黄小林, 钟德月, 刘思奇,等.轴向运动碳纳米管增强复合材料板的自由振动研究[J].河南理工大学学报（自然科学版）,2022,41(1):153-158.

HUANG X L, ZHONG D Y, LIU S Q, et al. Study on free vibration of axially moving carbon nanotube-reinforced composite plate [J].Journal of Henan Polytechnic University(Natural Science) ,2022,41(1):153-158.

轴向运动碳纳米管增强复合材料板的自由振动研究

黄小林, 钟德月, 刘思奇, 魏耿忠

桂林电子科技大学 建筑与交通工程学院,广西 桂林541004

摘要:为了研究轴向运动碳纳米管增强复合材料（carbon nanotube reinforced composite, CNTRC）板的自由振动特性,基于经典薄板理论和哈密顿原理导出轴向运动CNTRC板的运动方程,采用伽辽金法求解不同边界条件下其自由振动频率,并通过数值算例讨论碳纳米管体积分数和分布方式、轴向运动、面内力、宽厚比、边界条件等因素对自由振动的影响。结果表明,碳纳米管显著提高了板的自振频率,轴向运动降低了板的自振频率；自振频率随面内拉力的增大而提高,随面内压力的增大而降低。另外,边界条件和碳纳米管的分布方式对自由振动频率也有一定的影响。

关键词:轴向运动板;碳纳米管;自由振动;哈密顿原理;伽辽金法

doi:10.16186/j.cnki.1673-9787.2020040104

基金项目:国家自然科学基金资助项目（11362004）

收稿日期:2021/01/21

修回日期:2020/10/15

出版日期:2022/01/10

Study on free vibration of axially moving carbon nanotube-reinforced composite plate

HUANG Xiaolin, ZHONG Deyue, LIU Siqi, WEI Gengzhong

School of Architecture and Transportation Engineering, Guilin University of Electronic Technology, Guilin 541004 , Guangxi, China

Abstract: In this study,the vibration characteristics of axially moving carbon nanotube reinforced composite (CNTRC) plates were investigated,and motion equation of the CNTRC were derived based on the composite thin plate theory and Hamilton’s principle.Then,the Galerkin method was used to solve the series solution of the natural vibration frequency under differernt boundary conditions.In addition,the effects of many factors on free vibration,such as the axial velocity,in-plane force,width-to-thickness ratio,boundary conditions,volume fraction,and distribution methods of carbon nanotubes were analyzed by numerical examples.The results showed that the natural frequency of the plate was significantly increased by carbon nanotubes.However,the natural frequency of the plate was decreased by the axial motion reduces.The natural vibration frequency of the plate increased with the increase of in-plane tension,but decreased with the increase of in-plane pressure.Moreover,the boundary conditions and the distribution of carbon nanotubes also had a certain effect on the free vibrations frequency.

Key words:axially moving plate;carbon nanotubes;free vibration;Hamilton's  principle;Galerkin method

 轴向运动碳纳米管增强复合材料板的自由振动研究_黄小林.pdf