Study on Uncertain Vibroacoustic Characteristics of Underwater Composite Shells
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摘要: 现有研究多针对水下复合材料壳体振声响应的确定性分析, 但实际工程中结构、材料以及重流体参数等均存在不确定性。为此, 文中提出一种基于区间分析与Kriging代理模型的高效预测方法, 用于重流体环境下复合层合阶梯圆柱壳的不确定性振声响应分析。以浸没于无限域重流体中的复合层合阶梯圆柱壳为研究对象, 基于一阶剪切变形理论、能量法和基尔霍夫-亥姆霍兹积分构建振声耦合模型, 引入区间分析法描述参数波动, 采用Kriging代理模型替代高耗时边界元运算, 研究了各不确定性参数对复合层合阶梯圆柱壳声压级响应的影响, 在此基础上分析了影响较为明显的不确定性参数数值变化时响应曲线的偏移规律。结果表明, 多源不确定性导致显著的频率偏移与响应波动区间拓宽。该方法有效解决了重流体环境下复杂阶梯结构不确定性振声分析的难题, 为水下复合材料结构的声学鲁棒性设计提供了技术支撑。Abstract: The existing studies mostly focus on the deterministic analysis of the vibroacoustic response of underwater composite shells, but the structure, material, and heavy fluid parameters in actual engineering are uncertain. Therefore, this paper presented an efficient prediction method based on interval analysis and a Kriging agent model, which is suitable for the analysis of uncertain vibroacoustic responses for composite laminated stepped cylindrical shells in a heavy fluid environment. The research object was a composite laminated stepped cylindrical shell immersed in an infinite domain heavy fluid. Based on the first-order shear deformation theory, energy method, and Kirchhoff-Helmholtz integral, a vibroacoustic coupled model was established. The interval analysis method was introduced to describe the parameter fluctuation. The Kriging agent model was used to replace the time-consuming boundary element operation. The influence of various uncertain parameters on the sound pressure level response of the composite laminated stepped cylindrical shell was studied. On this basis, the offset law of the response curve with respect to variations in the values of the uncertain parameters that have a significant influence was analyzed. The results show that the multi-source uncertainty causes significant frequency shift and response fluctuation range widening. The proposed method effectively solves the problem of uncertain vibro-acoustic analysis for complex stepped structures in heavy fluid environments, and provides technical support for the acoustic robustness design of underwater composite structures.
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Key words:
- underwater shell /
- compound material /
- vibroacoustic response /
- interval uncertainty /
- Kriging model /
- heavy fluid
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图 1 受外部激励作用的复合层合阶梯圆柱壳示意图
Figure 1. Diagram of composite laminated stepped cylindrical shell under external excitation
图 3 复合层合阶梯圆柱壳声压级对比
Figure 3. Comparison of SPL of composite laminated stepped cylindrical shells
图 4 阶梯圆柱壳与均匀圆柱壳声压级对比
Figure 4. Comparison of SPL between stepped and uniform cylindrical shells
图 5 不同铺层角下阶梯圆柱壳声压级对比
Figure 5. Comparison of SPL of stepped cylindrical shells with different layer angles
图 6 呈现不确定性时复合层合阶梯圆柱壳声压级响应幅频曲线
Figure 6. Amplitude-frequency curves of SPL response of composite laminated stepped cylindrical shells with uncertainty in the material parameter
图 7 所有参数呈现不确定性时, 复合层合阶梯圆柱壳声压级响应幅频曲线
Figure 7. Amplitude-frequency curves of SPL response of composite laminated stepped cylindrical shells with uncertainties in all material parameters
图 8 ω = 63 Hz时各不确定性工况下复合层合阶梯圆柱壳声压级响应波动区间
Figure 8. Uncertainty bounds of SPL response for the composite laminated stepped cylindrical shell at ω = 63 Hz
图 9 各不确定性工况下复合层合阶梯圆柱壳声压级响应幅频曲线
Figure 9. Amplitude-frequency curves of SPL response of composite laminated stepped cylindrical shells under various uncertain operating conditions
图 10 不同G12取值时复合层合阶梯圆柱壳不确定性声压级响应区间
Figure 10. Uncertainty bounds of SPL response for the composite laminated stepped cylindrical shell with different values of G12
图 11 不同R取值时复合层合阶梯圆柱壳不确定性声压级响应区间
Figure 11. Uncertainty bounds of SPL response for the composite laminated stepped cylindrical shell with different values of R
图 12 不同$ {{\boldsymbol{\rho }}}_{{\boldsymbol{f}}} $取值时复合层合阶梯圆柱壳不确定性声压级响应区间
Figure 12. Uncertainty bounds of SPL response for the composite laminated stepped cylindrical shell with different values of $ {{\boldsymbol{\rho}} }_{{\boldsymbol{f}}} $
表 1 文中方法与传统Monte Carlo仿真方法性能对比
Table 1. Performance comparison of the proposed method with traditional Monte Carlo simulation methods
响应计算
方法实际耦合
模型调用次数代理模型
预测次数总耗时/h 复相关
系数R2Monte Carlo 3 500 0 144.01 基准 Kriging 150 3 500 6.17 0.949 98 
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表 2 复合层合阶梯圆柱壳不确定性参数
Table 2. Uncertainty parameters of composite laminated stepped cylindrical shells
参数 确定性取值 不确定性区间 $ {E}_{1}\text{/(GPa)} $ 200 $ \left[190,210\right] $ $ {E}_{2}\text{/(GPa)} $ 10 $ \left[9.5,10.5\right] $ $ {\mu }_{12} $ 0.3 $ \left[0.285,0.315\right] $ $ {G}_{12}\text{/(GPa)} $ 6 $ \left[5.7,6.3\right] $ $ {G}_{13}\text{/(GPa)} $ 6 $ \left[5.7,6.3\right] $ $ {G}_{23}\text{/(GPa)} $ 4 $ \left[3.8,4.2\right] $ $ \alpha {\text{/(}}^{\circ }\text{)} $ $ \left[0,90,0\right] $ $ \left[ \begin{array}{c}\left[-2,2\right]\\\left[88,92\right]\\\left[-2,2\right]\end{array} \right] $ $ \rho {\text{/(kg/m}}^{3}\text{)} $ 1500 $ \left[1\;425,1\;575\right] $ $ R\text{/(m)} $ 1 $ \left[0.95,1.05\right] $ $ h_{\xi}\text{/(m)} $ [0.04 0.06 0.05] $\left[ {\begin{array}{*{20}{c}}{[0.039\;6,0.040\;4]}\\{[0.059\;4,0.060\;6]}\\{[0.049\;5,0.050\;5]}\end{array}} \right] $ $ {\rho }_{{f}}{\text{/(kg/m}}^{3}\text{)} $ 1025 $ \left[973.75.1\;076.25\right] $ $ c_{{f}}\text{/(m/s)} $ 1500 $ \left[1\;425,1\;575\right] $
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