Analysis of natural characteristics of functionally graded carbon nanotube reinforced composite conical-cylindrical shells

doi:10.19936/j.cnki.2096-8000.20260628.001

Abstract

Abstract: The free vibration characteristics of functional gradient carbon nanotube reinforced composite conical-cylindrical shells under arbitrary boundary conditions are investigated. The study encompasses both the uniform distribution of carbon nanotubes and four different functionally graded distribution scenarios. The effective material properties of this type of composite are obtained using a generalized mixture rule. Based on Love’s shell theory and Sanders’ shell theory, a theoretical model of the conical shell is established, and a theoretical model of the cylindrical shell is derived through a parameter degradation method. The energy function of the combined shell is presented, and arbitrary boundary conditions at the ends of the shell, as well as continuity conditions at the junctions of the sub-shells, are simulated using artificial spring techniques. The circumferential and axial displacement components of the shell are expressed using Fourier series and Chebyshev polynomials, respectively, and the Rayleigh-Ritz method is employed to formulate the vibration equations of the FG-CNTRC conical-cylindrical shell. Subsequently, the natural frequencies of the combined shell structure are computed and compared with results from previous literature and experimental findings, thereby strongly validating the reliability and effectiveness of the proposed model and methods. Through a parameter sensitivity analysis, the influence of key factors, such as circumferential wave number, thickness-to-radius ratio, radius ratio, half apex angle, and the volume fraction and distribution form of carbon nanotubes, on the inherent vibration characteristics of the FG-CNTRC conical-cylindrical shell is investigated.

Key words: functionally graded carbon nanotube reinforced composite, conical-cylindrical shell, artificial spring, arbitrary boundary, Rayleigh-Ritz method

CLC Number:

TB332

ZHANG Yunfeng, WU Zhihua, WANG Wenqi, TIAN Zedong. Analysis of natural characteristics of functionally graded carbon nanotube reinforced composite conical-cylindrical shells[J]. COMPOSITES SCIENCE AND ENGINEERING, 2026, 0(6): 1-9.

References

[1] 马涛, 赵忠民, 刘良祥等. 功能梯度材料的研究进展及应用前景[J]. 化工科技, 2012, 20(1):71-75.
[2] 周宸, 陈明达, 杨建, 等. 纤维增强树脂基复合材料层合板振动性能的研究进展[J]. 复合材料科学与工程, 2023(2):126-132.
[3] BAGHERI H, KIANI Y, ESLAMI M R. Free vibration of joined conical-cylindrical-conical shells[J]. Acta Mechanica, 2018, 229(7):2751-2764.
[4] 李涵, 李欣业, 白斌, 等. 变厚度旋转圆柱壳的自由振动研究[J]. 振动工程学报, 2023, 36(5):1258-1265.
[5] DINH G N, VU T M, NGUYEN V T,et al. Novel numericalapproach for free vibration of nanocomposite joined conical-cylindrical-conical shells[J]. AIAA Journal, 2021, 59(1):366-378.
[6] WANG J X, WANG Y Q, CHAI Q D. Free vibration analysis of a spinning functionally graded spherical-cylindrical-conical shell with general boundary conditions in a thermal environment[J]. Thin-Walled Structures, 2022, 180:109768.
[7] SHANG X C. An exact analysis for free vibration of a composite shell structure-hermetic capsule[J]. Applied Mathematics and Mechanics, 2001, 22(9):1035-1045.
[8] IRIE T, YAMADA G, MURAMOTO Y. Free vibration of joined conical-cylindrical shells[J]. Journal of Sound and Vibration, 1984, 95(1):31-39.
[9] EFRAIM E, EISENBERGER M. Exact vibration frequencies of segmented axisymmetric shells[J]. Thin-Walled Structures, 2006, 44(3):281-289.
[10] BAGHERI H, KIANI Y, ESLAMI M. Free vibration of joined conical-conical shells[J]. Thin-Walled Structures, 2017, 120:446-457.
[11] 张帅, 李天匀, 朱翔, 等. 改进傅里叶级数法求解封口锥柱球组合壳的自由振动[J]. 振动工程学报, 2021, 34(3):601-609.
[12] WANG Y Q, CHAI Q D, XING W C. Vibrations of joined conical-cylindrical shells with bolt connections:theory and experiment[J]. Journal of Sound and Vibration, 2023, 554:117695.
[13] 张宇航, 刘文光, 刘超. 任意边界条件下旋转功能梯度锥-柱连接壳行波模态分析[J]. 船舶力学, 2024, 28(1):154-168.
[14] 瞿叶高, 华宏星, 孟光, 等. 圆柱壳-圆锥壳组合结构振动分析的新方法[J]. 工程力学, 2013, 30(3):24-31.
[15] KWON H, BRADBURY C R, LEPAROUX M. Fabrication of functionally graded carbon nanotube-reinforced aluminum matrix composite[J]. Advanced Engineering Materials, 2011, 13(4):325-329.
[16] SHEN H S, XIANG Y. Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 213/214/215/216:196-205.
[17] WANG Z X, SHEN H S. Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments[J]. Nonlinear Dynamics, 2012, 70(1):735-754.
[18] LIEW K M, NG T Y, ZHAO X. Free vibration analysis of conical shells via the element-free kp-Ritz method[J]. Journal of Sound and Vibration, 2005, 281(3/4/5):627-645.
[19] PELLICANO F. Vibrations of circular cylindrical shells:theory and experiments[J]. Journal of Sound and Vibration, 2007, 303(1/2):154-170.