scholarly journals Dynamic anti-plane behavior of rare earth giant magnetostrictive medium with a circular cavity defect in semi-space

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhiwei Liu ◽  
Hui Qi
Keyword(s):  
Wave Function ◽  
Rare Earth ◽  
Incident Wave ◽  
Concentration Factor ◽  
Incident Angle ◽  
Complex Function ◽  
Magnetic Potential ◽  
Circular Cavity ◽  
Horizontal Boundary ◽  
Linear Algebraic Equations

AbstractAn analytical solution to the anti-plane dynamics problem of semi-space rare earth giant magnetostrictive media with circular cavity defects near the horizontal boundary under the action of SH wave is studied. Based on the Helmholtz theorem and the theory of complex function, the elastic-magnetic dynamic equation of magnetostrictive medium is established, and the semi-space incident wave field is written. In addition, based on the theory of complex function and the method of wave function expansion, the expression of the wave function of the scattered displacement field and the corresponding magnetic potential of the scattered wave under the condition of no stress and magnetic insulation of the horizontal boundary are obtained. Then, based on the conditions of free boundary stress, continuous magnetic induction intensity and continuous magnetic potential around the circular cavity, the infinite linear algebraic equations are established. Finally, the analytical expressions of dynamic stress concentration factor and magnetic field intensity concentration factor around circular cavity in semi-space rare earth giant magnetostrictive medium are obtained. Numerical examples show that the analysis results depend on the following parameters: permeability, dimensional-piezomagnetic coefficient, frequency of the incident wave, incident angle, distance between the circular cavity and horizontal boundary. These results have certain reference value for the study of non-destructive testing and failure analysis of rare earth giant magnetostrictive materials.

scholarly journals Dynamic Anti-plane Behavior of Rare Earth Giant Magnetostrictive Medium With a Circular Cavity Defect in Semi-space

2020 ◽  
Author(s):  
Zhi Liu ◽  
Hui Qi
Keyword(s):  
Rare Earth ◽  
Incident Wave ◽  
Concentration Factor ◽  
Incident Angle ◽  
Complex Function ◽  
Magnetic Potential ◽  
Image Method ◽  
Circular Cavity ◽  
Horizontal Boundary ◽  
Linear Algebraic Equations

Abstract An analytical solution to the anti-plane dynamics problem of semi-space rare earth giant magnetostrictive media with circular cavity defects near the horizontal boundary under the action of SH wave is studied. Based on the Helmholtz theorem and the theory of complex function, the elastic-magnetic dynamic equation of magnetostrictive medium is established, and the semi-space incident wave field is written. In addition, the scattered displacement field and the corresponding magnetic potential of the scattered wave under the condition of no stress and magnetic insulation of the horizontal boundary are obtained by image method. Then, based on the conditions of free boundary stress, continuous magnetic induction intensity and continuous magnetic potential around the circular cavity, the infinite linear algebraic equations are established. Finally, the analytical expressions of dynamic stress concentration factor and magnetic field intensity concentration factor around circular cavity in semi-space rare earth giant magnetostrictive medium are obtained. Numerical examples show that the analysis results depend on the following parameters: permeability, dimensional-piezomagnetic coefficient, frequency of the incident wave, incident angle, distance between the circular cavity and horizontal boundary. These results have certain reference value for the study of non-destructive testing and failure analysis of rare earth giant magnetostrictive materials.

Dynamic Stress Concentration of a Circular Cavity Subjected by Steady Plane SH Waves in an Elastic Quarter with a Semi-Circular Canyon

2014 ◽  
Vol 644-650 ◽  
pp. 1581-1584
Author(s):  
Hui Qi ◽  
Li Ming Cai ◽  
Xiang Nan Pan ◽  
Chun Gao
Keyword(s):  
Wave Function ◽  
Stress Component ◽  
Expansion Method ◽  
Fourier Series Expansion ◽  
Image Method ◽  
Circular Cavity ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Steady State Responses ◽  
Steady Plane

Steady state responses of a circular cavity and a semi-circular canyon subjected by plane SH wave in an elastic quarter are presented by using Fourier-Hankel wave function expansion method and image method with Fourier series expansion on the boundary conditions to determine linear algebraic equations of unknown wave function coefficients. Especially, displacement and stress component expressions are formulated for incident, reflected, scattering waves, respectively. This method can provide an analytical ideas and methods for further studies of elastodynamic interface problems.

The Scattering Field of SH-Wave in Half-Space With a Semi-Cylindrical Hill and a Horizontal Circular Tunnel

2005 ◽  
Author(s):  
Guoqing Wang ◽  
Liming Dai ◽  
Diankui Liu
Keyword(s):  
Wave Function ◽  
Half Space ◽  
Stress Condition ◽  
Complex Function ◽  
Sh Wave ◽  
Coordinate Method ◽  
Linear Algebraic Equations ◽  
Scattering Field ◽  
Moving Coordinate ◽  
The Hill

The scattering field of SH-wave in a half-space with a semi-cylindrical hill and a subsurface horizontal hole is studied in the present research by utilizing a complex function and the moving-coordinate method. Based on the concept of ‘conjunction,’ the domain considered is divided into two subdomains. The first subdomain is a cylindrical one which includes the surface of the hill, while the rest is the second subdomain. In the cylindrical subdomain, a standing wave function is constructed which automatically satisfies the zero-stress condition at the hill surface and arbitrary-stress condition at the other part of the circular subdomain. For the second subdomain, which contains a semi-cylindrical canyon and a subsurface hole, a scattering wave function is assumed, which satisfies the zero-stress condition on the horizontal surface. By employing the moving-coordinate method, the solutions of the mathematical model established for the SH-wave can be obtained with the satisfaction of the continuous conditions of stress and displacement across the junction interface together with the zero-stress condition at the surface of the tunnel. The solutions such obtained consist of a series of infinite linear algebraic equations, which can be solved numerically with consideration of the first finite terms corresponding to the frequencies of the wave. For demonstrating the application of the model developed, the displacements of the horizontal and semi-cylindrical hill surfaces are quantified with different properties of wave and geometry parameters.

Scattering of a shear horizontal wave by a circular cavity in a piezoelectric bi-material strip based on guided wave theory

2020 ◽  
Vol 25 (4) ◽  
pp. 968-985 ◽  
Author(s):  
Hui Qi ◽  
Meng Xiang ◽  
Jing Guo
Keyword(s):  
Integral Equation ◽  
Electric Fields ◽  
Concentration Factor ◽  
Scattering Problem ◽  
Reference Value ◽  
Wave Theory ◽  
Guided Wave ◽  
Circular Cavity ◽  
Two Phase ◽  
Shear Horizontal

The scattering problem of a shear horizontal guided wave in a piezoelectric bi-material strip is analysed by means of the "mirror method," the Green’s function method and guided wave theory. A harmonic out-of-plane line-source force is applied at the junction of two-phase materials. Then, the bi-material strip is divided into two parts, and a pair of in-plane electric fields and a pair of counter-planar forces are applied to the vertical boundary. According to the boundary conditions, the Fredholm integral equation of the first kind is established by using the conjunction method. By effectively truncating the integral equation, the integral equation is simplified to an algebraic equation. The electric field intensity concentration factor and dynamic stress concentration factor around the circular cavity are obtained. The research content of this article is of great reference value in non-destructive testing, providing a reference for the judgement of the reliability of a piezoelectric bi-material strip.

Dynamic Anti-Plane Characteristic for a Quarter-Infinite Piezoelectric Medium with a Cylindrical Lining

2012 ◽  
Vol 602-604 ◽  
pp. 2179-2184
Author(s):  
Li Li Sun ◽  
Tian Shu Song ◽  
Jian Liu
Keyword(s):  
Stress Concentration ◽  
Electric Field ◽  
Field Intensity ◽  
Incident Wave ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Electric Field Intensity ◽  
Dynamic Stress ◽  
Dynamic Stress Concentration Factor ◽  
Whole Space

Use the mirror method to transform the quarter space to the whole space under the complex coordinate system, and with the help of the boundary conditions around the cylindrical lining to solve the unknown coefficient. To do some numerical calculations of the dynamic stress concentration factor and the electric field intensity concentration factor around the cylindrical lining by using the program. In the numerical calculations stage, by changing the medium’s parameters, the structure’s geometry influence and the frequencies of incident wave to obtain more results on dynamic stress concentration factor (DSCF) and electric field intensity concentration factor (EFICF).The calculating results indicate that, under the action of SH wave the DSCF and EFICF around the cylindrical lining are similar to each other, and regularly distributed along the edge of the cylindrical lining. While the magnitude of DSCF and EFICF are larger than any other situations when the frequency of the incident wave was low. And the results are similar to results of the whole space condition too.

NEUTRON–PROTON PAIRING EFFECT ON ONE-PROTON AND TWO-PROTON SEPARATION ENERGIES IN RARE-EARTH PROTON-RICH NUCLEI

2012 ◽  
Vol 21 (12) ◽  
pp. 1250100 ◽  
Author(s):  
F. HAMMACHE ◽  
N. H. ALLAL ◽  
M. FELLAH
Keyword(s):  
Wave Function ◽  
Rare Earth ◽  
Particle Number ◽  
Good Description ◽  
Mean Field ◽  
Pairing Effect ◽  
Pairing Correlations ◽  
The One ◽  
Proton Pairing ◽  
Realistic Choice

The one-proton and two-proton separation energies are studied for "ordinary" and rare-earth proton-rich nuclei by including the isovector neutron–proton (np) pairing correlations using the BCS approximation. Even–even as well as odd nuclei are considered. In the latter case, the wave function is defined using the blocked-level technique. The single-particle energies used are those of a deformed Woods–Saxon mean field. It is shown that the np isovector pairing effects on the one-proton and two-proton separation energies are non-negligible. However, the only isovector BCS approximation seems to be inadequate for a good description of these quantities when including the np pairing effects: either a particle-number projection or the inclusion of the isoscalar pairing effect seems to be necessary. Another possible improvement would be a more realistic choice of the pairing strengths.

scholarly journals Reflection and transmission of P-waves at a very rough interface between two isotropic elastic solids

2021 ◽  
Author(s):  
Pham Chi Vinh ◽  
Do Xuan Tung ◽  
Nguyen Thi Kieu
Keyword(s):  
Incident Wave ◽  
Elastic Layer ◽  
Incident Angle ◽  
P Wave ◽  
Rough Interface ◽  
Elastic Solids ◽  
P Waves ◽  
Reflection And Transmission ◽  
Reflected Waves ◽  
Transmission Coefficients

This paper deals with the reflection and transmission of P-waves at a very rough interface between two isotropic elastic solids. The interface is assumed to oscillate between two straight lines. By mean of homogenization, this problem is reduced to the reflection and transmission of P-waves through an inhomogeneous orthotropic elastic layer. It is shown that a P incident wave always creates two reflected waves (one P wave and one SV wave), however, there may exist two, one or no transmitted waves. Expressions in closed-form of the reflection and transmission coefficient have been derived using the transfer matrix of an orthotropic elastic layer. Some numerical examples are carried out to examine the reflection and transmission of P-waves at a very rough interface of tooth-comb type, tooth-saw type and sin type. It is found numerically that the reflection and transmission coefficients depend strongly on the incident angle, the incident wave frequency, the roughness and the type of interfaces.

Scattering of SH-Wave by an Interface Cylindrical Elastic Inclusion with a Semicircular Debonded above Subsurface Cavity

2013 ◽  
Vol 753-755 ◽  
pp. 1846-1850
Author(s):  
Chun Xiang Zhao ◽  
Hui Qi ◽  
Jing Fu Nan
Keyword(s):  
Green Function ◽  
Elastic Inclusion ◽  
Complex Function ◽  
Fredholm Integral Equations ◽  
Circular Cavity ◽  
Sh Wave ◽  
Polar Coordinate ◽  
Set Up ◽  
Material Space ◽  
Horizontal Interface

The Scattering of SH-wave by a cylindrical elastic inclusion on horizontal interface in bi-material space with a semicircular debonded above subsurface circular cavity have been considered using the methods of complex function and Green function. Firstly, we divide the solution domain along the interface and disconnected boundary into two half-spaces, an upper one and a lower one. And Green function was constructed by using the methods of complex function and multi-polar coordinate. Secondly, the bi-material media was connected along the horizontal interface using the idea of interface conjunction, then undetermined anti-plane forces were loaded at the linking sections respectively to satisfy continuity conditions, and a series of Fredholm integral equations of the first kind to determine that the unknown forces could be set up through continuity conditions on surface. Finally, some examples for DSCF around cylindrical elastic inclusion edge are presented and discussed. Numerical results show that subsurface circular cavitys existence notablely influences DSCF of around cylindrical elastic inclusion edge with a semicircular debonded above subsurface circular cavity.

Rare Earth Wave Function Determination by Polarized Neutron Diffraction in REA12

1977 ◽  
pp. 168-173 ◽  
Author(s):  
B. Barbara ◽  
J. X. Bourcherle ◽  
J. P. Desclaux ◽  
M. F. Rossignol ◽  
J. Schweizer
Keyword(s):  
Wave Function ◽  
Rare Earth ◽  
Neutron Diffraction ◽  
Polarized Neutron
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