Reduced order integration for the radiation efficiency of a rectangular plate.

Y Yu,C Hopkins

doi:10.1121/10.0005268

Abstract

A reduced order integration is proposed for the prediction of radiation efficiency and radiation impedance for a rectangular plate. The formula is simplified using the spatial windowing approach and avoids the singular point at zero radiation distance. Compared with other formulas using similar approaches, the formulation in this letter is computationally efficient and does not require the assumption of an equivalent square plate to reduce the calculation time.

Highlights

The radiation efficiency of a simple rectangular plate can be efficiently calculated using a modal approach, such as from Leppington et al.1,2 For multilayer or stiffened rectangular plates, Villot et al.3 introduced a spatial windowing approach in the wavenumber domain that has shown reasonable agreement with measured sound reduction indices
Davy et al.8 rewrote the integral equations for the traveling wave case to remove singularities; for the double integral, it is still computationally costly when compared to Leppington et al and Bonfiglio et al This led to an approximate formula that combined the traveling and mode shape method, which significantly reduced calculation times
This paper describes an improvement to the spatial windowing approach that maintains the accuracy of Villot et al for rectangular plates but increases computational efficiency

Summary

Introduction

The radiation efficiency of a simple rectangular plate can be efficiently calculated using a modal approach, such as from Leppington et al. For multilayer or stiffened rectangular plates, Villot et al. introduced a spatial windowing approach in the wavenumber domain that has shown reasonable agreement with measured sound reduction indices. For multilayer or stiffened rectangular plates, Villot et al. introduced a spatial windowing approach in the wavenumber domain that has shown reasonable agreement with measured sound reduction indices. This has a double integral that can be reduced to a single integral when the plate dimensions have an aspect ratio less than 1:2. Based on the azimuthally averaged radiation impedance, it is shown that the fifth order integration can be reduced to a single integral without the singularities that occur in the approach of Rhazi and Atalla and without the errors incurred by Bonfiglio et al in assuming a square plate

Order reduction of the radiation efficiency integral

Comparison of radiation efficiency calculations