Metastructures composed of translational and/or torsional resonators coupled into periodically supported beams: Bandgap analysis

Metastructures, developed using local resonant arrays, show very effective attenuation behavior at low frequencies in vibroacoustic applications. This study sheds light on metastructures built out of periodically supported Euler-Bernoulli beams as host structures for local resonators in the form of translational and/or torsional resonator assemblies. The approach used for analyzing these periodic structures is based on a combination of the spectral element method and the transfer matrix method. Exact expressions are developed to investigate how combining translational and torsional resonators affects complex banded spectra. Non-classical boundary conditions are imposed to investigate their effect on bandgap features and distributions. Expressions are further developed to analyze the effect of various system parameters on the location and width of bandgaps, in addition to wave attenuation levels. It is worth noting that simple supports stiffened by torsional spring could expand bandgaps, over which elastic waves cannot freely propagate.