The bandgap characteristics of a flexural beam with periodic arrays of inertial amplification cantilever-type resonators

This paper presents the investigation of a metastructure, built with periodic arrays of inertial amplification (IA) cantilever-type resonators on a host beam, to improve its low-frequency flexural wave attenuation performance. The IA mechanism is composed of an additional mass and three rigid bars, which are connected by hinges and embedded on the host beam and cantilever-type resonators, respectively. The dynamical model of an IA cantilever-type resonant beam (IACRB) is established by the spectral element method, and its bandgap characteristics and vibration transmissibility are verified numerically and experimentally. The bandgaps of the lumped mass cantilever-type resonant beam are compared to those of the IACRB, showing that the latter has better low-frequency wave attenuation ability. To reveal the underlying physics, the effects of the amplification ratio, IA span, and length ratio of cantilever-type resonators on the band diagram of the IACRB are investigated. It is found that the variation of the amplification ratio results in the bandgap near-coupling phenomenon and the bandgap transposition phenomenon. The increase of IA span by changing position 1 weakens the coupling effect of local resonance and IA. However, the increase of IA span by changing position 2 creates the super-wide pseudo-bandgap as well, which is potential in engineering practices. The variation of the length ratio of cantilever-type resonators decreases its first bending modal frequency and shifts the IA bandgap to a lower frequency range slightly. The modal analysis results of the IACRB show that the proposed mechanism affects the modal distributions of the host structure. The modal frequencies existing in bandgaps are caused by the local vibration mode of the ends of the IACRB.