【作者】 兰姣霞；

【导师】 树学锋；

【作者基本信息】 太原理工大学 ， 固体力学， 2002， 硕士

【摘要】 本文首先推导了当温度场和应变场耦合时椭圆板的非线性热弹耦合振动的基本方程，其中包括横向热振动方程、协调方程和能量方程。为了求解方便，引入无量纲参数将其无量纲化。我们采用Galerkin法进行离散化后得到一耦合的非线性常微分方程组，利用Runge-Kutta法进行数值求解，得到的主要结论如下：影响椭圆板非线性热弹耦合振动的因素主要有耦合系数、温度幅值、组合参数τd~2、椭度以及初始位移参数；当给定的初始位移较小时，热弹耦合效应使椭圆板的振动频率加快，当给定的初始位移较大时，热弹耦合效应使椭圆板的振动频率减小；边界条件对耦合效应有较大的影响，较强的边界条件使椭圆板热弹耦合自由振动的频率变低，但振荡幅度增大。其次，我们用同样的方法研究了圆柱壳的非线性热弹耦合振动，主要结论如下：影响圆柱壳非线性热弹耦合振动的因素主要有耦合系数、温度幅值、长径比、径厚比以及初始位移参数；耦合系数越大，轴向应力、轴向力以及轴向弯矩越小。 最后利用有限元程序LS-DYNA对轴对称圆柱壳受高速热冲击作用进行了计算机仿真分析，得到了位移时间曲线和单元的应力时间曲线，同文献已有的结果吻合的较好。数值模拟表明：边界条件对位移和应力的影响非常小；位移随着线热膨胀系数、热传导系数的增大而增大，但是随着比热容的增大而减小；应力的最大值随着线热膨胀系数的增大而增大，而随着比热容的增大而减小，而热传导系数k对应力的影响比较小。更多还原

【Abstract】 The basic equations of elliptic plate, when temperature and stress fields are coupled, are developed, which include transverse thermal vibration equation , the compatibility equation and energy equations. In order to solve them easily, we introduced the dimensionless quantities and non-dimensionlized the obtained equations. A nonlinear ordinarydifferential equations are obtained by Galerkin’s method. The numericalresults are presented by employing Runge-Kutta method. The important results are given as follows: The coupling coefficient the amplitude of temperature, the parameter, the ration of length of long axis to that of short axis and initial displacement are main factors which influence the thermoelastic vibration of elliptic plate; When the initial displacement is smaller, thermoelastic coupling makes the frequency of the elliptic plate larger and when the initial displacement is larger, thermoelastic coupling makes the frequency of the elliptic plate smaller; The boundary conditions has strong influence on the coupling effect, the stronger it is, the smaller frequency of free vibration is but the larger amplitude is. Second, the thermoelastic coupling vibration of cylindrical shell are discussed by means of the same method. The coupling coefficient, amplitude of temperature, initial displacement, ratio of length to radius and that of radius to thickness are main factors which influence the thermoelastic vibration of cylindrical shell; The higher the coupling coefficient is, the lower the axial force, the axial stress and the axial moment are.The finite element code LS_DYNA is used to investigate the response of the axisymmetry cylindrical shell under the thermal impact, and the curves of displacement vs time and that of stress vs time are obtained. The results from simulation agree well with the conclusions ofconference [21], and indicate that the boundary conditions have no obvious effect on the displacement and stress; that the displacement and stress increase with linear heat expanding ratio, and those decrease with the specific heat of material; that the displacement increases with the heat transfer ratio, but the stress does not .更多还原