Graduate Thesis Or Dissertation
 

On the diffraction of a cylindrical pulse by a half plane

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/p8418r17w

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  • The effect of a pulse produced by an acoustic or electromagnetic line source oriented parallel to the edge of a perfectly conducting half plane is considered. The Green's functions for the modified Helmholtz equation are found by solving for the Green's functions for a cylinder of sectorial cross-section, then allowing the radius of the sector to go to infinity to form a wedge, and finally opening the wedge to form a half plane. The Green's function for the sectorial domain itself, is determined by first solving the eigenvalue problem for the sectorial domain. The solution for the half plane is represented in the form of a Laplace transform integral. Then the solution for a "Dirac" pulse, which is the inverse Laplace transform of the Green's function for the modified Helmholtz equation, is directly available and the result of an arbitrary pulse can be synthesized from it by integration. The results for several pulses are produced by this method and explicitly show the "transient" terms.
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