Experimental and Theoretical Study of Localised Bulk Strain Waves

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Project Detail:
Longitudinal bulk strain solitons are long localised nonlinear waves of quasi-permanent form which owe their existence in solid waveguides (e.g. rods, bars, plates, thin-walled structures) to a balance between nonlinear wave-steepening effects and linear wave dispersion. They have a very low attenuation compared to linear ultrasonic waves, which means that they can travel long distances within the bulk, making them ideal candidates for non-destructive testing (e.g. of long pipelines). So far, the waves have been directly observed only in waveguides made of optically transparent materials such polymethylmethacrylate and polystyrene [1].

Recently, considerable progress has been made in modelling the scattering of solitons in damaged areas of layered waveguides [2, 3]. Results indicate that certain characteristics of the solitons could be used to localise defects in lengthy solid waveguides, but there have been only partial experimental studies [4].

The proposed project will be a systematic study of the behaviour of localised waves in waveguides made of transparent and non-transparent materials such as steel. The research will involve: 1) Experimental work focused on the generation, coupling and propagation of solitons using high-speed optical techniques such as Digital Image Correlation [5] and Holographic Interferometry [6] (using high-speed cameras and a custom-made pulsed laser) and 2) Mathematical modelling of those processes by nonlinear partial differential equations of Boussinesq type. The modelling will employ a combination of asymptotic approximations and numerical simulations and requires familiarity with computational packages such as MATLAB or similar.

References
1. G.V. Dreiden, A.M. Samsonov, I.V. Semenova, and A.G. Shvartz, Strain solitary waves in a thin-walled wavguide, Appl. Phys. Lett. 105 (2014) 211906.
2. K.R. Khusnutdinova, M.R. Tranter, Modelling of nonlinear wave scattering in a delaminated elastic bar, Proc. Roy. Soc. A 471 (2015) 20150584.
3. K.R. Khusnutdinova, M.R. Tranter, On radiating solitary waves in bi-layers with delamination and coupled Ostrovsky equations, Chaos 27 (2017) 013112.
4. G.V. Dreiden, K.R. Khusnutdinova, A.M. Samsonov, I.V. Semenova, Bulk strain solitary waves in bonded layered polymeric bars with delamination, J. Appl. Phys. 112 (2012) 063516.
5. M.A. Sutton, J.J. Orteu, and H. Schreier, Image correlation for shape, motion and deformation measurements: Basic concepts, theory and applications (Springer US, 2009).
6. T. Kreis, Handbook of holographic interferometry: Optical and digital methods (Wiley, 2004).

Entry requirements:
Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Physics, Engineering, Optics, Applied Mathematics or a related subject. A relevant Master’s degree and/or experience in one or more of the following will be an advantage: Optical Measurements, Waves in solids, Experimental Science.

Contact details:
Name: Dr Pablo Ruiz
Email address: [Email Address Removed]
Telephone number: +44 1509 227660

How to apply:
All applications should be made online at http://www.lboro.ac.uk/study/apply/research/. Please quote the reference ‘PR24042017’ on all correspondence and on the application form, and ensure that you select ‘Mechanical and Manufacturing Engineering’ under ‘programme name’ on the application form.

Application details:
Reference number: PR24042017
Preferred Start date: June or October 2017
Closing Date: 30 September 2017

Supervisors:
Primary supervisor: Dr. P.D. Ruiz, Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough University
Secondary supervisor: Dr. K.R. Khusnutdinova, Department of Mathematical Sciences, Loughborough University