The effect of wall elasticity on the properties of a Helmholtz resonator

Abstract

The effect of compliant walls on the properties of a Helmholtz resonator is examined. The effective stiffness of the resonator is decreased by the wall compliance, while the effective mass is unchanged to leading order. The radiation resistance is also decreased due to a cancellation between the radiation from the cavity opening and the radiation from the cavity walls. This leads to a reduction in the cross section at resonance by the factor [Zs/(Zs+Z0f)]4, where Zs is the wall impedance and Z0f is the total fluid loading on the breathing mode of the cavity.