Sound absorption by subwavelength membrane structures: A geometric perspective

Decorated membranes comprising a thin layer of elastic film with small rigid platelets fixed on top have been found to be efficient absorbers of low-frequency sound. In this work we consider the problem of sound absorption from a perspective aimed at deriving upper bounds under different scenarios, i.e., whether the sound is incident from one side only or from both sides, and whether there is a reflecting surface on the back side of the membrane. By considering the negligible thickness of the membrane, usually on the order of a fraction of one millimeter, we derive a relation showing that the sum of the incoming sound waves' (complex) pressure amplitudes, averaged over the area of the membrane, must be equal to that of the outgoing waves. By using this relation, and without going to any details of the wave solutions, it is shown that the maximum absorption achievable from one-sided incidence is 50%, while the maximum absorption with a back-reflecting surface can reach 100%. The latter was attained by the hybridized resonances. All the results are shown to be in excellent agreement with the experiments. This generalized perspective, when used together with the Green function's formalism, can be useful in gaining insights into the constraints on what are achievable in scatterings and absorption by thin film structures and delineating them.