Single-phase metamaterial plates for broadband vibration suppression at low frequencies

Abstract

By studying platonic crystals based on lattices of cavities containing N-beam resonators, we conclude that crystals made of 1-beam resonators easily produce low-frequency omnidirectional bandgaps. Based on this favorable property, hardly obtained for resonant cavities containing a higher number of beams N ≥ 2, we have designed single-phase metamaterial plates for the suppression of low frequency flexural waves in a broad range of frequencies. These metamaterials are obtained by using resonant cavities containing a multiple number M of identical 1-beam resonators uniformly distributed in the cavity. Square lattices of this type of resonators have been studied by using the impedance matrix approach and the multiple scattering method. This semi-analytical method has been employed to show the existence of complete bandgaps whose width can be optimized by increasing M. For the case M = 4, the largest number of resonators studied here, three complete bandgaps separated by two narrow passbands appear in the band structure. The formation of these complete bandgaps originates from the dynamic interaction between different local resonators as well as their interaction with the propagating waves in the host plate. By using composite structures consisting of platonic crystal slabs with complementary bandgaps, these separated bandgaps easily merge into a broadband wave attenuation region. The normalized width, defined as the percentage of the bandwidth to its central frequency, reaches 95.3%, representing an enhancement of about one order of magnitude compared with the absolute bandwidth obtained for the case of a single 1-beam resonator in the cavity. It is shown that the gaps can be easily tuned to lower frequencies by changing the geometrical parameters, such as the length of the beam, the radius and thickness of the smaller circular plate. Since the metamaterial is made of a single-phase material without attaching heavy masses, the work reported here provides a simple approach to construct low-cost structures with potential applications in aeronautic and astronautic industries for broadband vibration suppression at low frequencies.