Adaptation of the HQ device for suppressing wave propagation in elastic beams

In this work, we study the application of the Herschel-Quincke (HQ) principle to the case of bending waves in a beam structure. This type of device is well known in acoustic tubes where an HQ filter consists of the bifurcation of a primary tube into two tubes of different lengths placed in parallel. The resulting phase shift creates a destructive interference and so a zero transmission at selected frequencies. To adapt this principle to bending vibrations, a homogeneous solid beam is divided into two different strands with different thicknesses and of same length, so that the phase difference created between these two strands of different wave celerities also leads to the same interferential effects. A Timoshenko wave model is derived to analyse the scattering properties of such HQ filter for bending and longitudinal waves. The results are well confirmed by the reference finite element simulations.