碳纳米管旋转功能梯度锥-柱连接壳行波模态频率分析

PDF(2026 KB)

振动与冲击 ›› 2024, Vol. 43 ›› Issue (9) : 166-174.

论文

庞磊1，成龙1，刘文光1，张宇航1，吕志鹏2

作者信息 +

Modal frequency analysis of traveling waves in carbon nanotube rotating functionally gradient conical-cylindrical connected shell

PANG Lei1, CHENG Long1, LIU Wenguang1, ZHANG Yuhang1, L Zhipeng2

Author information +

文章历史 +

摘要

为了深化增强型复合材料在航空航天工程领域的应用，本文旨在研究碳纳米管对旋转功能梯度锥-柱连接壳行波模态频率的影响。采用人工弹簧模拟边界和壳体间的连接条件，并考虑碳纳米管分布形式的变化，基于细观力学模型推导了系统的能量方程。引入切比雪夫多项式构造位移函数，利用Rayleigh-Ritz法求解了锥-柱连接壳的模态频率方程。通过算例分析了陶瓷体积分数指数、边界条件和碳纳米管体积分数对旋转功能梯度锥-柱连接壳行波模态频率的影响。结果表明，当陶瓷体积分数指数为0～5区间内，V型分布对结构行波模态频率的影响最为显著；随着旋转速度的增加，边界约束效果越强，壳结构越稳定；基体中碳纳米管体积分数越大，结构行波模态频率越高。

Abstract

This paper focuses on the impact of carbon nanotubes on the vibration characteristics of rotating FGMs joined conical-cylindrical shells, aiming to enhance their performance and stability. First, artificial springs are employed to simulate the connection conditions between boundary conditions and shell structures. The energy equations of the system are derived by considering different distribution patterns of carbon nanotubes and utilizing the microscopic mechanics model. Furthermore, the displacement function is constructed by using Chebyshev polynomials, and the modal frequency equations of the structures are solved by using Rayleigh-Ritz method. The effects of parameters, including the ceramic volume fraction exponent, the boundary conditions, and the carbon nanotube volume fraction, on the traveling wave modal frequency of structures are thoroughly examined using numerical examples. The major results in the paper include: the traveling wave frequency is notably influenced by the V-shaped distribution within the gradient exponent range of 0 to 5; with an increase in rotational speed, the impact of boundary constraints intensifies, resulting in enhanced stability of the structure; increasing the volume fraction of carbon nanotubes leads to higher traveling wave modal frequencies of the structures.

导出引用

庞磊1，成龙1，刘文光1，张宇航1，吕志鹏2. 碳纳米管旋转功能梯度锥-柱连接壳行波模态频率分析[J]. 振动与冲击, 2024, 43(9): 166-174

PANG Lei1, CHENG Long1, LIU Wenguang1, ZHANG Yuhang1, L Zhipeng2. Modal frequency analysis of traveling waves in carbon nanotube rotating functionally gradient conical-cylindrical connected shell[J]. Journal of Vibration and Shock, 2024, 43(9): 166-174

参考文献

[1] BIRMAN VICTOR, BYRD LARRY W. Modeling and Analysis of Functionally Graded Materials and Structures[J]. Applied Mechanics Reviews, 2007, 60(5) : 195-216. [2] 黄小林, 刘思奇, 肖薇薇, 等. 弹性地基中含孔隙的功能梯度圆锥壳的振动分析[J].力学与实践, 2021,43(04): 536-543. HUANG Xiao-lin, LIU Si-qi, XIAO Wei-wei, et al. Vibration analysis of functionally graded porous conical shells rested on elastic foundations[J]. Mechanics in Engineering, 2021, 43(04): 536-543. [3] 刘超, 刘文光, 吕志鹏. 环向加筋对功能梯度圆柱壳模态频率的影响[J]. 振动与冲击, 2021, 40(24): 255-262. LIU Chao，LIU Wen-guang，LYU Zhi-peng. Effects of inner ring-stiffener on modal frequencies of functionally graded cylindrical shell[J]. Journal of Vibration and Shock, 2021, 40(24): 255-262. [4] 石先杰, 左朋. 温度场影响下功能梯度圆锥壳振动特性分析[J]. 振动与冲击, 2022, 41(18): 9-15+24. SHI Xian-jie, ZUO Peng. Vibration analysis of functionally graded conical shells in thermal environment[J]. Journal of Vibration and Shock, 2022, 41(18): 9-15+24. [5] FU T, WU X, XIAO Z, et al. Analysis of vibration characteristics of FGM sandwich joined conical–conical shells surrounded by elastic foundations[J]. Thin-Walled Structures, 2021, 165: 107979. [6] BAGHERI H, KIANI Y, ESLAMI M R. Free vibration of FGM conical–spherical shells[J]. Thin-Walled Structures, 2021, 160: 107387. [7] BAGHERI H, KIANI Y, BAGHERI N, et al. Free vibrations of functionally graded material cylindrical shell closed with two spherical caps[J]. Ships and Offshore Structures, 2022, 17(4): 939-951. [8] IIJIMA S. Helical microtubules of graphitic carbon[J]. Nature, 1991, 354(6348): 56-58. [9] QIN B, ZHONG R, WANG T, et al. A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions[J]. Composite Structures, 2020, 232: 111549. [10] MIAO X, LI C, JIANG Y. Free vibration analysis of metal-ceramic matrix composite laminated cylindrical shell reinforced by CNTs[J]. Composite Structures, 2021, 260: 113262. [11] KIANI Y, DIMITRI R, TORNABENE F. Free vibration of FG-CNT reinforced composite skew cylindrical shells using the Chebyshev-Ritz formulation[J]. Composites Part B: Engineering, 2018, 147: 169-177. [12] 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. [13] GIA NINH D, TRI MINH V, VAN TUAN N, et al. Novel numerical approach for free vibration of nanocomposite joined conical–cylindrical–conical shells[J]. AIAA Journal, 2021, 59(1): 366-378. [14] REZAIEE-PAJAND M, SOBHANI E, MASOODI A R. Semi-analytical vibrational analysis of functionally graded carbon nanotubes coupled conical-conical shells[J]. Thin-Walled Structures, 2021, 159: 107272. [15] 刘超, 刘文光, 吕志鹏等. 旋转FGMs层合圆柱壳行波模态频率分析[J]. 航空动力学报, 2022, 37(04): 721-733. LIU Chao, LIU Wen-guang, LÜ Zhi-peng, et al. Analysis on traveling wave modal frequency of a rotating FGMs laminated cylindrical shell[J]. Journal of Aerospace Power. 2022, 37(04): 721-733. [16] SAFARPOUR H, GHANBARI B, GHADIRI M. Buckling and free vibration analysis of high speed rotating carbon nanotube reinforced cylindrical piezoelectric shell[J]. Applied Mathematical Modelling, 2019, 65: 428-442. [17] MIAO X, LI C, PAN Y. Research on the dynamic characteristics of rotating metal–ceramic matrix DFG-CNTRC thin laminated shell with arbitrary boundary conditions[J]. Thin-Walled Structures, 2022, 179: 109475. [18] AFSHARI H, AMIRABADI H. Vibration characteristics of rotating truncated conical shells reinforced with agglomerated carbon nanotubes[J]. Journal of Vibration and Control, 2022, 28(15-16): 1894-1914. [19] DAMERCHELOO A R, KHORSHIDVAND A R, KHORSANDIJOU S M, et al. A study on dynamic analysis of rotating GNP-reinforced joined conical–conical shells[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2022, 44(6): 234. [20] HEIDARI-SOURESHJANI A, TALEBITOOTI M, PAKRAVAN I, et al. Critical speed and frequency behavior of rotating joined FG-CNTRC conical-conical shells[J]. Engineering Structures, 2022, 266: 114508. [21] HEIDARI-SOURESHJANI A, TALEBITOOTI R, TALEBITOOTI M. On the frequency characteristics of rotating combined conical-conical shells made of FG-CNTRC composite materials under thermal environments[J]. Mechanics Based Design of Structures and Machines, 2022: 1-25. [22] LOY C T, Lam K Y, Reddy J N. Vibration of functionally graded cylindrical shells[J]. International Journal of Mechanical Sciences, 1999, 41(3): 309-324. [23] 沈惠申.功能梯度碳纳米管增强复合材料结构建模与分析研究进展[J].力学进展, 2016, 46(00): 478-505. SHEN Hui-shen. Modeling and analysis of functionally graded carbon nanotube reinforced composite structures: A review[J]. Advances in Mechanics，2016, 46(00): 478-505. [24] CHAI Q, WANG Y Q. A general approach for free vibration analysis of spinning joined conical–cylindrical shells with arbitrary boundary conditions[J]. Thin-Walled Structures, 2021, 168: 108243. [25] CHEN Y, JIN G, LIU Z. Flexural and in-plane vibration analysis of elastically restrained thin rectangular plate with cutout using Chebyshev–Lagrangian method[J]. International Journal of Mechanical Sciences. 2014, 89: 264-278. [26] SARKHEIL S, FOUMANI M S. Free vibrational characteristics of rotating joined cylindrical-conical shells[J]. Thin-Walled Structures, 2016, 107: 657-670. [27] CHAI Q, WANG Y Q. Traveling wave vibration of graphene platelet reinforced porous joined conical-cylindrical shells in a spinning motion[J]. Engineering Structures, 2022, 252: 113718. [28] 梁斌, 项爽, 李戎, 等. 旋转功能梯度圆柱壳振动影响因素研究（英文）[J]. 船舶力学, 2013, 17(12): 1460-1472. LIANG Bin, XIANG Shuang, LI Rong, et al. Study of Effective factors for the vibration of rotating functionally graded cylindrical shells[J]. Journal of Ship Mechanics, 2013, 17(12): 1460-1472. [29] MALEKZADEH P, HEYDARPOUR Y. Free vibration analysis of rotating functionally graded truncated conical shells[J]. Composite Structures, 2013, 97: 176-188. [30] SHAKOURI M. Free vibration analysis of functionally graded rotating conical shells in thermal environment[J]. Composites Part B: Engineering, 2019, 163: 574-584. [31] CIVALEK Ö. Discrete singular convolution method for the free vibration analysis of rotating shells with different material properties[J]. Composite Structures, 2017, 160: 267-279. [32] QIN Z, PANG X, SAFAEI B, et al. Free vibration analysis of rotating function