Locally resonant acoustic metamaterials (LRAMs) effectively reduce low-frequency noise, since their locally resonant systems act as spatial frequency filters. However, they have narrow bandgaps (BGs), impose additional weight on the primary system, and work only at the adjusted frequency range. For widening BGs, the unit cells must be large in size or contain dense materials. As a solution to the disadvantages mentioned above of LRAMs, this paper proposes a novel three-dimensional lightweight re-entrant meta-structure composed of a cross-shaped beam scatterer embedded in a host plate with holes based on the square lattice metamaterial. By combining the re-entry networks mechanism and the Floquet-Bloch theory, on the basis of cross-shaped beam theory and perforation mechanism, we demonstrate that such a lightweight LRAM structure can filter elastic waves across a broad frequency range (not just a specific narrow region) while simultaneously reducing structure weight to a significant degree. The band structures, transmission loss spectrum (TL), and displacement vector fields are calculated utilizing the finite-element method (FEM) for a finite period structure comprising 5 unit cells. Meanwhile, vibration modes at the edges of BGs are studied carefully to elucidate the formation mechanism, dynamic response, and dispersion features of BGs. In addition, the influences of material and geometrical properties on the dispersion characteristics are examined by the sensitivity analysis, and the results are discussed with the equivalent spring-mass models. Numerical results demonstrate that the structure is capable of generating multiple ultra-wide BGs with over 680% resonant bandgap coverage factor with a high vibration insulation peak, where the sound reduction of the super-cell exceeds 120 dB within (0-12 kHz), based on the local resonance mechanism. This research provides a new physical insight into wide spatial frequency range filtering and light-weighting structures.
