功能梯度碳纳米管增强复合材料锥-柱组合壳的固有特性分析

doi:10.19936/j.cnki.2096-8000.20260628.001

复合材料科学与工程 ›› 2026, Vol. 0 ›› Issue (6): 1-9.DOI: 10.19936/j.cnki.2096-8000.20260628.001

• 基础与力学性能研究 • 下一篇

功能梯度碳纳米管增强复合材料锥-柱组合壳的固有特性分析

张云枫¹, 武志花^1,2*, 王文琪¹, 田泽东¹

1.天津工业大学机械工程学院,天津 300387;
2.天津市现代机电装备技术重点实验室,天津 300387

收稿日期:2025-04-25 出版日期:2026-06-28 发布日期:2026-07-03
通讯作者: 武志花(1990—),男,博士,讲师,硕士生导师,研究方向为复合材料结构动力学,wuzhihua@tiangong.edu.cn。
作者简介:张云枫(2000—),男,硕士研究生,研究方向为复合材料板壳动力学。
基金资助:
国家自然科学基金(12402023)

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

ZHANG Yunfeng¹, WU Zhihua^1,2*, WANG Wenqi¹, TIAN Zedong¹

1. School of Mechanical Engineering, Tiangong University, Tianjin 300387, China;
2. Tianjin Key Laboratory of Advanced Mechatronics Equipment Technology, Tianjin 300387, China

Received:2025-04-25 Online:2026-06-28 Published:2026-07-03

摘要/Abstract

摘要： 探讨了功能梯度碳纳米管增强复合材料锥-柱组合壳在任意边界条件下的自由振动特性。研究涵盖了碳纳米管的均匀分布以及四种不同的功能梯度分布情形,通过应用广义混合率求得了该类型复合材料的有效物性参数。基于Love壳理论及Sanders壳理论构建了圆锥壳的理论模型,并通过参数退化方法推导出圆柱壳的理论模型。给出了组合壳的能量函数,并利用人工弹簧技术模拟壳体端部的任意边界条件以及各子壳接合处的连续性条件。分别采用Fourier级数和Chebyshev多项式表示壳体的周向和轴向位移分量,并采用Rayleigh-Ritz法建立锥-柱组合壳的振动方程。随后求解了该组合壳结构的固有频率,并将其与既往文献中的计算结果以及试验结果进行对比分析,从而有力证实了该研究模型与所运用方法的可靠性和有效性。通过参数影响分析,研究了周向波数、厚径比、半径比、半顶角以及碳纳米管体积率与分布形式等关键因素对锥-柱组合壳固有振动特性的影响。

关键词: 功能梯度碳纳米管增强复合材料, 锥-柱组合壳, 人工弹簧, 任意边界, Rayleigh-Ritz法

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

中图分类号:

TB332

张云枫, 武志花, 王文琪, 田泽东. 功能梯度碳纳米管增强复合材料锥-柱组合壳的固有特性分析[J]. 复合材料科学与工程, 2026, 0(6): 1-9.

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.

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功能梯度碳纳米管增强复合材料锥-柱组合壳的固有特性分析

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

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