Modal Density Evaluation of a Fluid-Loaded Free-Damping Stiffened Plate

An analytical method is developed to evaluate the modal density of a fluid-loaded stiffened plate with a damping layer. The effects of the damping layer, ribs, and fluid load on the structure’s equivalent bending rigidity and surface density are analyzed. The vibration equation is obtained by applying the Hamilton principle, and the modal density is calculated by counting modes in the specific band. The modal density calculation method for both ribbed-type plates and uniform-type plates is verified through numerical simulation. The increase in the number of ribs has made the rib-off frequency at which the effect of the ribs can be neglected become higher, since the wavelength needs to be shorter when the ribbed plate can be treated as a uniform-type plate. The introduction of the damping layer has slightly increased the modal density compared to the uniform plate. In contrast, the introduction of fluid load has dramatically increased the modal density of the corresponding base plate in the low-frequency domain, and the effect of the fluid load can be ignored in the high-frequency domain.