A Semianalytical Vibration Analysis of Partially Wet Square Cantilever Plate With Numerical and Experimental Verification: Partially Wet Modeshapes

Abstract

A semianalytical study of a uniform homogenous partially submerged square cantilever plate vibration is presented. The structure is assumed to be a Kirchhoff's plate, clamped on one edge and free on the other edges. The lengthwise section of the plate is a cantilever clamped-free (CF) beam, while the widthwise section is a free-free (FF) beam. The plate modeshape is a weighted superposition of the product of the beam modeshapes, with unknown weights. The CF beam has only flexural modes. The FF beam has two rigid-body modes, i.e., translational and rotational modes. Rayleigh–Ritz method (RRM) is used to set up the free vibration eigenvalue problem. The eigenvector gives the unknown weights. The modeshapes generated are further used in the boundary element method (BEM) to calculate the fluid inertia, which participates in the vibration and leads to a consistent drop in frequencies. The dependence of this reduction on the submergence level is studied for the first six frequencies of the plate. The frequencies are also experimentally generated by the impact hammer test, both in the dry state, and under three distinct levels of submergence: 25%, 50%, and 75% from the free edge opposite to the clamped edge. The frequencies and modeshapes are also verified through numerical analysis using the commercial code ansys 16.0. Conclusions are drawn regarding the influence of fluid inertia distribution on the final plate modeshape, leading to insights into sound structural designs.