Vibration response analysis of fiber reinforced composite thin-walled truncated conical shell based on multilevel iterative correction
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摘要: 提出了一种纤维增强复合薄壁截锥壳的振动响应分析模型。针对纤维增强复合薄壁截锥壳的结构特点，考虑基础激励载荷方向与母线的夹角、纤维铺层方向与x轴的夹角，利用板壳振动理论、复弹性模量等方法对所研究结构进行了理论建模。利用双向梁函数法表示振型函数，并通过能量法和模态叠加法对其固有特性和振动响应进行求解。为了验证模型的正确性，基于自行搭建的振动测试平台，以TC300/环氧树脂基纤维增强复合薄壁截锥壳为对象，进行了振动特性测试。为减小因样件加工时产生的材料参数误差影响，开发了二分粒子群迭代法对材料参数进行修正。研究发现，测试结果与理论计算获得的共振响应误差最大不超过3.0%，验证了所提出的理论模型与计算方法的正确性和有效性。Abstract: A vibration response analysis model was established for a fiber-reinforced composite thin-walled truncated conical shell. Based on the structural characteristics of the fiber-reinforced composite thin-walled truncated conical shell, the theoretical modeling of the structure was carried out using plate shell vibration theory and complex elastic modulus methods, considering the angle between the basic excitation load direction and the generatrix, the angle between the fiber laying direction and the x-axis. The vibration mode function was expressed using the bi-directional beam function method, and the natural characteristics and vibration response were solved using the energy method and modal superposition method. In order to verify the correctness of the model, vibration characteristic tests were conducted on a TC300/epoxy resin-based fiber-reinforced composite thin-walled truncated cone shell using a self-built vibration test platform. To reduce the influence of material parameter errors caused by sample processing, a dichotomous particle swarm algorithm iteration method was developed to correct the material parameters. The results show that the maximum error between the test results and the theoretically calculated resonance response is within 3.0%, which verifies the correctness and effectiveness of the proposed theoretical model and calculation method.
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图 1 纤维增强复合薄壁圆锥壳理论模型
Figure 1. Theoretical model for fiber-reinforced composite thin-walled conical shells
u, ν, and w—Displacement functions in the X, θ, and Z directions, respectively; R2—Major radius; R1—Minor radius; L—Length of the generatrix; h—Shell thickness; α—Half-cone angle; β—Angle between the fiber direction and the X-axis
图 2 二分粒子群迭代法的计算流程
Figure 2. Computational process of the binary particle swarm iteration method
E' 1, E' 2, G' 12—Elastic modulus in different directions; η1, η2, η12—Loss factor in different directions
图 3 纤维增强复合材料薄壁圆锥壳幅频测试系统
Figure 3. Amplitude frequency test system for thin-walled conical shells of fiber-reinforced composites
图 4 纤维增强复合材料薄壁圆锥壳的固有频率-加速度曲线
Figure 4. Intrinsic frequency-acceleration curves of fiber-reinforced composite conical shells
图 5 纤维增强复合材料薄壁圆锥壳的固有频率及计算误差
Figure 5. Natural frequencies and computational inaccuracies of fiber-reinforced composite thin-walled conical shells
图 6 实验和计算获得的纤维增强复合材料薄壁圆锥壳的前4阶频率-响应曲线
Figure 6. Experimentally and computationally obtained frequency-response curves of the first 4th orders of thin-walled conical shells of fiber-reinforced composites
表 1 梁函数系数的取值
Table 1. Values of beam function coefficients
m λm σm 1 1.87510 0.734096 2 4.69409 1.018467 3 7.85476 0.999224 Note: λm and σm—Coefficients of the beam functions. 
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表 2 修正前后的材料参数、损耗因子
Table 2. Material parameters before and after correction, loss factor
Before iterative calculation After iterative calculation Loss factor Material parameters/GPa Material parameters/GPa E'1 E'2 G'12 E1 E2 G12 η1 η2 η12 120 8.5 4.74 114.9844351 8.1447308 4.5418851 0.0047909 0.0038328 0.0043119
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表 3 实验和计算获得的纤维增强复合材料薄壁圆锥壳的前4阶响应值及误差
Table 3. Experimentally and computationally obtained response values and errors of the first 4th order for thin-walled conical shells of fiber-reinforced composites
Mode Amplitude/m Error/% Experiment (C) Calculation (D) Calculation (E) |C−D|/D |C−E|/E 1 2.71×10−3 2.66×10−3 2.86×10−3 1.8 5.2 2 3.11×10−4 3.06×10−4 3.19×10−4 1.6 2.5 3 4.89×10−5 4.76×10−5 4.99×10−5 2.6 4.3 4 2.73×10−5 2.65×10−5 2.98×10−5 3.0 8.3
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