Statistical modal Energy distribution Analysis to determine the transmission loss of a plate with acoustic black hole indentations
Résumé
Passive vibration reduction in plates can be achieved by exploiting the acoustic black hole (ABH) effect. This relies on embedding circular indentations (i.e., ABHs) of power-law thickness profile in the plate, so that waves entering them slow down and concentrate their energy at the ABH center. There, they get dissipated by means of viscoelastic layers. To date, most works to determine the vibration field and sound radiated by ABH plates have been based on semi-analytical and numerical deterministic methods. This limits prediction capabilities for complex ABH systems in the mid to high frequency range. In this work, we address the computation of the transmission loss (TL) of an ABH plate between two cavities, by means of Statistical modal Energy distribution Analysis (SmEdA). SmEdA extends the applicability of statistical energy analysis (SEA) to mid frequencies as it circumvents some of the SEA restrictive hypotheses. While in a complex SEA system power flow is established between subsystems (groups of resonant modes), in SmEdA power flow is recognized between individual subsystem modes. The cavity modes in this work are computed analytically, whereas the modes of the ABH plates are obtained using a Gaussian basis function in the framework of the Rayleigh- Ritz method. SmEdA is then used to compute the TL of the ABH plate and compared to that of a uniform plate. It will be shown that an ABH plate can result in higher TL than that of a uniform plate, despite having less mass, confirming some experimental results in literature.
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