Semi-Discrete Coincidence in the Mid-Frequency Sound Transmission Through Rib-Stiffened Panels

Abstract

Abstract. Plates with attached beams or ribs, rather than monolithic plates, are commonly employed in civil and mechanical engineering for reasons of weight and static stiffness. Unfortunately, attaching stiffeners to a plain plate generally increases its radiation efficiency and reduces its airborne sound insulation. This contribution aims at gaining insight into the sound insulation of rib-stiffened plates in the mid-frequency range, where the modal behavior of the plate is still important, but the neighboring sound fields can already be considered as diffuse. A detailed finite element model of a PMMA plate with steel stiffeners attached is constructed and coupled to a reverberant sound field model of the adjoining room(s) within the recently developed hybrid finite element -statistical energy analysis framework. This framework is computationally very efficient, it enables to compute the coupling loss factors between the sound fields in a rigorous, straight forward way, and the uncertainties due to random wave scattering -which is the physical origin of the diffuse field -can be quantified. The finite element model of the plate is first calibrated by minimizing the difference between its lowest natural frequencies and mode shapes and the corresponding measured values. The hybrid model is then employed for predicting the sound reduction index across the building acoustics frequency range. These predictions are validated against airborne sound insulation measurements. Within a wide frequency range, pronounced dips are observed at specific natural frequencies of the plate, at which the wavelength of the corresponding mode shape is close to the free acoustic wavelength. Since there is an obvious connection with the coincidence phenomenon for infinite plates, the observed phenomenon is termed the semi-discrete coincidence phenomenon. It is shown that in the mid-frequency range, an important increase in airborne sound insulation can be achieved by suppressing only a few particular resonances of the considered rib-stiffened plate.7620