رسالة جامعية
Wave propagation in pipes of slowly-varying radius with compressible flow
| العنوان: | Wave propagation in pipes of slowly-varying radius with compressible flow |
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| المؤلفون: | Rasolonjanahary, Irina |
| بيانات النشر: | Applied Mathematics and Theoretical Physics University of Cambridge |
| سنة النشر: | 2018 |
| المجموعة: | Apollo - University of Cambridge Repository |
| مصطلحات موضوعية: | resonance, wave propagation, trapped mode, slowly-varying radius, compressible flow, thin elastic shell, acoustic |
| الوصف: | The work presented in this thesis studies acoustic perturbations in slowly varying pipes. The slow variation is introduced in the form of a small parameter ${\epsilon}$ and through this in turn gives rise to a slow axial scale $X$ such that $X = {\epsilon}x$ where $x$ is the normal axial coordinate. This allows an asymptotic approach and the WKB method is used to solve the subsequent mathematical problems. The first deals with the existence of a trapped mode in a hard-walled pipe of varying radius conveying fluid. For the derived leading order propagating mode solution, its amplitude becomes singular at transition points $X_{t}$ and $X_{t'}$ where $X_{t} > 0$ and $X_{t'} < 0$ and thus is unable to propagate past these points. Because of the break down in the solution, this leads to the theory that in the neighbourhood of these points there exists a boundary layer in which the original assumption about having slow variation does not hold. By first seeking the thickness of the layer, valid solutions can then be derived and then matched to the outer solutions in order to produce a uniform solution which holds for the entire axial domain. Once this is achieved, it is then used to derive trapped mode solutions. In this case, the theory used is that of two single turning points which are then combined to obtain the full solution. It is illustrated through consideration of examples and the dependence on ${\epsilon}$ is also shown through various plots. This problem will be considered for a symmetric and asymmetric duct and for differing duct parameters. Problems may arise when the two turning points lie close together and so we seek to improve on the method used by deriving a solution to trapped modes encompassing both turning points, which will be proposed together with some illustrations in order to justify its use and reliability. Next, the case of mode propagations on a thin elastic shell of varying radius conveying fluid is studied. The acoustic solutions of a straight shell in vacuo are first briefly ... |
| نوع الوثيقة: | doctoral or postdoctoral thesis |
| وصف الملف: | application/pdf |
| اللغة: | English |
| العلاقة: | https://www.repository.cam.ac.uk/handle/1810/277876Test |
| DOI: | 10.17863/CAM.25212 |
| الإتاحة: | https://doi.org/10.17863/CAM.25212Test https://www.repository.cam.ac.uk/handle/1810/277876Test |
| حقوق: | All rights reserved ; https://www.rioxx.net/licenses/all-rights-reservedTest/ |
| رقم الانضمام: | edsbas.97A3EC2F |
| قاعدة البيانات: | BASE |
| DOI: | 10.17863/CAM.25212 |
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