The Effect of a Heavy Fluid Loading on the Resonant Frequencies of a Vibrating Circular Plate Using the Modal Expansion

Abstract This study deals with using the modal expansion of vibrations of an elastic structure such as a thin circular plate. The effect of the resonant frequency shift is included as a result of loading from surrounding water. It is shown that rough a priori estimations of the resonant frequencies, using the nondimensionalized added virtual mass incremental (NAVMI) factors and the Helmholtz equation (we take into account the radiation of acoustic waves), allow to correctly determine the modes that must be taken into account in order to obtain physically correct numerical results. The heavy fluid loading (e.g., by water) results in a strong lowering of the resonant frequencies compared to the light fluid loading (e.g., by air) or no fluid loading (in vacuum). Consequently, if too few modes are included in numerical calculations, the results will be incorrect. This can be easily seen for frequencies above the coincidence frequency, when the radiation efficiency, instead of tending to unity, drops to zero or values much less than unity. It is, however, possible to avoid such danger since the use of the NAVMI factors and the Helmholtz equation allows obtaining correct numerical results even above the frequency of coincidence. The presented method allows releasing the frequency limitation resulting from the use of the approximation for frequencies close to zero together with the use of the Laplace equation, as is the case in the studies of other authors. The results seem to be of practical importance, especially for the higher frequencies.