Study on the Nonlinear Dynamic Model of a Single Fuel Assembly Based on the Bouc-Wen Hysteresis Model
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摘要: 为模拟单组燃料组件横向振动过程中的非线性现象，本研究在线性单梁模型的基础上，尝试引入刚度分两段下降的Bouc-Wen滞回模型，采用有限元离散方法建立了单组燃料组件横向振动的非线性动力学模型，同时结合部分力学特性试验数据，采用多目标遗传优化算法（NSGA-Ⅱ）识别该模型的未知参数。计算结果与试验数据对比发现：横向加卸载过程中归一化位移的均方根误差（RMSE）为0.027；5种不同初始条件下自由振动响应频率的相对误差小于6%，阻尼比相对误差小于3%。因此非线性动力学模型可较好地模拟随横向位移增大燃料组件结构出现的刚度下降、等效频率下降和等效阻尼比上升现象。本研究为燃料组件横向力学响应特性的准确模拟提供了方法学参考，并且本文模型适用范围广，可能有助于大变形情况下燃料组件设计裕量的挖掘。
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关键词:
- 燃料组件 /
- 横向振动 /
- Bouc-Wen滞回模型 /
- 非线性动力学模型
Abstract: To simulate the nonlinear phenomena during lateral vibration of a single fuel assembly, this study introduces a Bouc-Wen hysteresis model with two-stage stiffness degradation based on the linear single-beam model. Using the finite element discretization method, we established a nonlinear dynamic model for lateral vibration of the single fuel assembly. Furthermore, combined with partial mechanical property test data, the multi-objective genetic optimization algorithm (NSGA-Ⅱ) was employed to identify unknown parameters of the model. The comparison between computational results and experimental data reveals the following: The root mean square error (RMSE) of normalized displacement during the lateral loading-unloading process is 0.027. Under five different initial conditions, the relative errors of free vibration response frequencies are less than 6%, and the relative errors of damping ratios are less than 3%. These results demonstrate that the nonlinear dynamic model effectively captures key phenomena observed in fuel assemblies, including stiffness degradation, frequency reduction, and damping ratio increase with growing lateral displacement. This study provides a methodological reference for the accurate simulation of lateral mechanical response characteristics in fuel assemblies. Furthermore, the developed nonlinear model exhibits broader applicability and may facilitate the exploration of design margins for fuel assemblies under large-deformation scenarios.-
Key words:
- Fuel assembly /
- Lateral vibration /
- Bouc-Wen hysteresis model /
- Nonlinear dynamic model
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图 1 Bouc-Wen滞回模型的载荷-位移曲线示意图
F—外载荷；u—横向位移；uy—屈服点；Fy—屈服载荷；①~⑥—完整加卸载路径。
Figure 1. Schematic Diagram of Load-Displacement Curve of Bouc-Wen Hysteresis Model
图 2 定位格架与燃料棒连接示意图
Figure 2. Schematic Diagram of the Connection between Spacer Grid and Fuel Rod
图 3 燃料组件简化单梁模型示意图
Figure 3. Schematic Diagram of Fuel Assembly Simplified Single Beam Model
图 4 整体刚度分两段下降的Bouc-Wen滞回模型的载荷-位移曲线示意图
Figure 4. Schematic Diagram of Load-Displacement Curve of the Bouc-Wen Hysteresis Model with Two-Stage Stiffness Degradation
图 6 格架位置横向外载荷与横向位移关系
Figure 6. Relationship between Lateral External Load and Lateral Displacement at the Spacer Grid Position
图 7 定位格架处横向位移12 mm时自由振动结果对比
Figure 7. Comparison of Free Vibration Results under 12 mm Lateral Displacement at Spacer Grid Position
图 8 定位格架处横向位移17 mm时自由振动结果对比
Figure 8. Comparison of Free Vibration Results under 17 mm Lateral Displacement at Spacer Grid Position
表 1 Bouc-Wen滞回模型参数取值范围
Table 1. Parameter Range of the Bouc-Wen Hysteresis Model
参数 α D γ n 取值范围 0~1 >0 −0.5~0.3 1~20 
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表 2 燃料组件梁模型物理参数
Table 2. Physical Parameters of the Fuel Assembly Beam Model
参数 数值 弹性模量/Pa 9.84×1010 横截面积/m2 0.00478 线密度/(kg·m−1) 165 长度/m 4.06 泊松比 0.346
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表 3 非线性动力学模型最终参数
Table 3. Final Parameters of the Nonlinear Dynamic Model
参数 取值范围 最终取值 α 0.5~1.0 0.632 αA 0~1 0.266 αB 0~1 0.102 DA (2~4)×10−3 3.232 DB (4~8)×10−3 5.461 βA 0~0.5 0.347 βB 0~0.5 0.405 I (5.5~7.5)×10−7 6.070 k (1.4~2.5)×10−3 2.175 α (3.5~6.5)×10−3 4.199
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表 4 自由振动等效阻尼比对比
Table 4. Comparison of Equivalent Damping Ratios for Free Vibration
初始横向位移/mm 6 9 12 15 17 等效阻尼比试验值 0.0558 0.0750 0.0929 0.1056 0.1123 等效阻尼比计算值 0.0545 0.0750 0.0902 0.1063 0.1145 等效阻尼比相对误差/% 2.33 0.00 2.91 0.66 1.96
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表 5 自由振动等效频率对比
Table 5. Comparison of Equivalent Frequencies for Free Vibration
初始横向位移/mm 6 9 12 15 17 等效频率试验值/Hz 3.23 3.03 2.94 2.94 3.03 等效频率计算值/Hz 3.20 3.15 3.09 3.05 3.01 等效频率相对误差/% 0.93 3.96 5.10 3.74 0.66
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表 6 自由振动归一化横向位移的RMSE
Table 6. RMSE of Normalized Displacements of Free Vibration
初始横向位移/mm 6 9 12 15 17 RSME 0.0545 0.0534 0.0277 0.0453 0.0506
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