Hydroelastic vibrations of flexible rectangular tanks partially filled with liquid

In this paper, the three-dimensional vibratory characteristics of flexible rectangular tanks partially filled with liquid are studied. The surface waves of the liquid are taken into account in the analysis. Both the bulging modes of the tank-wall vibration and the sloshing modes of the liquid oscillation are investigated. The vibrating modes of the liquid–tank system are divided into four distinct categories: double symmetric modes (SS); antisymmetric–symmetric modes (AS); symmetric–antisymmetric modes (SA) and double antisymmetric modes (AA). Each of these categories is separately investigated. The velocity potential of the liquid is analytically deduced by using a combination of the superposition method and the method of separation of variables. According to the liquid–tank interface conditions and the orthogonality of trigonometric functions, the coefficients in the solution of liquid velocity potential are expressed in the integral forms including the tank–wall dynamic deflection. A set of reasonable static beam functions is constructed as the admissible functions of the tank-wall vibration. The eigenfrequency equation of the liquid–tank system is derived by using a combination of the Rayleigh–Ritz method and the Galerkin method. Convergence study demonstrates the high accuracy and small computational cost of the proposed approach. Finally, some numerical results are presented for the first time. Copyright q 2006 John Wiley & Sons, Ltd.