Скачать или смотреть WHTW01 | Dr. Ian Thompson | Diffraction in Mindlin plates

WHTW01 | Dr. Ian Thompson | Diffraction in Mindlin plates

Speaker: Dr Ian Thompson (University of Liverpool)
Date: 16th Aug 2019 - 11:30 to 12:00
Venue: INI Seminar Room 1
Title: Diffraction in Mindlin plates
Event: (WHTW01) Factorisation of matrix functions: New techniques and applications
Abstract: Plate theory is important for modelling thin components used in engineering applications, such as metal panels used in aeroplane wings and submarine hulls. A typical application is nondestructive testing, where a wave is transmitted into a panel, and analysis of the scattered response is used to determine the existence, size and location of cracks and other defects. To use this technique, one must first develop a clear theoretical understanding the diffraction patterns that occur when a wave strikes the tip of a fixed or free boundary. Diffraction by semi-infinite rigid strips and cracks in isotropic plates modelled by Kirchhoff theory was considered by Norris & Wang(1994). Although both problems require the application of two boundary conditions on the rigid or free boundary, the resulting Wiener-Hopf equations can be decoupled, leading to a pair of scalar problems. Later, Thompson & Abrahams (2005 & 2007) considered diffraction caused by a crack in a fibre reinforced Kirchhoff plate. The resulting problem is much more complicated than the corresponding isotropic case, but again leads to two separate, scalar Wiener-Hopf equations. In this presentation, we consider diffraction by rigid strips and cracks in plates modelled by Mindlin theory. This is a more accurate model, which captures physics that is neglected by Kirchhoff theory, and is valid at higher frequencies. However, it requires three boundary conditions at an interface. The crack problem and the rigid strip problem each lead to one scalar Wiener-Hopf equation and one 2x2 matrix equation (four problems in total). The scalar problems can be solved in a relatively straightforward manner, but the matrix problems (particularly the problem for the crack) are complicated. However, the kernels have some interesting properties that suggest the possibility of accurate approximate factorisations.<br>
<br>
<br><br>References<br>A. N. Norris and Z. Wang. Bending-wave diffraction from strips and cracks on thin plates. Q. J. Mech. Appl. Math., 47:607-627, 1994.<br>I. Thompson and I. D. Abrahams. Diffraction of flexural waves by cracks in orthotropic thin elastic plates.I Formal solution. Proc. Roy. Soc. Lond., A, 461:3413-3434, 2005.<br>I. Thompson and I. D. Abrahams. Diffraction of flexural waves by cracks in orthotropic thin elastic plates.II. Far field analysis. Proc. Roy. Soc. Lond., A, 463:1615-1638, 2007.

-------------------

FOLLOW US
🌐| Website: https://www.newton.ac.uk
🎥| Main Channel:    / @isaacnewtoninstitute  
🐦| Twitter:   / newtoninstitute  
💬| Facebook:   / newton.institute  
📷| Instagram:   / isaacnewtoninstitute  
🔗| LinkedIn:   / isaac-newton-institute-for-mathematical-sc...  

SEMINAR ROOMS
🥇| INI Seminar Room 1:    / @iniseminarroom1  
🥈| INI Seminar Room 2:    / @iniseminarroom2  
🛰️| INI Satellite Events:    / @inisatellite  

ABOUT
The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.

👉 Learn more about us and our events here: https://www.newton.ac.uk