<p>Lithium-ion batteries typically consist of stacked, wound micron-sized cell structures (cathode/separator/anode), exhibiting periodic structural characteristics akin to phononic crystals. In this study, we present a theoretical model based on Biot’s theory and Floquent-Bloch theorem to investigate wave propagation in a one-dimensional, multi-layered porous lithium-ion battery structure. We employ a numerical approach to compute the bandgap characteristics of this multi-layered porous anode. Our results demonstrate excellent agreement with those obtained from finite element simulations, incorporating a solid mechanics module, thereby validating the feasibility and accuracy of the proposed method. Considering the dynamic variations in electrode porosity and mechanical properties during battery cycling, our findings reveal a fundamental connection between the State of Charge (SOC) and the bandgap characteristics of lithium-ion batteries. A comparative analysis of the effects of structural properties (with and without Biot theoretical assumptions) on the frequency range of transverse and longitudinal bandgaps is also presented. Notably, we observe that the frequency difference of the bandgap shifts systematically during the charging cycle both with and without Biot theoretical assumptions. This mapping relationship provides valuable theoretical insight for the acoustic non-destructive characterization of battery state parameters.</p>