AN ANALYTICAL SOLUTION FOR THE SELF- AND MUTUAL RADIATION RESISTANCES OF A RECTANGULAR PLATE

• Published in: Journal of sound and vibration Vol. 245; no. 1; pp. 1 - 16
• Main Author: LI, W.L.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 02.08.2001; Elsevier
• Subjects: Acoustics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Structural acoustics and vibration; Radiation resistance; Numerical integration; Acoustic radiation; Series expansion; Rectangular plate; Simple support; Asymptotic approximation; Aspect ratio; Analytical solution; Wave number; Acoustic power; Structural acoustics
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.2000.3552

It is widely accepted that, for an arbitrary acoustic wavenumber, the radiation resistance of a simply supported rectangular plate has to be calculated through numerical integration. In this study, an analytical solution for the self- and mutual radiation resistances is obtained in the form of the power series of the non-dimensional acoustic wavenumber. Unlike the previous analytical or asymptotic solutions, it is not subject to any of the restrictions usually imposed upon the acoustic wavenumber. A few numerical examples are given simply to verify the solution and elucidate the reliance of the self- and mutual radiation resistances on the acoustic wavenumber and the plate aspect ratio. It is shown that the present formulae are extremely efficient by cutting the CPU time by orders of magnitude in comparison with the traditional numerical integration scheme. This investigation successfully fills the long-existing gap in solutions for the moderate wavenumbers that are often of primary concern in an acoustic analysis.