不同组分下FGM薄板的热模态分析

发布时间：2018-03-12 06:26

本文选题：FGM薄板　切入点：有限元法　出处：《河北工程大学》2017年硕士论文　论文类型：学位论文

【摘要】：功能梯度材料(FGM)是一种新一代先进的非均匀复合材料,这种材料是由两种或者两种以上性质不同的材料构成的。由于它的材料属性沿一个或多个方向呈连续梯度变化,FGM基本上消除了宏观界面,因而其物理特性在结构内没有突变。在结构动力学的研究方面上,模态分析相当的重要,而模态分析的重点又在于热模态的分析。随着当代高速度航空器以及航天器的迅猛发展,热模态分析的必要性更是得到了加强。因此,研究结构的热模态具有重要的理论和实际意义。本文致力于研究功能梯度薄板在热荷载作用下的非线性振动问题。重点研究功能梯度薄板的固有频率和组分对其影响。首先,取Al 1100/ZrO2FGM薄板作为研究对象,然后进一步定义其物参模型,并基于经典薄板理论,导出了FGM薄板的基本动力方程。其次,由基本动力方程推导出其有限元基本方程,进而利用层合板有限单元法并对ABAQUS软件进行了python二次开发,编写相关的有限元程序,从而利用ABAQUS对FGM薄板进行程序化计算,通过计算获得其数值计算结果,然后,进一步对其计算结果进行了正确性检验。最后,根据计算结果获得了FGM薄板在四边固支和四边简支两种边界条件下,薄板开孔和未开孔时,不同组分下的固有频率和其对应的模态振型图,同时对不同组分下FGM薄板的热模态进行了分析。分析结果表明:无论FGM薄板四端固支还是四端简支,组分对其固有频率的影响都很大,而对其模态振型图的影响很小。并且随着组分的不断增大,薄板的固有频率在不断的增大,但其对应的模态振型图几乎没有变化。在薄板开孔情况下,组分对其固有频率的影响与薄板未开孔时一样:随着组分的不断增大,薄板的固有频率也在不断的增大,而其相应的模态振型图几乎没有变化。但随着孔径的不断增大,不仅薄板固有频率不断增大,而且其对应的模态振型图发生了显著的变化。
[Abstract]:Functionally graded material (FGM) is a new generation of advanced nonuniform composites. This material is made up of two or more materials with different properties. Since its material properties change continuously in one or more directions, FGM basically eliminates the macroscopic interface. Therefore, there is no abrupt change in the physical properties of the structure. In the study of structural dynamics, modal analysis is quite important. The emphasis of modal analysis is on thermal mode analysis. With the rapid development of modern high speed aircraft and spacecraft, the necessity of thermal mode analysis has been strengthened. It is of great theoretical and practical significance to study the thermal modes of structures. This paper is devoted to the study of nonlinear vibration of functionally graded thin plates under thermal loading, with emphasis on the effects of natural frequencies and components of functionally graded thin plates on them. Taking Al 110% ZrO 2FGM thin plate as the object of study, then defining its physical parameter model, and based on the classical thin plate theory, the basic dynamic equation of FGM thin plate is derived. Secondly, the basic finite element equation is derived from the basic dynamic equation. Then, by using the laminated plate finite element method and the python secondary development of ABAQUS software, the relevant finite element program is compiled, and then the FGM thin plate is programmed by ABAQUS. The numerical results are obtained by calculation, and then, Furthermore, the correctness of the calculation results is verified. Finally, according to the calculation results, it is obtained that the thin plate with or without holes is fixed in four sides and simply supported in four sides. The natural frequencies of different components and their corresponding modal shapes are analyzed. The thermal modes of FGM thin plates with different components are also analyzed. The results show that whether the FGM thin plates are fixed at four ends or simply supported at four ends, The component has a great influence on its natural frequency, but it has little effect on the modal mode pattern, and with the increasing of the component, the natural frequency of thin plate increases continuously. In the case of thin plate opening, the effect of component on its natural frequency is the same as when the plate is not perforated: with the increasing of component, the natural frequency of thin plate is also increasing. However, with the increase of the aperture, not only the natural frequency of the thin plate is increasing, but also the corresponding modal mode pattern has a significant change.
【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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