Dynamic Anti-Plane Characteristic of an Infinite Piezoelectric Medium With a Non-Circular Cavity

2005 ◽  
Author(s):  
Tianshu Song ◽  
Lili Sun ◽  
Diankui Liu
Keyword(s):  
Electric Field ◽  
Dynamic Stress ◽  
Mapping Method ◽  
Piezoelectric Medium ◽  
Circular Cavity ◽  
Characteristic Parameters ◽  
Stress Concentrations ◽  
Plane Shear ◽  
Concentration Factors ◽  
Piezoelectric Characteristic

In this paper, dynamic stress concentrations are studied in an infinite piezoelectric medium with a non-circular cavity under time harmonic incident anti-plane shear wave and inplane electric field. Based on complex variable and conformal mapping method, the dynamic stress concentration factors and the electric field concentration factors at the boundary of the non-circular cavity are obtained by applying the orthogonal function expansion technique. Numerical examples about an infinite piezoelectric medium with an elliptic cavity are provided with different elliptic axial length ratios, different wave numbers and different piezoelectric characteristic parameters. The calculating results show that dynamic analyses are very important to an infinite piezoelectric medium with a non-circular cavity at lower frequencies and larger piezoelectric characteristic parameters.

Dynamic Stress Concentration on a Semi-Infinite Piezoelectric Medium With a Circular Cavity Near the Surface

2007 ◽  
Author(s):  
Tianshu Song ◽  
Shilong Wang
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Piezoelectric Medium ◽  
Dynamic Stress Concentration ◽  
Circular Cavity ◽  
Characteristic Parameters ◽  
Time Harmonic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Piezoelectric Characteristic

Dynamic interaction is investigated theoretically between a circular cavity and the surface in a semi-infinite piezoelectric medium subjected to time-harmonic incident anti-plane shearing in the present paper. The formulations are based on the method of complex variable and wave function expandedness. Dynamic stress concentration factors at the edge of the circular cavity are obtained by solving boundary value problems with the method of orthogonal function expansion. The calculating results are plotted so as to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the structural geometries influence upon the dynamic stress concentration factors.

Dynamic Antiplane Interaction of Subsurface Circular Cavities in a Semi-Infinite Piezoelectric Medium

2009 ◽  
Author(s):  
Tianshu Song ◽  
Tamman Merhej ◽  
Qingna Shang ◽  
Dong Li
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Numerical Solutions ◽  
Piezoelectric Medium ◽  
Dynamic Stress Concentration ◽  
Characteristic Parameters ◽  
Time Harmonic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Piezoelectric Characteristic

In the present work, dynamic interaction is investigated theoretically between several circular cavities near the surface in a semi-infinite piezoelectric medium subjected to time-harmonic incident anti-plane shearing. The analyses are based upon the use of complex variable and multi coordinates. Dynamic stress concentration factors at the edges of the subsurface circular cavities are obtained by solving boundary value problems with the method of orthogonal function expansion. Some numerical solutions about two interacting subsurface circular cavities in a semi-infinite piezoelectric medium are plotted so as to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the structural geometries influence on the dynamic stress concentration factors.

Dynamic Anti-Plane Behaviors of Interacting Circular Cavities in an Infinite Piezoelectric Medium

2008 ◽  
Author(s):  
Tianshu Song ◽  
Dong Li ◽  
Lili Sun
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Piezoelectric Medium ◽  
Dynamic Stress Concentration ◽  
Wave Load ◽  
Plane Shear ◽  
Time Harmonic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Piezoelectric Characteristic

In this article, dynamic interaction is investigated theoretically between several circular cavities in an infinite piezoelectric medium under time-harmonic incident anti-plane shear wave load. The theoretical formulations are based upon the use of complex variable and multi-coordinates. Dynamic stress concentration factors at the edges of the circular cavities are obtained by solving boundary value problems with the method of orthogonal function expansion. As examples, some calculating results of two interacting circular cavities in an infinite piezoelectric medium are plotted to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the structural geometries influence on the dynamic stress concentration factors.

Dynamic Anti-Plane Behavior of the Interaction Between a Crack and a Circular Cavity in a Piezoelectric Medium

2006 ◽  
Vol 324-325 ◽  
pp. 29-32 ◽  
Author(s):  
Tian Shu Song ◽  
Hong Liang Li ◽  
Jung Qiang Dong
Keyword(s):  
Stress Intensity ◽  
Stress Concentration ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Piezoelectric Medium ◽  
Circular Cavity ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Concentration Factors ◽  
Stress Concentration Factors

In this paper, the dynamic interaction is investigated theoretically between a crack and a circular cavity in an infinite piezoelectric medium under time-harmonic incident anti-plane shearing. The formulations are based on the method of complex variable and Green’s function. The resulting dynamic stress intensity factors at the crack’s tip and dynamic stress concentration factors at the cavity’s edge are obtained with crack-division technique. Numerical results are plotted to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the geometry of the crack and the circular cavity influence upon the dynamic stress intensity factors and dynamic stress concentration factors.

A Piezoelectric Screw Dislocation Interacting with a Dielectric Crack in a Hexagonal Piezoelectric Material

2005 ◽  
Vol 9 ◽  
pp. 183-190
Author(s):  
Jin Xi Liu ◽  
X.L. Liu
Keyword(s):  
Electric Field ◽  
Screw Dislocation ◽  
Electric Displacement ◽  
Image Force ◽  
Mapping Method ◽  
Piezoelectric Medium ◽  
Intensity Factors ◽  
Potential Jump ◽  
Piezoelectric Screw Dislocation ◽  
Dielectric Crack

This paper is concerned with the interaction of a piezoelectric screw dislocation with a semi-infinite dielectric crack in a piezoelectric medium with hexagonal symmetry. The solution of the considered problem is obtained from the dislocation solution of a piezoelectric half-plane adjoining a gas medium of dielectric constant ε0 by using the conformal mapping method. The intensity factors of stress, electric displacement and electric field and the image force on the dislocation are given explicitly. The effect of electric boundary conditions on the dislocation-crack interaction is analyzed and discussed in detail. The results show that ε0 only influences the electric displacement and electric field intensity factors and the image force produced by the electric potential jump.

Dynamic Stress Intensity Factor for a Radial Crack on a Circular Cavity in a Piezoelectric Medium

2010 ◽  
Vol 452-453 ◽  
pp. 273-276
Author(s):  
Tian Shu Song ◽  
Dong Li ◽  
Ming Yue Lv ◽  
Ming Ju Zhang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Stress ◽  
Radial Crack ◽  
Dynamic Stress Intensity Factor ◽  
Crack Tip ◽  
Piezoelectric Medium ◽  
Circular Cavity ◽  
Dynamic Stress Intensity Factors

The problem of dynamic stress intensity factor is investigated theoretically in present paper for a radial crack on a circular cavity in an infinite piezoelectric medium, which is subjected to time-harmonic incident anti-plane shearing. First, a pair of electromechanically coupled Green’s functions are constructed which indicate the basic solutions for a semi-infinite piezoelectric medium with a semi-circular cavity. Second, based on the crack-division technique and conjunction technique, integral equations for the unknown stresses’ solution on the conjunction surface is established, which are related to the dynamic stress intensity factor at the crack tip. Third, the analytical expression on dynamic stress intensity factor at the crack tip is obtained. At last, some calculating cases are plotted to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the geometry of the crack and the circular cavity influence upon the dynamic stress intensity factors. While some of the calculating results are compared with the same situation about a straight crack and with static solutions.

Dynamic Anti-Plane Behaviors on Two Dissimilar Piezoelectric Media with an Interfacial Non-Circular Cavity

2012 ◽  
Vol 525-526 ◽  
pp. 293-296
Author(s):  
Tian Shu Song ◽  
Dong Li ◽  
Ming Ju Zhang ◽  
Yue Fa Zhou
Keyword(s):  
Characteristic Parameter ◽  
Mapping Method ◽  
Wave Number ◽  
Circular Cavity ◽  
Piezoelectric Media ◽  
Conformal Mapping Method ◽  
Time Harmonic ◽  
Expansion Technique ◽  
Stress Concentration Factors ◽  
Piezoelectric Characteristic

Dynamic anti-plane behaviors are studied on two dissimilar piezoelectric media with an interfacial non-circular cavity subjected to time harmonic incident anti-plane shearing. Based on Greens function and conformal mapping method, the dynamic stress concentration factors at the edge of the non-circular cavity are obtained by applying the orthogonal function expansion technique. Numerical cases about two dissimilar piezoelectric media with an elliptic cavity are provided with different elliptic axial length ratio, different wave number and different piezoelectric characteristic parameter. The calculating results show that dynamic analyses are of importance at lower frequencies and larger piezoelectric characteristic parameters.

Dynamic Stress of a Circular Cavity Buried in a Semi-Infinite Functionally Graded Material Subjected to Shear Waves

2006 ◽  
Vol 74 (5) ◽  
pp. 916-922 ◽  
Author(s):  
Xue-qian Fang ◽  
Chao Hu ◽  
Shan-yi Du
Keyword(s):  
Boundary Condition ◽  
Stress Concentration ◽  
Functionally Graded Material ◽  
Dynamic Stress ◽  
Shear Waves ◽  
Functionally Graded ◽  
Circular Cavity ◽  
Graded Material ◽  
Concentration Factors ◽  
Stress Concentration Factors

The multiple scattering of shear waves and dynamic stress in a semi-infinite functionally graded material with a circular cavity is investigated, and the analytical solution of this problem is derived. The analytical solutions of wave fields are expressed by employing the wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the cavity. The image method is used to satisfy the traction-free boundary condition of the material structure. As an example, the numerical solution of the dynamic stress concentration factors around the cavity is also presented. The effects of the buried depth of the cavity, the incident wave number, and the nonhomogeneity parameter of materials on the dynamic stress concentration factors are analyzed. Analyses show that when the nonhomogeneity parameter of materials is <0, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of dynamic stress around the cavity. When the nonhomogeneity parameter of materials is >0, it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.

Dynamical Stress Concentration in an Elastic Plate

1962 ◽  
Vol 29 (2) ◽  
pp. 299-305 ◽  
Author(s):  
Yih-Hsing Pao
Keyword(s):  
Stress Concentration ◽  
Elastic Plate ◽  
Wave Length ◽  
Thin Elastic Plate ◽  
Circular Cavity ◽  
Stress Concentrations ◽  
Compressional Waves ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Dynamical Stress

Stress concentrations around a circular cavity in an infinitely extended, thin elastic plate, during passage of plane compressional waves, are discussed. The dynamical stress concentration factors are found to be dependent on the incident wave length and Poisson’s ratio for the plate, and, at certain wave lengths, they are larger than those encountered under statical loading.

Dynamic Anti-Plane Behaviors of a Semi-Infinite Piezoelectric Medium with a Circular Cavity and a Crack near the Surface

2008 ◽  
Vol 385-387 ◽  
pp. 389-392
Author(s):  
Tian Shu Song ◽  
Dong Li ◽  
Xin Wang Wang ◽  
Sheng Li Dong
Keyword(s):  
Stress Intensity ◽  
Stress Concentration ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Piezoelectric Medium ◽  
Dynamic Stress Concentration ◽  
Circular Cavity ◽  
Dynamic Stress Intensity Factors ◽  
Time Harmonic ◽  
Stress Concentration Factors

Dynamic interaction is investigated theoretically between a circular cavity and a crack near the surface in a semi-infinite piezoelectric medium subjected to time-harmonic incident anti-plane shearing in this paper. The formulations are based on the method of complex variable and Green’s function. Dynamic stress concentration factors at the edge of the circular cavity and dynamic stress intensity factors at the crack tip are obtained by solving boundary value problems with the method of orthogonal function expansion. The calculating results are plotted to show how the frequencies and the orientation of incident wave, piezoelectric characteristic parameters of the material and the structural geometries influence upon the dynamic stress concentration factor (DSCF) and dynamic stress intensity factor (DSIF).

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