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The system stiffness of a negative stiffness membrane structure is widely investigated in metamaterial research, and some special performances have been achieved. While for acoustics, low-frequency absorption still remains a big issue, so in this work, a negative stiffness membrane structure with its theoretical calculation model and experimental verification of sound absorption is established. Moreover, the nonlinear stiffness changes of the thin film under different deformation conditions and different spacing between two permanent magnets are systematically analyzed, obtaining the theoretical stiffness analytical equation of the negative stiffness thin-film structure system. Combined with finite element simulation analysis, the stiffness variation rule and influencing factors of the negative stiffness membrane system are discussed. Specifically, the impact of the mass radius, mass thickness, and film thickness on the magnetic force and system stiffness is analyzed. Based on the acquired testing results, the proper addition of the magnetic suction structure will induce a shift of the absorption peak to a lower frequency region. This work provides useful insights for the further development of the low-frequency sound absorption theory and testing prototype with a negative stiffness membrane structure.