A modal/spectral analysis of mass distribution effects in a fluid-loaded plate

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Feit and Johnson [ 2309(A) (1991)] showed that the signal scattered by a plate is greatly affected by the spatial distribution properties of an attached mass. Ginsberg et al. [ASME Proc., paper 93-WA/NCA-20 (1993)] used the surface variational principle (SVP), which describes the surface pressure and displacement as a set of interacting waves, to examine a fluid-loaded plate with attached point mass in an infinite baffle. In their analysis the mass distribution was represented as a Fourier series in an effort to determine how coarse the model could be, and still accurately represent the direct point mass solution. Their conclusion was that a series length of eight terms is adequate to describe the system behavior in the frequency range kL≤3, but a series of fewer than six terms is substantially inaccurate. The current work uses the in-vacuo modes of the spectrally smoothed mass–plate system as Ritz functions for displacement. The solution in terms of these modes is compared to the results obtained from the Fourier series representation, in order to identify why a critical number of terms is required for the spectral description of mass distribution.