大挠度圆柱壳在温度场中的热弹耦合振动分析

基金项目: 国家自然科学基金资助项目(10372067);山西省自然科学基金资助项目(20021004)

Analysis of Thermal-Elastic Coupling Vibration of Large Deflection Cylindrical Shell

Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China;

摘要: 对温度场与与应力场耦合时的圆柱壳的非线性热弹耦合的振动问题，推导得到了基本的振动方程，热传导方程和协调方程，对短圆柱壳运用伽辽金(Galerkin)法求解,得出振幅随时间变化的数值解，得到一些有价值的结论．即随着温度幅值和耦合系数的增大，振动衰减的速度变缓，热弹耦合效应减弱．随着长径比、长厚比的增大，振幅衰减的速度变快，同时热振动频率也随之增大，即热弹耦合效应增强．耦合系数越大，轴向应力、轴向力以及轴向弯矩越小．
- 圆柱壳 /
- 热弹耦合振动 /
- 伽辽金法
Abstract: The governing equation and energy equations for thermal-elastic coupling vibration of cylindrical shell were developed.The Garlerkin method was used in numerical process.Some useful result can be concluded from numerical result.With the increase of the amplitude of temperature and coupling coefficient,the speed of vibration decaying becomes slower and the coupling effect becomes weaker.The larger the ration of length to radius and length to thickness,the faster the decaying of the vibration amplitude and the vibration frequency increase.It means the coupling effect gets stronger.The larger the coupling coefficient,the smaller the axial stress,the axial force and the bendind moment are.
- cylindrical shell /
- thermal-elastic coupled vibration /
- Garlerkin method

[1]	王洪纲.热弹性力学概论[M].北京:清华大学出版社，1998，1—54.
[2]	曹志远.板壳振动理论[M].北京:中国铁道出版社，1989，220—245.
[3]	严宗达，王洪礼.热应力[M].北京:高等教育出版社，1993，1—36.
[4]	Chang W P,Wan S M.Thermomechanically coupled nonlinear vibration of plates[J].Internat J Non-Linear Mech,1986,21(5)：375—389. doi: 10.1016/0020-7462(86)90021-1
[5]	Chang W P,Jen S C.Nonlinear free vibration of heated orthotropic rectangular plate[J].Internat J Solids and Structures,1986,22(3)：267—281. doi: 10.1016/0020-7683(86)90091-0
[6]	戴德成,任勇生.矩形板的非线性热弹耦合振动[J].振动工程学报，1990,3(2)：65—72.
[7]	树学锋，张晓晴，张晋香.周边固支圆板非线性热弹耦合振动分析[J].应用数学和力学，2000,21(6)：647—654.
[8]	树学锋，张晓晴.简支圆板非线性热弹耦合振动问题的研究[J].工程力学,2000，17(2)：97—101.
[9]	兰姣霞，张晓晴，树学锋.轴对称圆柱壳非线性热弹耦合振动的基本方程[J].华北工学院学报，2000，21(6)：513—516.

点击查看大图