Analytical Solution for Dynamic Response of Underground Rectangular Fluid Tank Subjected to Arbitrary Dynamic Loads

Abstract

In this paper, the dynamic response of underground rectangular fluid tank resting on an elastic foundation and subjected to arbitrary dynamic loads is developed in the form of analytical solution. The dynamic responses investigated are deflection, bending moment, and shear force of the tank. The underground rectangular tank is assumed to be a frame composed of horizontal and vertical beams resting on an elastic foundation. The mechanical resistance of elastic foundation is modeled using spring elements that account for soil resistance due to compressive strains in the soil. The fluid in the tank is assumed as inviscid and irrotational, and the influence of free-surface wave is ignored. An analytical solution of free vibration modes of empty tank (dry modes) is derived at first, and then the free vibration modes of fluid tank infilled with water (wet modes) can be obtained by the dry modes. Based on the wet modes, the explicit formulations of dynamic responses of the tank are finally obtained by the modal superposition method. The solutions for several cases, such as empty tank and fully filled fluid tank subjected to harmonic loads, are also discussed. Further parametric analysis is carried out to investigate the influence of the soil–structure relative stiffness ratio on dynamic responses of the fully filled fluid tank.