Hydroelastic analysis of partially or totally immersed Mindlin plates with a hybrid isogeometric-based approach

Abstract

In this study, the dynamic characteristics of a cantilevered Mindlin plate, partially or totally in contact with fluid on both sides, are examined using the proposed hybrid isogeometric finite element – boundary element framework. The interaction problem is divided into two parts through the implementation of the linear hydroelasticity theory, allowing for the independent treatment of structural and fluid problems. In the structural part of the analysis, the thick plate is modeled as first-order shear deformable by adopting Reissner–Mindlin plate theory, with the material assumed to be homogeneous and isotropic. The resulting eigenvalue problem is then solved by the isogeometric finite element method (IGAFEM). In the second part of the analysis, assuming the fluid is ideal and incorporating the in vacuo dynamic characteristics as boundary conditions, fluid-structure interaction effects are determined by the isogeometric boundary element method (IGABEM) in terms of generalized added mass coefficients. Subsequently, parametric studies for various plate thicknesses and submergence depths are conducted. The analysis reveals that wet natural frequencies differ noticeably from their in vacuo counterparts due to the presence of the free surface of the fluid. In addition, the effect of the radiated free surface waves from the vibrating structure are included into the mathematical model by imposing linearized free surface condition, through the frequency-dependent added mass and hydrodynamic damping effects of the fluid. The numerical accuracy of the proposed approach is verified against the commercial finite element software ANSYS, showing favourable agreement in the predicted natural frequencies and corresponding mode shapes.