功能梯度材料薄板热模态分析

发布时间：2018-05-31 16:45

本文选题：一维FGM薄板 + 热模态　；参考：《河北工程大学》2017年硕士论文

【摘要】：功能梯度材料(简称FGM)是指材料的组分、结构以及物性参数等某一项性能或者综合性能呈连续变化,并以此来适应不同的环境,从而实现某一特定功能的新型复合材料。气动热弹性的研究重点是热振动及热颤振问题,而热振动及热颤振问题的研究基础就是热模态分析。因此,对功能梯度材料的有关热模态问题的分析研究非常重要。本文利用层合板有限单元法,对由ZrO2和Al 1100组成的新型FGM薄板的热模态问题进行了分析,并对本方法的正确性进行了检验。讨论了孔隙率、位移边界条件及中心开孔对FGM薄板热模态的影响。本文以有限单元法为基础,对热荷载作用下的FGM薄板的热应力计算公式进行了推导,并利用最小势能原理,推导出结构在受热情况下的等效热载荷。然后对热振动的有关理论进行了阐述,并详细地推导了初位移刚度矩阵及初应力刚度矩阵的表达式。接着在不考虑初始位移的影响的基础上,从变分原理出发,较为详细地推导了传统的非线性板单元的初始位移刚度矩阵和初始应力刚度矩阵。最后基于经典薄板理论,通过Python的ABAQUS二次开发,分别对位移边界条件为四边固定和简支的一维功能梯度材料薄板的热模态问题进行了分析。数值算例的分析结果表明:在FGM薄板孔隙率控制参数Az一定的情况下,随着薄板温度的升高,FGM薄板的固有频率会不断减小。在FGM薄板温度一定的情况下,随着薄板孔隙率控制参数Az的增大,FGM薄板的固有频率会不断增大。在FGM薄板温度和孔隙率控制参数Az一定的情况下,开孔会对FGM薄板的固有频率产生很大的影响,并且随着薄板开孔半径r的增大,FGM薄板的固有频率会不断增大;在FGM薄板温度和开孔半径r一定的情况下,FGM开孔薄板的固有频率会随着孔隙率控制参数Az的增大而不断增大;在FGM薄板孔隙率控制参数Az和开孔半径r一定的情况下,随着薄板温度的增加,FGM开孔薄板的固有频率会不断减小。当FGM薄板的温度、孔隙率控制参数以及中心开孔半径均相同时,位移边界条件为四边固支的FGM薄板的固有频率比简支的FGM薄板的固有频率要高。本文的研究为功能梯度材料在高温下的动力学分析提供了一定的基础。
[Abstract]:Functionally graded material (FGM) is a new type of composite material whose composition, structure, physical properties and other properties change continuously, which can adapt to different environments and realize a certain function. The research focus of Aerothermal elasticity is thermal vibration and thermal flutter, and the research foundation of thermal vibration and thermal flutter is thermal modal analysis. Therefore, it is very important to study the thermal mode problems of functionally graded materials. In this paper, the thermal modal problem of a new type of FGM thin plate composed of ZrO2 and Al 1100 is analyzed by means of laminated plate finite element method, and the correctness of this method is verified. The effects of porosity, displacement boundary conditions and central opening on the thermal mode of FGM thin plate are discussed. Based on the finite element method, the formula for calculating the thermal stress of FGM thin plate under thermal load is derived, and the equivalent thermal load of the structure under heating is derived by using the principle of minimum potential energy. Then the theory of thermal vibration is expounded and the expressions of initial displacement stiffness matrix and initial stress stiffness matrix are derived in detail. Then, based on the variational principle, the initial displacement stiffness matrix and the initial stress stiffness matrix of the traditional nonlinear plate element are deduced in detail, without considering the influence of the initial displacement. Finally, based on the classical thin plate theory and Python's ABAQUS secondary development, the thermal mode problems of one-dimensional functionally graded material thin plates with four-edge fixed and simply supported displacement boundary conditions are analyzed respectively. The results of numerical examples show that the natural frequency of FGM thin plate decreases with the increase of the temperature of the thin plate under the condition of constant porosity control parameter Az. With the increase of the porosity control parameter Az, the natural frequency of the FGM thin plate will increase with the constant temperature of the plate. Under the condition of constant temperature and porosity control parameter Az, the opening will have a great influence on the natural frequency of the FGM thin plate, and the natural frequency of the FGM thin plate will increase with the increase of the opening radius r of the thin plate. The natural frequency of FGM thin plate increases with the increase of the porosity control parameter Az, and the porosity control parameter Az and the opening radius r of the FGM thin plate with the same porosity control parameter Az and the opening radius r, the natural frequency of the FGM thin plate increases with the increase of the porosity control parameter Az and the opening radius r. The natural frequency of FGM thin plate decreases with the increase of temperature. At the same time, when the temperature, porosity control parameters and central opening radius of FGM thin plate are homogeneous, the natural frequency of FGM thin plate with four edges fixed by displacement boundary condition is higher than that of simply supported FGM thin plate. The research in this paper provides a basis for the kinetic analysis of functionally graded materials at high temperature.
【学位授予单位】：河北工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34

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