考虑底板与池壁相互作用和池壁剪切变形影响的圆形水池动力特性计算

考虑圆形水池池壁剪切变形的影响、底板对池壁的径向约束作用和转动约束作用，将圆形水池底板与池壁的相互作用简化成端部受切向弹性约束和转动弹性约束下的弹性地基Timoshenko梁，基于Timoshenko梁振动的修正理论，导出了底部环向简支、顶部分别为自由、铰支和固支三种边界条件下的振动频率超越方程；根据池壁和弹性地基梁微分方程的类比性，阐述了利用ANSYS建立圆形水池振动模态分析的有限元方法。利用二分法对底板环形简支的圆形水池的振动频率进行了计算，分析了顶部不同边界条件、池高、池的半径和底板对池壁弯曲约束刚度对池壁振动频率的影响。得到了圆形水池轴对称振动可采用弹簧-质量模型进行基频估算、该文所建立的分析方法只能分析圆形水池的轴对称振动模态、圆形水池底板与池壁相互作用对基频影响不明显、壁厚的剪切变形和转动惯量对高阶振动影响大等结论。

DYNAMIC PROPERTY ANALYSIS OF CIRCULAR WATER TANK WITH INTERACTION BETWEEN BASE PLATE AND THICK WALL AND SHEAR DEFORMATION EFFECT OF TANK WALL

Considering the shear deformation effect of the thick wall for circular water tank, and the interactions of radial constraint and rotating constraint between the base plate and the thick wall, the interacting model was simplified as an elastic foundation Timoshenko beam supported by elastically tangential constraint and rotating constrain at the end. The modified vibrating theory of Timoshenko beam was used to derive the transcendent equation about the vibrating frequency for circular water of loop supported at bottom and free, hinged and clamped at top. According to the analogy of differential equations between circular water wall and elastic foundation beam, the finite element calculation to solve vibrating model problem of circular water wall by ANSYS software was performed. By using bisection method, the vibrating frequencies of circular water wall with loop supported at bottom were analyzed. The influences of different boundary conditions at top, the height and radius of circular water wall, and the constraint bending stiffness of base plate were analyzed for the vibrating frequencies. Some conclusions are drawn that spring-quality model can be used to simulate the fundamental frequency, and the present method can be adapt to axisymmetric vibration analysis. The interaction between base plate and wall is unapparent, while the shear deformation of wall and inertia moment affect high order frequencies of the circular water wall.