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Abstract This study investigates the vibration properties of a new class of composite structures made by single or multiple-core structured fabrics encased in a sealed plastic skin, which is deflated. The core structured fabrics are formed by interlocked truss-like grains. The work focuses on how the flexural response and energy dissipation of these materials are influenced by mechanical (vacuum pressure), packing (single/multiple layers), and geometry (particle type and dimensions) of the fabrics. This article presents a comprehensive set of quasi-static and dynamic three-points bending tests taken on beam-like specimens encompassing single or multiple layers of fabrics made with different types of truss-like grains (cubic, octahedral, and spherical) having different size (of the grain and truss element) and characterized by increasingly higher levels of vacuum pressure exerted by the coating bag (5–80 kPa). The work demonstrates that this new class of structures can be designed to cover a broad range of flexural stiffnesses and fundamental resonance frequencies, whose values can be further tuned online by varying the vacuum in the bags. For instance, for a nominal vacuum of 40 kPa, the bending stiffnesses and fundamental resonance frequency of the samples considered in this study spanned between 0.03×106–1.4×106Nmm2 and 6–63Hz, respectively. Finally, these structures are characterized by quite stable and low-energy dissipation effects. For instance, apart from layouts with a single core fabric, the loss factor of the samples considered in this study ranged between 0.04 and 0.1.