Free vibration analysis of non-rectangular plates in contact with bounded fluid using element free Galerkin method

Free vibration characteristics of a flexible non-rectangular bottom of a fluid-filled rectangular tank are investigated using a semi-analytical technique. Element free Galerkin method (EFG) based on moving kriging (MK) shape functions is used along with the Mindlin plate theory to model the flexible plate. Two different types of non-rectangular structural domains, viz., skew and trapezoidal configurations are considered in the present study. The fluid is assumed to be incompressible, inviscid and the effect of surface waves is ignored. Potential flow theory is assumed and the velocity potential is used to calculate the kinetic energy of the fluid. The results obtained are first validated with available solutions in the literature for elastic rectangular plates in contact with the fluid. Thereafter, the effects of various structural and fluid domain parameters on natural frequencies of thin isotropic and laminated composite skew/trapezoidal bottom of a rectangular tank filled with fluid are investigated in detail. New results on the vibration of non-rectangular plates in contact with the fluid, hitherto not found in the literature are presented here for the first time.