Multimodal coupling of periodic lattices and application to rod vibration damping with a piezoelectric network

An elastic lattice of point masses can be a suitable representation of a continuous rod for the study of longitudinal wave propagation. By extrapolating the classical tuned mass damping strategy, a multimodal tuned mass damper is introduced from the coupling of two lattices having the same modal properties. The aim of the study is then to implement this multimodal control on a rod coupled to an electrical network. The electromechanical analogy applied to a lattice gives the required network, and the energy conversion is performed with piezoelectric patches. The coupled problem is modeled by a novel semi-continuous transfer matrix formulation, which is experimentally validated by a setup involving a rod equipped with 20 pairs of piezoelectric patches. The broadband efficiency of the multimodal control is also experimentally proved with vibration reductions up to 25 dB on the four first resonances of the rod. Finally, the practical interest of the network is pointed out, as it limits the required inductance. This is confirmed by the present purely passive setup that only involves standard low value inductors.