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Estimates for the logarithmic-mean trend of admittance using Skudrzyk’s method, for models related to Figure 2a. Black solid: plate with mass per unit area matching the membrane, from equation (7); black dashed: plate with mass increased by a factor 10; blue solid: membrane, from equation (8); blue dashed: asymptotic value for membrane, from equation (9); red solid: membrane with the addition of a 1.5 g bridge mass; red dashed: as red solid but with the addition of stiffness 20 kN/m and a dashpot of impedance 1 Ns/m.

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