Prediction of the sound radiation from a vibrating body often requires a computation of the acoustic pressure on the body’s surface, given the normal surface vibration. This paper explores what computational advantages a variational formulation may have over other formulations, such as those which solve the Helmholtz integral equation directly. The variational formulation is developed here for bodies of revolution in axisymmetric vibration and specialized to finite cylinders. The general implementation technique of the variational formulation is the Rayleigh-Ritz method which yields a set of simultaneous linear equations for the unknown coefficients in the expansion of the surface pressure in terms of a finite set of basis functions. A case is made to the effect that computations based on the variational formulation can often yield results of desirable accuracy with substantially less computational time. A prerequisite for such an achievement is that one makes a good selection of the basis functions. Such a selection may be aided by physical insight and common sense.
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January 1989
This article was originally published in
Journal of Vibration, Acoustics, Stress, and Reliability in Design
Research Papers
Faster Calculations of Sound Radiation from Vibrating Cylinders Using Variational Formulations
Xiao-Feng Wu
Xiao-Feng Wu
School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
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Xiao-Feng Wu
School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
J. Vib., Acoust., Stress, and Reliab. Jan 1989, 111(1): 101-107 (7 pages)
Published Online: January 1, 1989
Article history
Received:
January 30, 1988
Online:
November 23, 2009
Citation
Wu, X. (January 1, 1989). "Faster Calculations of Sound Radiation from Vibrating Cylinders Using Variational Formulations." ASME. J. Vib., Acoust., Stress, and Reliab. January 1989; 111(1): 101–107. https://doi.org/10.1115/1.3269803
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