本文選題：FGM薄板　切入點(diǎn)：有限元法　出處：《河北工程大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：功能梯度材料(FGM)是一種新一代先進(jìn)的非均勻復(fù)合材料,這種材料是由兩種或者兩種以上性質(zhì)不同的材料構(gòu)成的。由于它的材料屬性沿一個或多個方向呈連續(xù)梯度變化,FGM基本上消除了宏觀界面,因而其物理特性在結(jié)構(gòu)內(nèi)沒有突變。在結(jié)構(gòu)動力學(xué)的研究方面上,模態(tài)分析相當(dāng)?shù)闹匾?而模態(tài)分析的重點(diǎn)又在于熱模態(tài)的分析。隨著當(dāng)代高速度航空器以及航天器的迅猛發(fā)展,熱模態(tài)分析的必要性更是得到了加強(qiáng)。因此,研究結(jié)構(gòu)的熱模態(tài)具有重要的理論和實(shí)際意義。本文致力于研究功能梯度薄板在熱荷載作用下的非線性振動問題。重點(diǎn)研究功能梯度薄板的固有頻率和組分對其影響。首先,取Al 1100/ZrO2FGM薄板作為研究對象,然后進(jìn)一步定義其物參模型,并基于經(jīng)典薄板理論,導(dǎo)出了FGM薄板的基本動力方程。其次,由基本動力方程推導(dǎo)出其有限元基本方程,進(jìn)而利用層合板有限單元法并對ABAQUS軟件進(jìn)行了python二次開發(fā),編寫相關(guān)的有限元程序,從而利用ABAQUS對FGM薄板進(jìn)行程序化計算,通過計算獲得其數(shù)值計算結(jié)果,然后,進(jìn)一步對其計算結(jié)果進(jìn)行了正確性檢驗(yàn)。最后,根據(jù)計算結(jié)果獲得了FGM薄板在四邊固支和四邊簡支兩種邊界條件下,薄板開孔和未開孔時,不同組分下的固有頻率和其對應(yīng)的模態(tài)振型圖,同時對不同組分下FGM薄板的熱模態(tài)進(jìn)行了分析。分析結(jié)果表明:無論FGM薄板四端固支還是四端簡支,組分對其固有頻率的影響都很大,而對其模態(tài)振型圖的影響很小。并且隨著組分的不斷增大,薄板的固有頻率在不斷的增大,但其對應(yīng)的模態(tài)振型圖幾乎沒有變化。在薄板開孔情況下,組分對其固有頻率的影響與薄板未開孔時一樣:隨著組分的不斷增大,薄板的固有頻率也在不斷的增大,而其相應(yīng)的模態(tài)振型圖幾乎沒有變化。但隨著孔徑的不斷增大,不僅薄板固有頻率不斷增大,而且其對應(yīng)的模態(tài)振型圖發(fā)生了顯著的變化。
[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.
【學(xué)位授予單位】：河北工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TB34

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