On the influence of internal oscillators on the performance of metastructures: Modelling and tuning conditions

A longitudinally excited metastructure with periodically distributed internal oscillators is considered with a view to determining how the tuning condition between their frequency and the frequency of the metastructure as a whole affects vibration attenuation. First, the mechanical model is created, and the tuning condition related to the first resonance frequency of the metastructure with blocked internal oscillators and the first resonance frequency of internal oscillators themselves is obtained in an original analytical form. Then, this condition is used to design the stiffness of the internal oscillators and they are allowed to oscillate in the metastructure, yielding vibration attenuation around the first resonance. The influence of the number of internal oscillators as well as the mass ratio between the mass of one internal oscillator and external oscillator of the metastructure is investigated. Experimental validations, accompanied with numerical results, of these theoretical results are provided subsequently. In addition, the theoretical concept is extended to other resonances, demonstrating its adaptivity and generality, and these cases are then validated via numerical experiments in FEM simulations.