Vibration response analysis of fiber reinforced composite thin-walled truncated conical shell based on multilevel iterative correction
-
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.
-
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. 
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
-
[1] 曹志远. 板壳振动理论[M]. 北京: 中国铁道出版社, 1989.CAO Zhiyuan. Vibration theory of plate and shell[M]. Beijing: China Railway Publishing House, 1989(in Chinese). [2] QATU M S. Vibration of laminated shells and plates[M]. Amsterdam: Elsevier, 2004. [3] 邢誉峰, 刘波. 板壳自由振动的精确解[M]. 北京: 科学出版社, 2015.XING Yufeng, LIU Bo. An exact solution for the free vibration of plates and shells[M]. Beijing: Science Press of Beijing, 2015(in Chinese). [4] ZOU Y, TONG L, STEVEN G P. Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures-A review[J]. Journal of Sound and Vibration, 2000, 230(2): 357-378. [5] 李晖, 孙伟, 许卓, 等. 纤维增强复合薄板振动测试与分析方法[M]. 北京: 机械工业出版社, 2020.LI Hui, SUN Wei, XU Zhuo, et al. Vibration test and analysis method of fiber reinforced composite sheet[M]. Beijing: China Machine Press, 2020(in Chinese). [6] 王爱勤. 圆锥(柱)体在复杂载荷作用下振动响应的计算[J]. 西安公路交通大学学报, 1998,18(3):66-69.WANG Aiqin. Vibration responses of conical body under complex loads[J]. Journal of Xi'an Highway University,1998,18(3):66-69(in Chinese). [7] 杨绍武. 复杂载荷作用下功能梯度圆锥壳的非线性动力学研究[D]. 北京: 北京信息科技大学, 2015.YANG Zhaowu. Study on nonlinear dynamics of functionally graded conical shells under complex loads[D]. Beijing: Beijing Information Science and Technology University, 2015(in Chinese). [8] DEY S, MUKHOPADHYAY T, KHODAPARAST H H, et al. Stochastic natural frequency of composite conical shells[J]. Acta Mechanica,2015,226(8):2537-2553. doi: 10.1007/s00707-015-1316-4 [9] ANSARI R, TORABI J. Numerical study on the buckling and vibration of functionally graded carbon nanotube-reinforced composite conical shells under axial loading[J]. Composites Part B: Engineering,2016,95:196-208. doi: 10.1016/j.compositesb.2016.03.080 [10] MERCAN K, BALTACIOGLU A K, CIVALEK Ö. Free vibration of laminated and FGM/CNT composites annular thick plates with shear deformation by discrete singular convolution method[J]. Composite Structures,2018,186:139-153. doi: 10.1016/j.compstruct.2017.12.008 [11] 谢坤. 纵向激励下桨—轴—艇耦合模型声振响应半解析计算方法及特性研究[D]. 武汉: 华中科技大学, 2018.XIE Kun. Study on semi-analytic methods and vibro-acoustic characteristics of coupled propeller-shaft-hull structures subjected to longitudinal excitations[D]. Wuhan: Huazhong University of Science and Technology, 2018(in Chinese). [12] 张永强. 薄壁圆锥壳构件的动力学相似设计方法研究[D]. 沈阳: 东北大学, 2020.ZHANG Yongqiang. Research on dynamic similarity design method for thin-walled conical shell structures[D]. Shenyang: Northeastern University, 2020(in Chinese). [13] LEI Z X, LIEW K M, YU J L. Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment[J]. Composite Structures,2013,106:128-138. doi: 10.1016/j.compstruct.2013.06.003 [14] LI H, ZHOU Z X, SUN H, et al. Theoretical study on the influence of hard coating on vibration characteristics of fiber-reinforced composite thin shell[J]. Coatings,2018,8(3):87. doi: 10.3390/coatings8030087 [15] HEIDARI SOURESHJANI A, TALEBITOOTI R, TALEBITOOTI M. A semi-analytical approach on the effect of external lateral pressure on free vibration of joined sandwich aerospace composite conical-conical shells[J]. Aerospace Science and Technology,2020,99:105559. doi: 10.1016/j.ast.2019.105559 [16] ZHANG H, ZHU R P, SHI D Y, et al. A simplified plate theory for vibration analysis of composite laminated sector, annular and circular plate[J]. Thin-Walled Structures,2019,143:106252. doi: 10.1016/j.tws.2019.106252 [17] KAMALOO A, JABBARI M, TOOSKI M Y, et al. Nonlinear free vibrations analysis of delaminated composite conical shells[J]. International Journal of Structural Stability and Dynamics,2020,20(1):2050010. doi: 10.1142/S0219455420500108 [18] YANG S W, ZHANG W, HAO Y X, et al. Nonlinear vibrations of FGM truncated conical shell under aerodynamics and in-plane force along meridian near internal resonances[J]. Thin-Walled Structures,2019,142:369-391. doi: 10.1016/j.tws.2019.04.024 [19] SAFARPOUR M, RAHIMI A R, ALIBEIGLOO A. Static and free vibration analysis of graphene platelets reinforced composite truncated conical shell, cylindrical shell, and annular plate using theory of elasticity and DQM[J]. Mechanics Based Design of Structures and Machines,2020,48(4):496-524. doi: 10.1080/15397734.2019.1646137 [20] REZAIEE-PAJAND M, SOBHANI E, MASOODI A R. Free vibration analysis of functionally graded hybrid matrix/fiber nanocomposite conical shells using multiscale method[J]. Aerospace Science and Technology,2020,105:105998. doi: 10.1016/j.ast.2020.105998 [21] MAJI P, SINGH B N. Free vibration responses of 3D braided rotating cylindrical shells based on third-order shear deformation[J]. Composite Structures,2021,260:113255. doi: 10.1016/j.compstruct.2020.113255 [22] SOBHANI E, MASOODI A R, AHMADI-PARI A R. Vibration of FG-CNT and FG-GNP sandwich composite coupled conical-cylindrical-conical shell[J]. Composite Structures,2021,273:114281. doi: 10.1016/j.compstruct.2021.114281 [23] SHI X J, ZUO P, ZHONG R, et al. Vibration analysis of combined functionally graded cylindrical-conical shells coupled with annular plates in thermal environment[J]. Composite Structures, 2022, 294: 115738. -
下载:
点击查看大图
计量
- 文章访问数: 497
- HTML全文浏览量: 192
- PDF下载量: 22
- 被引次数: 0
