黏弹性基体中FG-CNTRCs圆柱壳热振动特性分析  

Analysis on Thermal Vibration Characteristic of FG-CNTRCs Cylindrical Shell Resting on Viscoelastic Foundation

作　　者：吴栋 雷勇军[1,2] 于宝石 唐雨 张大鹏 WU Dong;LEI Yongjun;YU Baoshi;TANG Yu;ZHANG Dapeng(College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China;Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions,Changsha 410073,China)

机构地区：[1]国防科技大学空天科学学院,湖南长沙410073 [2]空天任务智能规划与仿真湖南省重点实验室,湖南长沙410073

出　　处：《湖南大学学报（自然科学版）》2023年第6期188-198,共11页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(11902348,11872372);湖南省自然科学基金资助项目(2020JJ5650);国防科技大学科研计划资助项目(ZK20-27)。

摘　　要：建立了考虑碳纳米管(Carbon Nanotubes,CNTs)尺度效应的宏观功能梯度碳纳米管增强复合材料(Functionally Graded Carbon Nanotubes Reinforced Composites,FG-CNTRCs)圆柱壳自由振动特性的理论模型.综合考虑CNTs的取向和尺度效应,基于Eshelby-Mori-Tanaka(EMT)方法和非局部理论建立了宏观CNTRCs的非局部EMT本构模型.基于Kirchhoff-Love圆柱壳假设,采用Hamilton原理推导了热环境中visco-Pasternak基体中FG-CNTRCs圆柱壳的自由振动控制方程,利用Navier法得到两端简支圆柱壳的固有频率,并与文献中结果进行对比,验证了模型和方法的正确性.分析了非局部参数、CNTs的体积分数和分布方式、圆柱壳的长厚比、环境温度以及地基参数等对简支FG-CNTRCs圆柱壳自由振动特性的影响.研究发现,考虑CNTs的尺度效应后会降低FG-CNTRCs圆柱壳的抗弯刚度,环境温度对简支FG-XCNTRCs圆柱壳固有频率虚部的影响随CNTs体积分数的增大而增大,且长厚比和地基的阻尼参数对虚部的影响有耦合作用.A theoretical model for the free vibration characteristics of Functionally Graded Carbon Nanotubes Reinforced Composites(FG-CNTRCs)thin cylindrical shells considering the scale effect of Carbon Nanotubes(CNTs)was established.First,the nonlocal Eshelby-Mori-Tanaka(EMT)constitutive model of macroscopic CNTRCs was developed based on the EMT method and nonlocal theory by considering the orientation and scale effect of CNTs.Then,based on the Kirchhoff-Love cylindrical shell assumption,the free vibration governing equations for FG-CNTRCs cylindrical shells on the visco-Pasternak foundation in the thermal environment ware derived by applying the Hamilton principle.The natural frequencies of the simply supported cylindrical shells at both ends were obtained by the Navier method,and the results were compared with those in the literature to verify the correctness of the model and method.Finally,the effects of nonlocal parameters,volume fraction and distribution of CNTs,length-to-thickness ratio of cylindrical shell,ambient temperature,and foundation parameters on the free vibration characteristics of simply-supported FG-CNTRCs cylindrical shell were analyzed.It is found that considering the scale effect of CNTs can reduce the bending stiffness of FG-CNTRCs cylindrical shells.The influence of ambient temperature on the imaginary part of the natural frequency of simply supported FG-X-CNTRCs cylindrical shell increases with the increase of CNTs volume fraction,and the influence of length-thickness ratio and foundation damping parameters on the imaginary part is coupled.

关 键 词：尺度效应 碳纳米管 功能梯度复合材料 热行为 黏弹性地基 

分 类 号：O343.6[理学—固体力学]