On lateral response of structures containing a cylindrical liquid tank under the effect of fluid/structure resonances

Abstract

The lateral response of a single degree of freedom (SDOF) structural system containing a rigid circular cylindrical liquid tank, under harmonic and earthquake excitations is considered. The governing differential equations of motion for the combined system is derived considering the first 3 liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The system is considered nonlinear due to the convective term of liquid acceleration and the nonlinear surface boundary conditions, both caused by the inertial nonlinearity. The harmonic and seismic response of the system is investigated in the neighborhood of 1:1 and 1:2 internal resonances between the SDOF system and the first asymmetric sloshing mode. These resonance cases can be regarded as autoparametric if an internal resonance exists between the sloshing mode (1,1) and the structural system, while the frequency of the external harmonic excitation is tuned to the system's structural frequency. In addition, the effect of system's horizontal and vertical displacement on lateral components of acceleration as well as the effect of sloshing wave amplitude on liquid-induced dynamic pressure is investigated. The numerical results illustrates the efficiency of the liquid sloshing modes in reducing the seismic response of the structural system to a large extent, particularly when the fundamental frequency of the system is close to the dominant frequency of the earthquake record. Also, the increase in the Fourier amplitudes of the sloshing modes is an indication of energy transfer from structure to liquid due to nonlinear interaction. Considering 3 sloshing modes shows that the amplitude of asymmetric liquid mode (1,1) in some cases becomes smaller in comparison to the case with 1 mode, and the other sloshing modes absorb part of the energy imparted from the SDOF system.