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Title of Thesis

Akhtar Hussain
Institute/University/Department Details
Department of Mathematics/ Quaid-i-Azam University, Islamabad
Number of Pages
Keywords (Extracted from title, table of contents and abstract of thesis)
acoustic waves, water acoustics, plane harmonic acoustic wave, elastic half plane, cylindrical wave, spherical wave, wiener-hopf techniques, saddle point method

In this thesis, we have attempted a few problems in the theory of acoustic wave propagation which are relevant in under water acoustics. Firstly, we investigate the scattering of a plane harmonic acoustic wave from an absorbing half plane attached to an elastic half plane. The planes are subjected to heavy fluid loading limit in which the effect of the fluid inertia on the plate is dominant. Functional Wiener-Hopf equation is obtained and the diffraction problem is solved using the Fourier transform and the saddle point method. Analytic expressions for the non attenuating subsonic surface wave travelling on the elastic plate and the scattered field are obtained. We extend this problem to consider cylindrical wave and spherical wave excitations. Finally, the transient fields (impulse response) in the cases of plane wave, line source and point source are studied and the corresponding time dependent surface waves and diffracted waves are obtained.

Download Full Thesis
935.4 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents 0
40.86 KB
2 1 Mathematical Preliminaries 10
82.96 KB
  1.1 The Wiener- Hopf Techniques 10
  1.2 General Scheme Of Wiener- Hopf Techniques 14
  1.3 Saddle Point Method 17
  1.4 Saddle Point Near A Pole 21
3 2 The Scattering Of An Acoustic Wave From The Absorbing-Elastic Coupling Of Two Half Planes 24
107.29 KB
  2.1 Formulation Of The Problem 25
  2.2 Solution Of The Problem 29
  2.3 Subsonic Surface Wave 39
  2.4 The Scattered Field 40
4 3 The Scattering Of An Acoustic Wave From Absorbing-Elastic Coupling Of Two Half Planes Due To Line/Point Source 42
158.66 KB
  3.1 Formulation Of The Line Source Problem 43
  3.2 Solution Of The Problem 45
  3.3 Point Source Problem 51
  3.4 Solution Of The Point Source Problem 52
5 4 Transient Response Of Absorbing Half Plane Coupled With An Elastic Half Plane 56
120.64 KB
  4.1 Plane Wave Incidence 57
  4.2 Line Source Incidence 61
  4.3 Point Source Incidence 63
6 5 Appendix A 67
551.09 KB
  5.1 Appendix B 73
  5.2 References 83
  5.3 Figures 84