STUDY ON NONLINEAR DYNAMICS OF RIGID-LIGUID COUPLING RECTANGULAR TANKS UNDER HORIZONTAL EXCITATION
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摘要: 首先应用H-O原理建立了矩形贮箱刚-液耦合系统平动的耦合动力学模型，在贮箱水平运动情况下，给出满足边界条件的速度势函数和液面波高的级数表达式，采用伽辽金法离散，将动力学模型转化为常微分方程组，在给定贮箱运动规律和给定外力规律两种形式下，分析了刚-液耦合系统固有频率变化规律，并应用多尺度法对系统的一阶主共振进行解析分析，研究了液体稳态解的幅频曲线，均发现跳跃及软、硬特性随液深转换的现象，在给定水平外力下，得到液体稳态解的同时还可得到刚体稳态解，两者定性性态相同。最后用数值法验证了解析解的正确性。Abstract: Based on ideal fluid assumption, the coupling dynamic equations of rigid tank and nonlinear sloshing of liquid are established through H-O principle with surface tension and damping considered. The modified potential function and wave height function are introduced to describe the moving boundary of fluid and rigid tank which is forced in surge. Galerkin’s method is used to discrete the dynamics equations into ordinary differential equations. Both the movement and the motivation of rigid tank are considered. The natural frequencies of the rigid-liquid coupling system are formulated with liquid depth, the length of the tank, and etc. The nonlinear dynamics of the rigid-liquid coupling system is investigated analytically. Using the multi-scale method, the amplitude-frequency response is obtained and the jumping phenomenon is observed. It is also observed that as the depth of liquid decreases, the soft and hard characteristics transform to each other. Subsequently, the effects of all factors are studied in detail. Under the condition of giving horizontal excitation, we also can analyze the stable solution of the rigid, which is the same as liquid in qualitative analysis. Finally, compared to the numerical solution, the analytic solution proves to be feasible.
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