Metamaterials are part of the expanding field of composite materials with engineered structures, though some areas remain underdeveloped. One of these involves the analysis of complex band structures ( k ( ω ) -approach), more particularly to truss cells, in comparison to purely real ones ( ω ( k ) -approach). We seek to fill this knowledge gap by presenting and discussing the employment of both approaches on truss cells, while analyzing how stiffness and mass impact the band structure. Two-dimensional truss metamaterial cells, addressing distinct band gap (BG) phenomena and with real band structure already described in the literature, are evaluated under varying conditions of residual strain and mass distribution between nodes and elements. It is demonstrated that these varying conditions modify band characteristics, with changes in frequency range and attenuation behavior based on the cell type and BG generation phenomenon. These changes are also related to the merging of BGs for two, or even three, distinct or equal phenomena. The study also examines how increasing mass in the elements weakens the association between natural frequencies with BG range and resonant modes, leading to the reduction of distinguishing features. Additional observations from the literature on the expected behavior of the band structure are verified and discussed.
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