A combined boundary-finite element procedure for dynamic analysis of plates with fluid and foundation interaction considering free surface effect. (15th November 2017) - Kutlu, Akif; Uğurlu, Bahadır; Omurtag, Mehmet Hakkı
Abstract: This study combines a mixed finite element formulation and a boundary element procedure for the free vibration analysis of Mindlin plates resting on Pasternak foundation and interacting with a quiescent fluid with a free surface on the other side. The plate-foundation system is represented by a two field mixed finite element formulation, based on the Hellinger-Reissner variational principle, and the fluid-structure interaction is incorporated into the analysis through a boundary element solution. The proposed formulation provides the added mass matrix in terms of the plate deflection, which is appended into the plate equation of motion. The method is applied to the free vibration problem of circular and elliptical bottom plates of rigid fluid storage tanks supported by elastic foundation. Effects of system parameters, such as thickness to width and fluid depth ratios, foundation parameters and plate ellipticity, are extensively studied. Highlights: The study avoids the expansion of the fluid velocity potential in terms of modal coordinates. As the ratio of the plate thickness to the characteristic length increases, the shear effect becomes more influential. The frequency parameter of the second mode is more sensitive to the shear foundation parameter compared to the fundamental. Frequency parameters get smaller and approach to asymptotes as the ellipticity of the plate's groves. Considering the free surface effect does not improve the solution and it can be neglected at all.