A dual reciprocity boundary element solution method for the free vibration analysis of fluid-coupled Kirchhoff plates

Abstract A boundary element solution method is proposed for linear vibration analysis of fluid-coupled thin plates. The method is based on replacing the associated biharmonic operator with two successive harmonic operators, leading to a coupled system of boundary integral equations with simpler properties: the fundamental solution has an elementary form, and complicated singularity removal techniques can be avoided. The fluid flow due to the plate motion is taken as a potential field, and its effect on the plate dynamics is incorporated into the analysis by invoking another boundary integral solution, described over the fluid–plate interface. The body terms in the plate boundary integral equations are considered by the dual reciprocity boundary element formulation. Three different radial basis functions are employed as interpolation functions, alone and augmented with polynomial and sine expansions, to represent the body terms. The performance of the method is investigated from several perspectives by adopting plates with different shapes and/or boundary conditions; excellent approximations are obtained in general: the convergence behavior is consistent, both dry and wet frequency parameters are predicted accurately, and the mode shapes are captured even with rough models. In some of the studied problems, however, deviated results are obtained for specific modes. Furthermore, it is observed that the performance of the method depends on the implemented DRM functions, and combining radial basis functions with global expansions does not yield noticeable improvements.