionmentioning

confidence: 99%

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Anti‐plane stress analysis for V‐notch in a piezomagnetic half space under SH wave

Zhang,

2024

Z Angew Math Mech

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In this paper, the anti‐plane stress analysis of a V‐notch with complex boundary conditions in a piezomagnetic half space is studied. Firstly, SH wave is considered as an external load acting on piezomagnetic half space, on the basis of repeated image superposition, the analytical expression of scattering wave is conducted, which satisfies the boundary conditions on the boundary of the half space. Then, the analytical expression of standing wave is established, which satisfies the stress free and magnetic insulation conditions on the boundaries of V‐notch by the fractional Bessel function expansion method and Graf addition theorem. Finally, Green's function method is applied, the half space is divided into two parts along the vertical interface, a pair of in‐plane magnetic field and out‐plane forces are applied on the vertical interface, and the first kind of Fredholm integral equations are set up and solved by applying orthogonal function expansion technique and effective truncation. Results clarified the influence on the dynamic stress concentration factor and magnetic field intensity concentration factor under proper conditions. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article.

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Section: Governing Equation and Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anti‐plane stress analysis for V‐notch in a piezomagnetic half space under SH wave

Zhang,

2024

Z Angew Math Mech

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“…Since Baron used the integral transformation method and the wave Symmetry 2021, 13, 246 2 of 12 function expansion method to give the analytical solution of the cylindrical cavity to the compression wave pulse scattering problem, the wave function expansion method has become the main analysis method to study the wave scattering problem [10]. So far, whether in the field of traditional seismic research or in the field of smart materials, the wave function expansion method has played an important role [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Anti-Plane Dynamics Analysis of a Circular Lined Tunnel in the Ground under Covering Layer

Chu

Zhang

et al. 2021

Symmetry

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Wave diffusion in the composite soil layer with the lined tunnel structure is often encountered in the field of seismic engineering. The wave function expansion method is an effective method for solving the wave diffusion problem. In this paper, the wave function expansion method is used to present a semi-analytical solution to the shear horizontal (SH) wave scattering problem of a circular lined tunnel under the covering soil layer. Considering the existence of the covering soil layer, the great arc assumption (that is, the curved boundary instead of the straight-line boundary) is used to construct the wavefield in the composite soil layer. Based on the wave field and boundary conditions, an infinite linear equation system is established by adding the application of complex variable functions. The finite term is intercepted and solved, and the accuracy of the solution is analyzed. Although truncation is inevitable, due to the Bessel function has better convergence, a smaller truncation coefficient can achieve mechanical accuracy. Based on numerical examples, the influence of SH wave incident frequency, soil parameters, and lining thickness on the dynamic stress concentration factor of lining is analyzed. Compared with the SH wave scattering problem by lining in a single medium half-space, due to the existence of the cover layer and the influence of its stiffness, the dynamic stress of the lining can be increased or inhibited. In addition, the lining thickness has obvious different effects on the dynamic stress concentration coefficient of the inner and outer walls of different materials.

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“…Guo et al [4] analyzed the problem of two non-symmetrical collinear cracks emanating from an elliptical hole in a piezoelectric solid. Hassan and Song [5] studied the dynamic stress intensity factor in the piezoelectric bi-materials model with two symmetrically permeable interfacial cracks near the edges of a circular cavity.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of the Dynamic Behavior for Interacting Cracks on Circular Cavities in Piezoelectric Material

Dong¹,

Wang²

2014

Proceedings of the 2015 International Conference on Material Science and Applications

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Abstract. The present paper is exposed theoretically to the influence on the dynamic stress intensity factor (DSIF) in the piezoelectric material model with two permeable radial cracks emanating from the edges of two circular cavities, subjected to the dynamic incident anti-plane shearing wave (SH-wave). Green's functions are established based on complex variable and wave function expansion methods. Conjunction and crack-simulation techniques are used to evaluate DSIFs at the cracks' tip. The problem is reduced to a series of Fredholm integral equations of first kind. The numerical results are obtained by solving the equations to show the influence of the structural geometry, and the wave frequencies of incident wave on the dimensionless DSIFs.

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Dynamic anti-plane analysis for two symmetrically interfacial cracks near circular cavity in piezoelectric bi-materials

Cited by 32 publications

References 10 publications

Anti‐plane stress analysis for V‐notch in a piezomagnetic half space under SH wave

Anti‐plane stress analysis for V‐notch in a piezomagnetic half space under SH wave

Anti-Plane Dynamics Analysis of a Circular Lined Tunnel in the Ground under Covering Layer

Modeling and Analysis of the Dynamic Behavior for Interacting Cracks on Circular Cavities in Piezoelectric Material

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