The Simplified Method for the Earthquake Induced Hydrodynamic Pressure on Elliptical Cylinder
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摘要: 首先，文章基于辐射波浪理论，在椭圆坐标系下采用分离变量法推导了水中椭圆形柱体地震动水压力的解析解。之后，采用有限元方法建立了地震作用下水与结构相互作用的动力方程，方程中水体对结构的作用为一满阵的附加质量矩阵。满阵的附加质量矩阵难以在商业有限元中实现，因此提出了集中的附加质量矩阵方法，其中结构柔性引起的附加质量为集中附加质量矩阵和修正系数的乘积，该修正系数与无量纲参数宽深比和长短轴比相关。最后，通过曲线拟合，提出了刚性椭圆柱体动水力的均布附加量简化公式，该简化公式是无量纲参数宽深比和长短轴比的函数。Abstract: Based on the radiation theory, the analytical solutions for the earthquake-induced hydrodynamic force on an elliptical cylinder caused by surrounded water are accurately derived in elliptical coordinate system.The dynamic equation for the dynamic interaction of water with elliptical cylinder is developed by finite element method, where the water-cylinder interaction is replaced by a full added mass matrix.However, the fully added mass matrix is difficult to be implemented in commercial software.Therefore, a lumped added mass matrix is presented to replace the fully added mass matrix with a correction factor, which is relevant to dimensionless parameters including width-depth ratio and ratio of long to short axis of the ellipse.In addition, the simplified formulas for the uniform added mass of the rigid elliptical cylinder are proposed by curve fitting method and these simplified formulas are the functions about the dimensionless parameters including width-depth ratio and ratio of long to short axis of the ellipse.
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Key words:
- Earthquake /
- Elliptical cylinder /
- Hydrodynamic pressure /
- Added mass
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图 1 椭圆柱体与水体相互作用分析模型
Figure 1. Analytical model of the interactiin of elliptic cylinder and water
图 3 圆柱解析解与本文解的对比
Figure 3. The proposed solution compared with the analytical solution for circular cylinders and this paper
图 4 椭圆柱数值解与本文解的对比
Figure 4. The proposed solution compared with the numerical solution for elliptical cylinders and this paper
图 5 地面位移时程和傅里叶谱
Figure 5. The time history of displacement of the ground motion and its Fourier spectrum
图 6 参考解和集中附加质量模型位移时程的对比
Figure 6. The comparison of time history of displacement of the cylinder obtained by reference solution and lumped added mass method
图 8 参考解和修正集中附加质量模型的位移时程比较
Figure 8. The comparison of time history of displacement of the cylinder obtained by reference solution and modified-lumped added mass method
图 9 附加质量系数解析解和简化公式的对比
Figure 9. The comparison of coefficient of the added mass obtained by analytical solution and simplified formula
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