Application of Skudrzyk’s ‘‘mean-value theory’’ to fluid-loaded plates

Abstract

The geometric-mean drive-point admittance of a complex structure can be found by examining the admittance of the corresponding infinite structure (i.e., ‘‘characteristic admittance,’’ Yc) [Skudrzyk, J. Acoust. Soc. Am. 67, 1105–1135 (1980)]. The frequency response of an infinite plate, for example, coincides with the geometric-mean response of a finite plate, i.e., the response equidistant from the resonance maxima and antiresonance minima, plotted on a logarithmic scale. Skudrzyk’s ‘‘mean-value theorem’’ was derived (and experimentally verified) without consideration of fluid coupling, which introduces a reactive effect that physically resembles a mass loading. The purpose of this research is to find whether the response of the fluid-loaded infinite plate still corresponds to the geometric-mean response of the fluid-loaded finite plate. Numerical results indicate that, in the presence of fluid loading and at low frequencies (below critical), the mean-line drive-point admittance of the finite plate still corresponds to the infinite-plate drive-point admittance that has been derived analytically [Crighton, J. Sound Vib. 54, 389–391 (1977)]. [Work supported by the Applied Research Laboratory.]