水平地震激励下卧式储罐考虑储液晃动的简化力学模型

Simplified mechanical model for a horizontal storage tank considering liquid sloshing under horizontal seismic excitation

立足于卧式储罐抗震设计,从横向与纵向两个地震动激励方向推导了卧式储罐抗震设计的简化力学模型。首先采用速度势刚性理论,根据边界条件推导出合理的势函数,并将半解析半数值的数学模型参数化,拟合得出简单的参数公式,并根据基底剪力及倾覆弯矩表达式构建了便于工程应用的卧式储罐考虑储液晃动简化动力学模型。其次采用微分原理推导了卧式储罐在轴向地震动作用时的简化力学模型,利用等效原则进一步简化了简化力学模型的计算过程。最后选取工程实例,进行了理论数学模型与有限元数值仿真模拟计算结果的对比分析,有限元解与数值解最大差异率未超过15%,由此进一步佐证了所构建的简化力学模型的可靠性。

Here,based on aseismic design of horizontal storage tanks,a simplified mechanical model for a horizontal storage tank under lateral and longitudinal seismic excitations was deduced.Firstly,using the velocity potential stiffness theory,a reasonable potential function was derived according to boundary conditions.Its semi-analytical and semi-numerical mathematical model was parameterized and fitted to a simple parametric formula.According to expressions for base shear force and overturning bending moment,a simplified dynamic model for a horizontal tank considering liquid sloshing was constructed to be easy to apply in engineering.The simplified mechanical model further considering action of horizontal seismic excitation was derived using the differential principle.The equivalent principle was used to further simplify the calculation process of the simplified mechanical model.Finally,engineering examples were selected,and contrastive analysis was done for numerical calculation results using the theoretical mathematical model and those using the finite element simulation.It was shown that the maximum difference rate between them is less than 15%,so the reliability of the proposed simplified mechanical model is verified.