Solution of the wave equation for open surfaces involving a line integral over the edge
Abstract
A simple mathematical model of a stationary source distribution for the supersonic-propeller noise-prediction formula of Farassat (1983) is developed to test the validity of the formula solutions. The conventional thickness source term is used in place of the Isom thickness formula; the relative importance of the line and surface integrals in the solutions is evaluated; and the numerical results are compared with those obtained with a conventional retarded-time solution in tables. Good agreement is obtained over elevation angles from 10 to 90 deg, and the line-integral contribution is found to be significant at all elevation angles and of the same order of magnitude as the surface-integral contribution at angles less than 30 deg. The amplitude-normalized directivity patterns for the four cases computed (x = 1.5 or 10; k = 5.0 or 50) are presented graphically.
- Publication:
-
Journal of Sound Vibration
- Pub Date:
- July 1984
- DOI:
- 10.1016/0022-460X(84)90267-0
- Bibcode:
- 1984JSV....95..136F
- Keywords:
-
- Engine Noise;
- Noise Prediction (Aircraft);
- Propellers;
- Supersonic Speed;
- Wave Equations;
- Amplitudes;
- Elevation Angle;
- Integral Equations;
- Mathematical Models;
- Acoustics