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The Mean Curvature of the Influence Surface of Wave Equation With Sources on a Moving SurfaceThe mean curvature of the influence surface of the space-time point (x, t) appears in linear supersonic propeller noise theory and in the Kirchhoff formula for a supersonic surface. Both these problems are governed by the linear wave equation with sources on a moving surface. The influence surface is also called the Sigma - surface in the aeroacoustic literature. This surface is the locus, in a frame fixed to the quiescent medium, of all the points of a radiating surface f(x, t) = 0 whose acoustic signals arrive simultaneously to an observer at position x and at the time t. Mathematically, the Sigma- surface is produced by the intersection of the characteristic conoid of the space-time point (x, t) and the moving surface. In this paper, we derive the expression for the local mean curvature of the Sigma - space of the space-time point for a moving rigid or deformable surface f(x, t) = 0. This expression is a complicated function of the geometric and kinematic parameters of the surface f(x, t) = 0. Using the results of this paper, the solution of the governing wave equation of high speed propeller noise radiation as well as the Kirchhoff formula for a supersonic surface can be written as very compact analytic expression.
Document ID
20040086493
Acquisition Source
Langley Research Center
Document Type
Reprint (Version printed in journal)
External Source(s)
doi:10.1002/(SICI)1099-1476(19991125)22:17<1485::AID-MMA89>3.3.CO;2-#
Authors
Farassat, F. (NASA Langley Research Center Hampton, VA, United States)
Farris, Mark (Midwestern State Univ. Wichita Falls, TX, United States)
Date Acquired
September 7, 2013
Publication Date
December 8, 1999
Publication Information
Publication: Journal Mathematical Methods in the Applied Sciences
Volume: 22
Subject Category
Acoustics
Distribution Limits
Public
Copyright
Public Use Permitted.

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