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.

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

On transformation strains and uniform fields in multiphase elastic media

1992 ◽  
Vol 437 (1900) ◽  
pp. 291-310 ◽  
Keyword(s):  
Concentration Factor ◽  
Elastic Stiffness ◽  
Local Fields ◽  
Influence Functions ◽  
Elastic Solids ◽  
Two Phase ◽  
General Properties ◽  
Multiphase Systems ◽  
Concentration Factors ◽  
Mechanical Influence

The effect of local eigenstrain and eigenstress fields, or transformation fields, on the local strains and stresses is explored in multiphase elastic solids of arbitrary geometry and material symmetry. The residual local fields caused by such transformation fields are sought in terms of certain transformation influence functions and transformation concentration factor tensors. General properties of these functions and concentration factors, and their relation to the analogous mechanical influence functions and concentration factors, are established, in part, with the help of uniform strain fields in multiphase media. Specific estimates of the transformation concentration factor tensors are evaluated by the self-consistent and Mori-Tanaka methods. It is found here that although the two methods use different constraint tensors in solutions of the respective dilute problems, their estimates of the mechanical, thermal, and transformation concentration factor tensors, and of the overall stiffness of multiphase media have a similar structure. Proofs that guarantee that these methods comply with the general properties of the transformation influence functions, and provide diagonally symmetric estimates of the overall elastic stiffness, are given for two-phase and multiphase systems consisting of, or reinforced by, inclusions of similar shape and alignment. One of the possible applications of the results, in analysis of overall instantaneous properties and local fields in inelastic composite materials, is described in the following paper.

Detection of Defects in Titanium Using Shear Horizontal Guided Waves

2021 ◽  
Author(s):  
Christian Peyton ◽  
Rachel S. Edwards ◽  
Steve Dixon ◽  
Ben Dutton ◽  
Wilson Vesga
Keyword(s):  
Guided Waves ◽  
Wave Mode ◽  
Guided Wave ◽  
Inspection System ◽  
Wave Direction ◽  
Finite Element Software ◽  
Small Defect ◽  
Back Face ◽  
The Relationship ◽  
Shear Horizontal

Abstract This paper investigates the interaction behaviour between the fundamental shear horizontal guided wave mode and small defects, in order to understand and develop an improved inspection system for titanium samples. In this work, an extensive range of defect sizes have been simulated using finite element software. The SH0 reflection from a defect has been shown previously to depend on its length as the total reflection consists of reflections from both the front and back face. However, for small defect widths, this work has found that the width also affects this interference, changing the length at which the reflection is largest. In addition, the paper looks at how the size of the defect affects the mode converted S0 reflection and SH0 diffraction. The relationship between the SH0 diffraction and defect size is shown to be more complex compared to the reflections. The mode converted S0 reflection occurs at an angle to the incident wave direction; therefore, the most suitable angle for the detection has been found. Simultaneous measurement of multiple waves would bring benefits to inspection.

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