Sound Radiation from Rectangular Panels with Rectangular Cut-out/s

Abstract

This is largely an analytical investigation and the objective of this study is to compute sound power radiated from rectangular panels that are placed in an infinite baffle (or a rigid wall) and that have rectangular cut-outs. The panel is simply-supported on the baffle and has either one or two cut-outs. The cut-outs cause a shift in the resonances of the panel and also alter the modeshapes. Here, the new resonances and modeshapes are computed using Rayleigh-Ritz method. The potential and kinetic energies of the panel occupying the cut-out region are subtracted from those of the full panel. The natural frequencies and modeshapes are compared with FEM and are found to be reasonably accurate for smaller cut-out sizes at lower modes. So a low frequency sound radiation is studied for the panel with small cut-out/s. An appropriate acoustical impedance model for the cut-out is chosen from the literature. First, a one-way coupled analysis is carried out which involves solving an integral equation. Here, the panel has either one cut-out or two cut-outs. Next, a fully coupled analysis is carried out. Again, the panel has either one or two rectangular cut-outs. Some of the integrals are numerically evaluated while others have a closed expression. The radiated power of the panel obtained analytically is compared with that obtained from a simulation using LMS Virtual Lab. Since the Rayleigh-Ritz method deals with averaged energies, potential and kinetic, the local distortions at the edges of a cut-out are not accounted for. This limits the frequency range to a low value (where the modes are not so different from the panel without cut-outs) and somewhat small size cut-outs.