The mean curvature of the influence surface of wave equation with sources on a moving surface

✍ Scribed by F. Farassat; Mark Farris

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 236 KB
• Volume: 22
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(19991125)22:17<1485::aid-mma89>3.0.co;2-8

✦ Synopsis

The mean curvature of the in#uence surface of the space}time point (x, t) appears in linear supersonic propeller noise theory and in the Kirchho! formula for a supersonic surface. Both these problems are governed by the linear wave equation with sources on a moving surface. The in#uence surface is also called the -surface in the aeroacoustic literature. This surface is the locus, in a frame "xed 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 -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 -surface of the space}time point (x, t) 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 Kirchho! formula for a supersonic surface can be written as very compact analytic expressions.