Herschel-Quincke filters adapted to bending waves in beams and plates

A Herschel-Quincke (HQ) filter is a device for controlling the transmission of guided waves: by adding one or more auxiliary branches to a waveguide, it is possible to construct delay lines, which induce destructive interference effects and consequently zero-transmission phenomena at targeted frequencies. We explore the use of this principle in the context of elastic waves in beams.The dispersive nature of bending waves and their coupling with longitudinal waves introduces complexity into the tuning of the zero transmission frequencies. A model, developed within the framework of Timoshenko's beam theory, provides the scattering matrix of an HQ filter composed of several branches. The model is confirmed by FE and thus demonstrates the interest of the approach for the control of vibrations. The architecture of the HQ device and the modelling approach are extended to a 3 branches configuration. The properties of the filter are analysed, leading to a discussion of the advantages and disadvantages of the HQ strategy.