Added mass of a membrane vibrating at finite amplitude

The properties of the added mass for a plane membrane suspended horizontall y between supports and vibrating naturally in a plane, in air, with a half- sine fundamental mode and finite amplitude are obtained by analysis. Thin a erofoil theory is applied, and the membrane is modelled as a vortex sheet. A ratio of added air-mass to the mass of the membrane itself, alpha, is def ined. It is found that alpha is equal to 0.68 divided by the mass ratio m/( rho l), where m is the mass per unit area of the membrane itself, rho the d ensity of the air flow and l the length of the membrane. It is also found t hat the added mass is equal to the mass of the air in a rectangle with heig ht 0.68l over the membrane. These results are confirmed by comparison with those obtained from a source-distribution Green's function approach. (C) 19 98 Academic Press.