The problem of fluid nonlinear forced sloshing in a two-dimensional tank is analyzed by using the multimodal method. The absolute velocity potential is introduced to describe the nonlinear motion of fluid in a moving frame. Based on the Bateman-Luke variational formulation, the nonlinear (free) boundary value problem is transformed into an equivalent functional extreme value problem. A fi-nite-dimensional nonlinear coupled modal system (a set of nonlinear ordinary differential equations) is obtained by expanding the functions of free surface wave-height and the absolute velocity potential into the generalized Fourier series. By using the Runge-Kutta algorithm, the nonli-near ordinary differential equations can be solved, and the nonlinear forced sloshing responses are further acquired. The time-history response to strong seismic excitation, the stead-state common resonance response to the horizontal harmonic excitation, and the stead-state parametric resonance response to the vertical harmonic excitation are respectively simulated and discussed for the fluid in a rectangular tank. The combined resonance responses of the free surface to the horizontal and vertical harmonic excitations are further predicted. The solutions by the multimodal method are compared with those by the other numerical formulations. The results show that the multimodal approach has its unique advantage in the long-time nonlinear analyses of stead-state responses.
李遇春,刘哲,王立时. 基于多维模态方法的流体二维非线性强迫晃动分析[J]. 振动与冲击, 2017, 36(16): 159-165.
LI Yu-chun, Liu Zhe, WANG Li-shi. A multimodal–based analysis for two-dimensional fluid nonlinear forced sloshing. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(16): 159-165.
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