Passive control of vibrations of a beam by means of Herschel–Quincke vibration filters

This work concerns the adaptation of the Herschel–Quincke filters (HQ) known in the case of plane acoustic waves in tubes to the case of bending waves in beams. The objective is to develop new techniques to design vibration filters in thin structures. In acoustics, an HQ filter consists of the insertion of a bifurcation in a primary tube, so as to create two tubes in parallel and of different length. The phase difference creates destructive interference at certain frequencies which gives rise to zero transmission. In the case of the bending waves considered here, the HQ interference is obtained by locally splitting a thin beam into two segments of the same length but of different thickness. The difference in travel time is then created by the difference in bending stiffness between the two segments. A semi-analytical wave decomposition model using Timoshenko's theory is developed to perform parametric studies of behaviour of such a device. Finite element simulations and experimental demonstrations confirm the predictions of a semi-analytical model. The results highlight the link between the geometric parameters of the device and its filtering properties. Therefore, this paper establishes a novel strategy of design of vibration filters, which utilizes the HQ effect for bending waves in beams.