摘要摘要：本文根据堆本体内窄间隙同轴设备支承筒的结构特征、边界条件和窄间隙环腔内流体流速，将结构简化为一端固定一端自由的同轴圆柱壳，将圆柱壳内外的流体简化为无旋、无黏、不可压缩流体。地震工况下同轴圆柱壳通过流体压力场实现耦合，其径向位移模态决定了窄间隙流体域的压力场，故采用级数形式的圆柱壳径向正交位移模态构建既满足一端固定一端自由边界条件，又满足波动方程的压力场基函数,并由此基函数推导一端固定一端自由同轴圆柱壳由间隙流体耦合时自由振动且出现梁、壳复合振型的附加质量理论公式。随着基函数级数项的增加由该公式计算的附加质量结果快速收敛，基函数项数大于50时附加质量计算精度满足要求。当该公式中n=1即仅考虑同轴圆柱壳的梁式振型时，本文推导的公式退化为Au-Yang M K[3]推导的同轴圆柱壳梁式振型附加质量公式。为方便工程应用，参考俄罗斯标准《核动力装置设备和管道强度计算规范》定义附加质量系数，以设计曲线形式给出本文推导的同轴圆柱壳流体附加质量结果。为验证以上理论公式，本文首先建立了不同高径比、不同间隙量和不同壁厚的同轴圆柱体流固耦合有限元模型，通过对比理论公式计算结果和包含窄间隙流体域的同轴圆柱壳有限元模型的模态结果可知，当圆柱壳高径比≤2.0时，主振型的频率误差在5%以内；同时笔者设计了双层同轴圆柱筒的流固耦合试验，通过对比模态试验的频率和振型结果进一步验证了本文推导理论公式的正确性。
Abstract：Abstract：Based on the structural features, boundary conditions and fluid flow velocity of the narrow gap coaxial equipment supporting cylinders in the reactor vessel, the structure is simplified to a coaxial cylindrical shell with one fixed end and free end, and the fluid inside and outside the cylindrical shell is simplified to irrotational, non-viscous, incompressible fluid. Under seismic conditions, the coaxial cylindrical shell is coupled through the fluid pressure field, and its radial displacement mode determines the pressure field in the narrow gap fluid domain. Therefore, the radial orthogonal displacement modes of the cylindrical shell in the form of series are constructed to satisfy the boundary condition with one fixed end and the other free end, and the pressure field basis function of the wave equation is satisfied. From this basis functions, the additional mass theoretical formula of the shell-typevibration modes of a coaxial cylindrical shell with a fixed end and a free end is derived considering fluid-solid interraction. With the increase of the basis function series terms, the additional mass results calculated by this formula converge quickly. When the number of basis function terms is greater than 50, the additional mass calculation accuracy meets the requirements. When n=1 in this formula, namely, only the beam mode of the coaxial cylindrical shell is considered, the formula deduced in this paper degenerates to the beam-type vibration mode additional mass formula of the coaxial cylindrical shell deduced by Au-Yang M K [3]. In order to facilitate engineering applications, the additional mass coefficient is defined with reference to the Russian standard "Nuclear Power Plant Equipments and Pipes Strength Calculation Specification", and the additional mass results of the coaxial cylindrical shell derived in this paper are given in the form of a design curve. In order to verify the above theoretical formulas, this paper establishes a finite element model of coaxial cylinders containing narrow gap fluid domains with different height-to-diameter ratios, different gaps and different wall thicknesses, and the comparable calculation results are obtained with the theoretical results. The modal results of the finite element model show that when the height-to-diameter ratio of the cylindrical shell is less than or equal to 2.0, the frequency error of the main vibration mode is within 5%; at the same time, the author designed a modal experiment of a double-layer coaxial cylinder taking fluid-structure interraction into account. The frequency and vibration mode results of the modal test further verify the correctness of the additional mass theoretical formula derived in this paper.
2022, Vol. 43 
