Transmission, trapping and filtering of waves in periodically constrained elastic plates

2011 ◽  
Vol 468 (2137) ◽  
pp. 76-93 ◽  
Author(s):  
S. G. Haslinger ◽  
N. V. Movchan ◽  
A. B. Movchan ◽  
R. C. McPhedran
Keyword(s):  
Plane Waves ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Quality Factors ◽  
Reflection And Transmission ◽  
Recurrence Algorithm ◽  
Transmission Resonances ◽  
Scattered Fields ◽  
Induced Transparency ◽  
Suppression Region

The paper discusses properties of flexural waves in elastic plates constrained periodically by rigid pins. A structured interface consists of rigid pin platonic gratings parallel to each other. Although the gratings have the same periodicity, relative shifts in horizontal and vertical directions are allowed. We develop a recurrence algorithm for constructing reflection and transmission matrices required to characterize the filtering of plane waves by the structured interface with shifted gratings. The representations of scattered fields contain both propagating and evanescent terms. Special attention is given to the analysis of trapped modes which may exist within the system of rigid pin gratings. Analytical findings are accompanied by numerical examples for systems of two and three gratings. We show geometries containing three gratings in which transmission resonances have very high quality factors (around 35 000). We also show that controlled lateral shifts of three gratings can give rise to a transmission peak with a sharp central suppression region, akin to the phenomenon of electromagnetic-induced transparency.

Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I Formal solution

2005 ◽  
Vol 461 (2063) ◽  
pp. 3413-3436 ◽  
Author(s):  
Ian Thompson ◽  
I. David Abrahams
Keyword(s):  
Formal Solution ◽  
Plane Waves ◽  
Flexural Wave ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Incident Plane ◽  
Principal Directions ◽  
Orthotropic Thin Plate ◽  
Non Destructive ◽  
Kirchhoff Theory

The problem of flexural wave diffraction by a semi-infinite crack in an infinite orthotropic thin plate is considered. Such models have application to the ultrasonic non-destructive inspection of thin components, such as aeroplane wings. For simplicity, the plate is modelled using Kirchhoff theory, and the crack is chosen to be aligned along one of the principal directions of material orthotropy. For incident plane waves, an exact analytical expression for the scattered field is derived by means of the Wiener–Hopf technique. In this model problem, the Wiener–Hopf kernel is scalar and its factorization is expressed in terms of simple, definite, non-singular contour integrals. A detailed numerical evaluation of the solution will be provided in the second part of this work.

scholarly journals Ultrasonic Scattered Field Distribution of One and Two Cylindrical Solids with Phased Array Technique

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Xiaozhou Liu ◽  
Jian Ma ◽  
Haibin Wang ◽  
Sha Gao ◽  
Yifeng Li ◽  
...  
Keyword(s):  
Plane Wave ◽  
Field Distribution ◽  
Scattered Field ◽  
Phased Array ◽  
Simulation Analysis ◽  
Plane Waves ◽  
Theoretical Solution ◽  
Steel Matrix ◽  
Field Distributions ◽  
Scattered Fields

AbstractThe scattered fields of plane waves in a solid from a cylinder or sphere are critical in determining its acoustic characteristics as well as in engineering applications. This paper investigates the scattered field distributions of different incident waves created by elastic cylinders embedded in an elastic isotropic medium. Scattered waves, including longitudinal and transverse waves both inside and outside the cylinder, are described with specific modalities under an incident plane wave. A model with a scatterer embedded in a structural steel matrix and filled with aluminum is developed for comparison with the theoretical solution. The frequency of the plane wave ranged from 235 kHz to 2348 kHz, which corresponds to scaling factors from 0.5 to 5. Scattered field distributions in matrix materials blocked by an elastic cylindrical solid have been obtained by simulation or calculated using existing parameters. The simulation results are in good agreement with the theoretical solution, which supports the correctness of the simulation analysis. Furthermore, ultrasonic phased arrays are used to study scattered fields by changing the characteristics of the incident wave. On this foundation, a partial preliminary study of the scattered field distribution of double cylinders in a solid has been carried out, and the scattered field distribution at a given distance has been found to exhibit particular behaviors at different moments. Further studies on directivities and scattered fields are expected to improve the quantification of scattered images in isotropic solid materials by the phased array technique.

Reflection and Transmission Coefficients of Plane Waves in Magnetoelectroelastic Layered Structures

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
J. Y. Chen ◽  
H. L. Chen ◽  
E. Pan
Keyword(s):  
Piezoelectric Materials ◽  
Plane Waves ◽  
Layered Structures ◽  
Organic Glass ◽  
Reflection And Transmission Coefficients ◽  
Material Structure ◽  
Layered System ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Novel Material

Reflection and transmission coefficients of plane waves with oblique incidence to a multilayered system of piezomagnetic and/or piezoelectric materials are investigated in this paper. The general Christoffel equation is derived from the coupled constitutive and balance equations, which is further employed to solve the elastic displacements and electric and magnetic potentials. Based on these solutions, the reflection and transmission coefficients in the corresponding layered structures are subsequently obtained by virtue of the propagator matrix method. Two layered examples are selected to verify and illustrate our solutions. One is the purely elastic layered system composed of aluminum and organic glass materials. The other layered system is composed of the novel magnetoelectroelastic material and the organic glass. Numerical results are presented to demonstrate the variation of the reflection and transmission coefficients with different incident angles, frequencies, and boundary conditions, which could be useful to nondestructive evaluation of this novel material structure based on wave propagations.

Reflection and Transmission of Plane Waves at the Planar Interface of a General Uniaxial Medium and Free Space

1991 ◽  
Vol 38 (4) ◽  
pp. 649-657 ◽  
Author(s):  
Akhlesh Lakhtakia ◽  
Vijay K. Varadan ◽  
Vasundara V. Varadan
Keyword(s):  
Free Space ◽  
Plane Waves ◽  
Planar Interface ◽  
Reflection And Transmission

Analysis for Scattering of Non-homogeneous Medium by Time Domain Volume Shooting and Bouncing Rays

2021 ◽  
Vol 36 (3) ◽  
pp. 245-251
Author(s):  
Jun Li ◽  
Huaguang Bao ◽  
Dazhi Ding
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Electromagnetic Waves ◽  
High Efficiency ◽  
Homogeneous Medium ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Transient Electromagnetic ◽  
Frequency Domain Methods ◽  
Scattered Fields

In order to evaluate scattering from hypersonic vehicles covered with the plasma efficiently, time domain volume shooting and bouncing rays (TDVSBR) is first introduced in this paper. The new method is applied to solve the transient electromagnetic scattering from complex targets, which combines with non-homogeneous dielectric and perfect electric conducting (PEC) bodies. To simplify the problem, objects are discretized into tetrahedrons with different electromagnetic parameters. Then the reflection and transmission coefficients can be obtained by using theory of electromagnetic waves propagation in lossy medium. After that, we simulate the reflection and transmission of rays in different media. At last, the scattered fields or radiation are solved by the last exiting ray from the target. Compared with frequency-domain methods, time-domain methods can obtain the wideband RCS efficiently. Several numerical results are given to demonstrate the high efficiency and accuracy of this proposed scheme.

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