SCATTERING OF WAVES BY HALF PLANES AND SLITS WITH MIXED BOUNDARY CONDITIONS

Abstract

Considerable attention has been given to the acoustic scattering from half planes. The aim of this thesis is to contribute something by studying some acoustic diffraction problems from the absorbing half plane. Although, the acoustic wave diffraction from an absorbing half plane with similar absorbing parameter has been studied in the literature, nevertheless no attempt has been made to consider the spherical wave diffraction from a bi-impedant half plane in still air. The absorption in the half plane is introduced through different absorbing parameters. The problem is formulated in terms of matrix Wiener-Hopf (W. H.) functional equation. Physically, it corresponds to a mathematical model for a noise barrier whose surface is treated with two different acoustically absorbent materials. The modified W.H. method is used to arrive at the solution. We further calculate the diffraction of a spherical acoustic wave from a porous barrier using a simple theory of porous materials [77] in still air. Our model assumes the balTier is made from a rigid material that is riddled with small pores that are approximately normal to the plane of the balTier. We take limited account of the compressibility of the gas in the pores. However, the gas in each pore behaves primarily as an incompressible cylinder, driven back and forth by the harmonic Wavefield, but opposed by the frictional force generated at the pore walls ( the flow resistance). The barrier is thin enough (with respect to wavelength) that sow1d is communicated from one side to the other by the motion of numerous incompressible cylinders. The approximate boundary conditions for such a situation are derived. A formal analytic solution to the complete problem is given, for the diffracted wavefield in the farfield region of the slit. The dependence on the barrier parameters of the power removed from the reflected wavefield by the diffraction at the slit is exhibited. In the case of noise radiated by aero engines and inside wind twmels, it is necessary to discuss acoustic diffraction in the presence of a moving fluid . Therefore, the theory of acoustic diffraction is further extended to include the case of moving fluid and the following two problems are addressed in this direction. (1) "The diffraction of spherical wave by a halfplane in a moving fluid". A finite region in the \ic inity llt" the edge of a half plane has an impedance boundary conditions; the remaining part of the half plane is taken as rigid. It is found that the fie ld is increased in case of moving fluid when compared with still air case. The fie ld is also independent of the direction of the flow. This model has potential application in engine noise shielding by aircraft wings. (2) "The diffraction of a spherical Gauss ian pulse by an uhsorhing half plane in a moving fluid for trailing edge (situation}". The trailing edge adds the complications of a trailing vortex sheet to the absorbing half plane. The motivation of this problem comes from a desire to understand the transient nature of the wavefields- since these can be expressed as linear combination of Gaussian pulses. The time dependence of the fie ld is tackled by the lise of temporal Fourier transform . It is found that field ratio of no wake to wake situation is independent of the type llf acoustic sources. Also near the edge of absorbing half plane, the fie ld of a spherical pulse caused by the Kutta-loukowski condition is in excess of that in its absence. Chapter 0 is devoted to the brief history of the problems of acoustic scattering. This chapter also contains the motivation for the work presented in this thesis. In chapkr 1, we calc ulate the diffracted field by a slit in an infinite poro us harrier. Charter 2 deals with the problems of scattering by a bi-impedant half plane. Chapter 3 is devoted to the scattering of a spherical wave by a rigid screen with an absorbent edge in a moving fluid. In chapter 4, we present the scattering of a spherical Gaussian pulse near an absorbing half plane in a moving fluid .