The imaginary part of input admittance: A physical explanation of fluid-loading effects on plates

Abstract

Crighton has remarked [1] on the surprising behavior of the input admittance (particularly the imaginary part or susceptance) of an infinite flat plate with heavy fluid loading: for a point force, it has asymptotically the sign appropriate to a spring, while for a line force the sign is that for a mass. However, one observes in both cases that the susceptance is more nearly spring-like with than without fluid loading; in a vacuum, the susceptance vanishes for the point source and is strongly massive for the line source. Physical explanations of these phenomena are found through an identity between the input admittance and a linear combination of time-averaged energy functions. The lower the wavenumber of a response component, the greater is its contribution to kinetic as compared to potential energy. The addition of fluid loading causes through the virtual mass effect, a greater reduction of response at low wavenumber than at high. Hence, the fluid causes the input admittance to become more nearly spring-like for both types of source, as observed in the precise analysis.