Annular double-leaf Herschel-Quincke filter for flexural wave mitigation in elastic plates

This work presents an analysis of a 2D plate equipped with an Herschel-Quincke (HQ) filter, which is a noise reduction device traditionally applied to plane acoustic waves in tubes. The basic principle of the HQ filter involves creating a path length difference between two propagating waves, leading to destructive interference and, as a consequence, an attenuation at specific frequencies. In this study, an HQ filter is proposed, consisting in two superposed annular plates of different thickness, embedded in a solid plate of infinite extension. Propagation in the two parallel plates creates destructive interferences, leading to complete vibration isolation between the central and the external zones. The aim of this study is to develop a consistent formulation for determining the zero transmission frequencies resulting from the annular HQ filter. The analysis follows the Kirchhoff–Love assumptions of classical plate theory and involves solving both the zero transmission frequency problem and a forced vibration problem. Initial results demonstrate the attenuation of flexural wave vibrations in the HQ plate. Additionally, the analysis of energy flow and insertion loss reveals issues of wave amplitude amplification, a phenomenon that can be predicted and that applies to any constrained system under external excitation.