The first report, “Part 1 - Vibration experiment”, has revealed that the nonlinear vibration response phenomena of beam-type vibration of a cylindrical water storage tank are caused by the coupling effect of beam-type vibration and oval-type vibration. This paper describes the modeling of the above phenomena into a nonlinear equivalent single-degree-of-freedom system and the results of the simulation analysis to investigate the mechanism of the nonlinear vibration responses of the tank when these two types of vibration are coupled. The conventional linear seismic response analysis method of the tank generally considers only beam-type vibration because the participation factor of oval-type vibration due to seismic excitations is theoretically zero. However, oval-type vibration was found to be generated and accompanied by the out-of-plane deformation of the tank sidewall when the test tank was experimentally subjected to large input acceleration excitations. So, it was considered that the geometrical nonlinearity due to oval-type vibrations was the main reason why the beam-type vibration response was nonlinear. Therefore, a static large-deformation analysis by the finite element method was conducted for the tank model whose sidewall had the oval-type vibration mode shape as the out-of-plane deformation in order to calculate the flexural rigidity of the tank. As a result, the flexural rigidity of the tank was found to decrease as the displacement of oval-type vibration increased. In other words, the geometrical nonlinearity caused by the oval-type vibration affects the flexural rigidity of the tank and generates the nonlinear vibration response. Furthermore, an equivalent single-degree-of-freedom system model was made to understand the nonlinear vibration response behavior of the tank, assuming that the flexural rigidity depended on the displacement of the oval-type vibration. Simulation of the frequency sweep test using this model showed that the resonance frequency decreased as the displacement of the oval-type vibration became larger. These results demonstrate the validity of the results mentioned in the first report, “Part 1 - Vibration experiment”.

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