Design of a smart periodic beam with coupling between local resonances and bragg band-gaps

The success of periodic structures is linked to their peculiar behaviour regarding wave propagation: they have frequency ranges, the so called band-gaps, in which an incoming wave is attenuated. Band-gaps can be generated with two mechanisms: Bragg scattering, directly related to the wavelength of the incoming wave, or local resonances, useful for sub-wavelength applications. In this paper we show that gluing a set of piezoelectric patches on a beam with a periodic disposition, it is possible to obtain both the effect, and possibly couple them. While Bragg band-gaps are ensured due to the periodic arrangements, local resonances are obtained connecting each piezoelectric patch to an RL shunt circuit. Non-dimensional design maps are generated to see both the effects and their interaction. Furthermore, it is shown that two subsequent Bragg band-gaps can be linked thanks to the contribution of the lumped resonators. Results obtained analytically with the Spectral Element method have been corroborated both with FE simulations and experimental tests, and the effects of the resistors on band gap linking are widely discussed