A Unified Mass–Spring–Damping Framework for Sound Absorption: From Classical Resonators to AI-Enabled Smart Structures

Broadband, low-frequency sound absorption within a compact device remains a central unsolved problem in noise control engineering, arising from fundamental trade-offs among resonator volume, absorption bandwidth, panel thickness, and frequency tunability that no passive, linear, time-invariant system can simultaneously circumvent. This review establishes a unified mass–spring–damping (MSD) framework applied systematically across the full spectrum of resonance-based absorber technologies. From first principles, we derive the mass–stiffness coupling result (the mass-disappearing result of Shen and Liu): fixing the resonance frequency imposes K=Mωres2, so acoustic mass and stiffness cannot be adjusted independently; the half-absorption bandwidth Π1=η/(Mωres)+Vωres/(c0Star) then depends explicitly on the cavity volume V (system stiffness) and on the damping coefficient η, rather than on mass as an independent lever. This explains why neck extension, space-coiling, and membrane loading—which merely add mass while leaving the cavity stiffness unchanged—fail to broaden the absorption band at fixed volume, and refocuses the design effort on stiffness reduction and damping control. Five non-dimensional performance metrics are introduced that collapse the scattered literature into a single, scale-independent language for rigorous comparison across all absorber families: normalised half-absorption bandwidth Π1, volume efficiency Π2, integral absorption criterion Π3 tied to the Rozanov causality bound, quality factor Q=1/Π1, and frequency-thickness ratio Π4. A two-degree-of-freedom acoustic–structural coupling model yields closed-form effective stiffness and damping, revealing how structural loss augments acoustic damping, how modal veering produces split absorption peaks, and how the anti-resonance frequency becomes a designable parameter. A critical distinction is drawn between mathematical negative stiffness (a fitting artefact) and physical negative stiffness via repulsive magnets, bistable elements, or negative-capacitance piezoelectric shunts, which genuinely reduces cavity stiffness, lowers resonance frequency, and widens bandwidth beyond the passive causality bound. The shunt electromechanical diaphragm further demonstrates α>0.9 at nine tonal frequencies spanning three octaves without mechanical modification. Finally, embedding MSD equations and Π1–Π4 bounds as hard physical priors in AI/LLM-assisted design frameworks is identified as the key step toward provably physically consistent absorber synthesis.