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Semi-discrete coincidence in the mid-frequency sound transmission through rib-stiffened panels
Book Contribution - Book Chapter Conference Contribution
Plates with attached beams or ribs, rather than monolithic plates, are commonlyemployed in civil and mechanical engineering for reasons of weight and static stiffness. Unfortunately,attaching stiffeners to a plain plate generally increases its radiation efficiency andreduces its airborne sound insulation. This contribution aims at gaining insight into the soundinsulation of rib-stiffened plates in the mid-frequency range, where the modal behavior of theplate 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 constructedand coupled to a reverberant sound field model of the adjoining room(s) within the recentlydeveloped hybrid finite element - statistical energy analysis framework. This framework is computationallyvery efficient, it enables to compute the coupling loss factors between the soundfields 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 ofthe plate is first calibrated by minimizing the difference between its lowest natural frequenciesand mode shapes and the corresponding measured values. The hybrid model is then employedfor predicting the sound reduction index across the building acoustics frequency range. Thesepredictions are validated against airborne sound insulation measurements. Within a wide frequencyrange, pronounced dips are observed at specific natural frequencies of the plate, atwhich 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, theobserved phenomenon is termed the semi-discrete coincidence phenomenon. It is shown that inthe mid-frequency range, an important increase in airborne sound insulation can be achievedby suppressing only a few particular resonances of the considered rib-stiffened plate.
Book: Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering: Eccomas 2016
Pages: 7620 - 7627