Introduction to Wiener-Hopf Methods in Acoustics and Vibration.
Abstract
The Wiener-Hopf technique is now firmly established as a powerful tool for research in certain types of boundary value problem arising in acoustics. Typical problems which may be solved exactly or asymptotically with this technique concern the sound and vibration levels generated by finite or semi-infinite planar or cylindrical surfaces, of local or extended reaction, immersed in a compressible fluid and subject to acoustic or mechanical forcing. However, even the simplest of these problems involves complications which are irrelevant to an understanding of the Wiener-Hopf method itself and its various extensions. Accordingly, this report was written in an attempt to display the operation of the technique in an even simpler physical and mathematical context, and thereby to encourage its more widespread use. The report deals with the application of Wiener-Hopf methods to one-dimensional wave motions on strings and beams, and in particular with the reflection and transmission from discontinuities in the mechanical properties of a string. Also included is a section illustrating how a generalized Wiener-Hopf problem can be set up for a three-part problem involving a string of finite length. Two dimensional wave problems are then exemplified in a discussion of the acoustic field generated by a vibrating half-plane, and the effect of uniform mean flow over the half-plane is included to show how different types of 'edge condition' may be accommodated.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1977
- Accession Number
- ADA048766
Entities
People
- David G. Crighton
Organizations
- The Catholic University of America