Coupled vibration analysis of fluid-filled baffled tank equipped with Kirchhoff plate

Abstract

In the present paper, free coupled vibration of partially fluid-filled baffled tank equipped with elastic thin plate is studied by a variational fluid-domain-decomposition scheme, focusing on obtaining the analytically approximate coupled plate bulging and fluid sloshing modes. Different types of fluid-coupled elastic thin plates are considered: partially submerged elastic baffle, elastic baffle partially covering the free fluid surface, immersed elastic baffle, and elastic thin plates forming the tank wall. The elastic thin plate is modeled by the Kirchhoff plate, and the lateral plate deflection is approximated using the summation of its dry (in vacuum) modes multiplied by unknown weight coefficients. The baffled tank is partially filled with a fluid having multi free surface and assumed to be inviscid, incompressible, and irrotational. The present scheme is based on a variational principle related to free linear vibration of the thin elastic plates coupled with bounded multi-layer immiscible fluid. The eigenfrequency equation of the coupled plate–fluid system obtained by the present scheme has a much more unified and compact form when compared with the previous domain-decomposition scheme employing the Rayleigh–Ritz method or the Galerkin method. This is realized by constructing the variational formulation of the coupled plate–fluid problem expressed in differential form. The convergence and accuracy of the present scheme are studied for both convex and non-convex liquid domains. The results from the present scheme agree well with published numerical or experimental results.