Study on acoustic vibration similarity law of complex stiffened cone-cylinder combined shell
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摘要:
目的 旨在解决复杂加筋组合壳结构缩尺模型的声振试验结果难以准确换算至原型的难题，分析两者的声振相似规律，为水下复杂加筋壳结构声振缩尺模型的试验研究提供依据。 方法 使用面单元模拟加筋方法构建复杂锥−柱组合壳模型及其缩尺模型，基于有限元−边界元法（FEM-BEM）混合方法，计算模型壳体的声振响应，并结合加筋圆锥壳模型试验，验证采用上述方法计算复杂组合壳声振响应的准确性，系统研究复杂组合壳的声振相似规律。 结果 结果表明：在相同的模型材料参数、边界条件和激励力下，复杂组合壳的模态频率与缩尺比成反比，对应频率的模态振型相同；在相同的激励力下，复杂组合壳的振动响应与缩尺比成反比，其声压与缩尺比和场点距离的乘积成反比；缩尺模型与原型的水下声辐射效率及声压指向性相同。 结论 在模型相似条件下，复杂组合壳结构表现出了良好的声振相似规律，满足相似条件下采用缩尺模型试验研究组合壳原型结构的声振特性要求。 -
关键词:
- 锥−柱组合壳 /
- 相似律 /
- 有限元−边界元法混合方法
Abstract:Objective Due to the difficulty of accurately converting the experimental results of acoustic radiation and vibration from scale models of complex stiffened combined shells into prototypes, the acoustic vibration similarity laws of this type of combined shell are studied in order to provide a basis for scale model experimental research on the acoustic vibration of such underwater structures. Method First, a complex stiffened cone-cylinder combined shell model and its scale model are constructed by shell element reinforcement simulation. Next, based on the hybrid finite element method-boundary element method (FEM-BEM) method, the acoustic vibration response of the combined shell is calculated. Combined with the model experiment, the accuracy of the calculated response of the complex shell structure using the hybrid FEM-BEM method is then verified. Finally, the acoustic vibration similarity laws of the complex stiffened cone-cylinder combined shell are studied systematically. Results The vibration modal frequency of the complex combined shell is in inverse proportion to the geometric scale ratio with the model under the same material parameter boundary conditions and excitation force, while the vibration modal in the corresponding frequency is the same. Under conditions of the same excitation force, the vibration response of the combined shell is also in inverse proportion to the geometric scale ratio, whereas the acoustic pressure is in inverse proportion to the product of the geometric scale ratio and measurement distance of the shell. The radiation efficiency and acoustic directivity of the scale model and prototype are the same. Conclusion The stiffened cone-cylinder combined shell shows good acoustic and vibration similarity under similar conditions to those of the model, and the model constructed using shell element reinforcement simulation is more consistent with the experimental results. -
图 1 加筋锥−柱组合壳几何结构及有限元模型
Figure 1. Geometric structure and finite element model of stiffened cone-cylinder combined shells
图 2 加筋圆锥壳试验测点分布及有限元模型
Figure 2. Distribution of test points and finite element model of stiffened cone shell
图 3 空气中振动加速度级的试验与仿真结果对比
Figure 3. Comparison of acceleration level between experimental and simulation results in air
图 4 水下振动加速度级试验与仿真结果对比
Figure 4. Comparison of acceleration level between experimental and simulation results in water
图 5 空气中的加筋锥−柱组合壳振动加速度级响应对比
Figure 5. Comparison of vibration acceleration level response of stiffened cone-cylinder combined shells in air
图 6 水下加筋锥−柱组合壳的振动加速度级响应对比
Figure 6. Comparison of vibration acceleration level response of stiffened cone-cylinder combined shells in water
图 7 水下加筋锥−柱组合壳的场点辐射声压对比
Figure 7. Comparison of field radiated sound pressure of stiffened cone-cylinder combined shells in water
图 8 水下加筋锥−柱组合壳的辐射声压指向性对比
Figure 8. Comparison of acoustic directivity of stiffened cone-cylinder combined shells in water
表 1 加筋锥−柱组合壳模型干模态频率
Table 1. Dry modal frequency of stiffened cone-cylinder combined shells
阶数 原型频率/Hz 缩尺模型频率/Hz 倍率关系 阶数 原型频率/Hz 缩尺模型频率/Hz 倍率关系 1 8.1769 32.840 4.02 8 37.943 151.81 4.00 2 17.115 69.110 4.04 9 39.324 162.42 4.13 3 17.180 69.355 4.04 10 39.446 163.10 4.13 4 24.460 100.34 4.10 11 51.852 207.72 4.01 5 30.703 125.35 4.08 12 52.672 211.19 4.01 6 33.470 133.94 4.00 13 52.715 211.39 4.01 7 37.721 150.92 4.00 14 52.753 211.47 4.01 
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表 2 加筋锥−柱组合壳模型湿模态频率
Table 2. Wet modal frequency of stiffened cone-cylinder combined shells
阶数 原型频率/Hz 缩尺模型频率/Hz 倍率关系 阶数 原型频率/Hz 缩尺模型频率/Hz 倍率关系 1 4.016 16.025 3.99 8 25.833 109.080 4.22 2 8.816 35.714 4.05 9 27.128 112.514 4.14 3 10.911 45.735 4.19 10 29.214 114.062 3.91 4 15.814 66.846 4.23 11 31.724 124.208 3.92 5 18.601 78.223 4.21 12 33.222 140.557 4.23 6 21.596 88.504 4.10 13 34.035 141.900 4.17 7 24.260 95.861 3.95 14 36.500 147.535 4.04
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表 3 辐射声压相似关系
Table 3. Similarity relation of radiated sound pressure
原型频率
/Hz缩尺模型
频率/Hz原型辐射声压
/(N·m−2）缩尺模型辐射
声压/(N·m−2）倍率关系 11 44 −0.000 496 −0.008 16.1 36 144 0.000 251 8 0.004 15.9 90 360 0.004 0.064 16
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