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RESEARCH PAPERS

Solution of the End Problem of a Liquid-Filled Cylindrical Acoustic Waveguide Using a Biorthogonality Principle

[+] Author and Article Information
W. F. Albers

General Electric Company, Box 1072, Schenectady, New York 12301

H. A. Scarton

Laboratory for Noise and Vibration Control Research, Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, New York 12180-3590

J. Vib. Acoust 114(3), 425-431 (Jul 01, 1992) (7 pages) doi:10.1115/1.2930280 History: Received September 15, 1987; Online June 17, 2008

Abstract

This paper treats the forced motion of an isothermal, Newtonian liquid in a semi-infinite cylindrical waveguide. Its bounding wall is assumed rigid, allowing neither normal nor tangential fluid velocities at its inner surface. Small amplitude acoustic waves are considered to be driven by a steady periodic motion due to the rotationally symmetric deflection of an end plate or membrane. A series expansion of the waveguide eigenmodes is used to construct the solution for the motion anywhere within the guide. Based on a biorthogonality property of the eigenmodes, each coefficient of the series is shown to be directly calculable in terms of axial velocity and radial shear stress at the driver face. Also, results of Galerkin solutions, based on driver axial velocity and zero radial velocity, are given for comparison.

Copyright © 1992 by The American Society of Mechanical Engineers
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