A refined analytical model for earthquake-induced sloshing in half–full deformable horizontal cylindrical liquid containers

Abstract

The coupled response of elastic deformable liquid containers of horizontal-cylindrical shape under external seismic excitation is examined, through an analytical methodology, assuming inviscid-incompressible fluid and irrotational-flow conditions. In particular, the case of a half–full horizontal-cylindrical deformable container is examined, considering an analytical series-type solution for the velocity potential function that describes the liquid motion under external excitation. This mathematical analysis extends the solution methodology presented in previous publications of the senior author, taking into account full coupling between sloshing and wall deformation in a rigorous manner, where wall deformation is considered through a sinusoidal assumed-shape function. In the mathematical formulation, the velocity potential is decomposed into three parts: (a) a first part, which represents liquid motion that follows the external excitation, (b) a “convective part”, representing liquid motion associated with free surface elevation (sloshing), and (c) a third part caused by the wall deformation. Using an elegant mathematical manipulation, the coupled transient overall response of the liquid-container system is obtained in an efficient manner. Numerical results are presented in terms of the principal natural frequencies of the coupled system, as well as the system response under strong seismic input, and emphasize on the effects of container aspect ratio on the dynamic behavior of the system. The mathematical formulation for the case of long cylinders results in a simplified model, identical to the simplified “physical model” presented in a previous publication.