Energy-based evaluation of sound absorption: Application to rigid duct network FE model under normal incidence

This paper introduces an energy-based methodology for evaluating sound absorption in acoustic materials numerically modeled as rigid duct networks. The approach builds on the concepts of acoustic intensity, formulating the absorption coefficient in terms of time-averaged rates of potential and kinetic energies, and enabling a direct interpretation of the energy balance between these local reactive measures and the active input power. The theoretical framework is derived from plane-wave assumptions and extended to a one-dimensional finite element (FE) discretization of duct networks using the Low Reduced Frequency model to account for viscothermal effects. Four samples are analyzed to assess the physical meaning of the method. Absorption obtained from the 1D-grid FE formulation is compared to 3D FE simulations performed with commercial software. Good agreement is observed when a length correction scheme is applied, with the energy formulation providing complementary interpretations of resonance phenomena and the role of local energy distributions. The results confirm that the energy-based framework not only reproduces classical impedance-based estimates but also offers additional physical understanding, even for irregular geometries. This approach provides a computationally efficient and conceptually valuable tool for sound absorption evaluation, with potential applications in material design, optimization and experimental validation.