Mode localization in metastructure with T-type resonators for broadband vibration suppression

This paper proposes a design scheme of a plate-type metastructure integrated with mistuned T-type resonators for broadband vibration suppression. We focus on the effect mechanism of mode localization of the resonators on the bandgap of the metastructure under simply supported boundary conditions. The mathematical model is formulated to accurately predict its dynamic behaviors based on the Hamilton's principle. The explicit bandgap edge expressions considering the mistuning factor are developed based on the modal analysis approach using the assumption of an infinite number of resonators. It is found that the bandwidths of the bandgaps targeted at a natural frequency of the metastructure depend not only on the mass ratio of the T-type resonator but also on the mistuning factors. With the influence of mistuning parameters on mode localization feature (i.e., the phenomena of the frequency veering and the exchange of mode shapes) of the T-type resonator theoretically and experimentally examined, the formation mechanism of broaden bandgaps of the metastructure is revealed. A coupling broad bandgap and double bandgaps can be generated by designing appropriate mistuning parameters. In particular, the phenomena of the bandgap boundaries veering and bandgap near-coupling can be formed through the interaction of double bandgaps to improve the performance of vibration suppression. The present work demonstrates that the proposed mode-localization-based metastructure can provide some insights and potential applications for broadband and multi-frequency vibration suppression of engineering structures.