球形储罐考虑储液晃动时的简化动力学模型基本理论

为了更加真实地反应球形储罐在地震动作用时的液固藕联振动动力响应,采用速度势刚性理论,根据边界条件推导出合理的势函数,进一步求出球形储罐在地震动作用时的动液压力、储液晃动波高、支承底部剪力及倾覆弯矩表达式,并分析了不同截断数m及球罐半径R对各参量的影响。将该推导的晃动分量系数和晃动频率与Lazaros值作对比,两者十分接近,验证了该推导过程的正确性。构建了便于工程应用的球形储罐考虑储液晃动简化动力学模型,分Ⅰ、Ⅱ、Ⅲ、Ⅳ四类场地进行了地震动响应研究并与有限元数值仿真模拟计算结果进行对比,有限元解与理论解十分接近,且理论解均值均大于有限元解均值,计算结果偏于安全,进一步佐证了所构建的简化力学模型的准确性及可靠性。

Basic theory for simplified dynamic model of a spherical tank considering stored liquid sloshing

In order to describe dynamic responses with liquid-structure interaction of a spherical tank under ground motion more accurately, the velocity potential rigidity theory was adopted, and a reasonable potential function was derived under boundary conditions. Further, dynamic liquid pressure, wave height of stored liquid sloshing, shear force and overturning moment at support bottom of the tank under ground motion were deduced. Effects of different truncation numbers and the tank’s radius on each parameter were analyzed. Comparing sloshing component coefficients and sloshing frequencies derived here with those deduced by Lazaros, they were very close to each other to verify the correctness of the authors’ derivations. Then, a simplified dynamic model for a spherical tank considering stored liquid sloshing was constructed. Seismic responses of the tank on sites of type,Ⅱ,Ⅲ and Ⅳ were studied, respectively. The results were compared with those of finite element numerical simulations. It was shown that the finite element solutions are very close to theoretical ones, all average values of the latter are larger than those of the former, and the latter’s computation results are biased to safety to verify the correctness and reliability of the proposed simplified dynamic model.