本文選題：一維FGM薄板 + 熱模態(tài)　； 參考：《河北工程大學(xué)》2017年碩士論文

【摘要】：功能梯度材料(簡稱FGM)是指材料的組分、結(jié)構(gòu)以及物性參數(shù)等某一項(xiàng)性能或者綜合性能呈連續(xù)變化,并以此來適應(yīng)不同的環(huán)境,從而實(shí)現(xiàn)某一特定功能的新型復(fù)合材料。氣動(dòng)熱彈性的研究重點(diǎn)是熱振動(dòng)及熱顫振問題,而熱振動(dòng)及熱顫振問題的研究基礎(chǔ)就是熱模態(tài)分析。因此,對(duì)功能梯度材料的有關(guān)熱模態(tài)問題的分析研究非常重要。本文利用層合板有限單元法,對(duì)由ZrO2和Al 1100組成的新型FGM薄板的熱模態(tài)問題進(jìn)行了分析,并對(duì)本方法的正確性進(jìn)行了檢驗(yàn)。討論了孔隙率、位移邊界條件及中心開孔對(duì)FGM薄板熱模態(tài)的影響。本文以有限單元法為基礎(chǔ),對(duì)熱荷載作用下的FGM薄板的熱應(yīng)力計(jì)算公式進(jìn)行了推導(dǎo),并利用最小勢(shì)能原理,推導(dǎo)出結(jié)構(gòu)在受熱情況下的等效熱載荷。然后對(duì)熱振動(dòng)的有關(guān)理論進(jìn)行了闡述,并詳細(xì)地推導(dǎo)了初位移剛度矩陣及初應(yīng)力剛度矩陣的表達(dá)式。接著在不考慮初始位移的影響的基礎(chǔ)上,從變分原理出發(fā),較為詳細(xì)地推導(dǎo)了傳統(tǒng)的非線性板單元的初始位移剛度矩陣和初始應(yīng)力剛度矩陣。最后基于經(jīng)典薄板理論,通過Python的ABAQUS二次開發(fā),分別對(duì)位移邊界條件為四邊固定和簡支的一維功能梯度材料薄板的熱模態(tài)問題進(jìn)行了分析。數(shù)值算例的分析結(jié)果表明:在FGM薄板孔隙率控制參數(shù)Az一定的情況下,隨著薄板溫度的升高,FGM薄板的固有頻率會(huì)不斷減小。在FGM薄板溫度一定的情況下,隨著薄板孔隙率控制參數(shù)Az的增大,FGM薄板的固有頻率會(huì)不斷增大。在FGM薄板溫度和孔隙率控制參數(shù)Az一定的情況下,開孔會(huì)對(duì)FGM薄板的固有頻率產(chǎn)生很大的影響,并且隨著薄板開孔半徑r的增大,FGM薄板的固有頻率會(huì)不斷增大;在FGM薄板溫度和開孔半徑r一定的情況下,FGM開孔薄板的固有頻率會(huì)隨著孔隙率控制參數(shù)Az的增大而不斷增大;在FGM薄板孔隙率控制參數(shù)Az和開孔半徑r一定的情況下,隨著薄板溫度的增加,FGM開孔薄板的固有頻率會(huì)不斷減小。當(dāng)FGM薄板的溫度、孔隙率控制參數(shù)以及中心開孔半徑均相同時(shí),位移邊界條件為四邊固支的FGM薄板的固有頻率比簡支的FGM薄板的固有頻率要高。本文的研究為功能梯度材料在高溫下的動(dòng)力學(xué)分析提供了一定的基礎(chǔ)。
[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.
【學(xué)位授予單位】：河北工程大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TB34

【相似文獻(xiàn)】

相關(guān)期刊論文 前10條

1 高彥峰,王秀峰,羅宏杰;功能梯度材料中的滲流現(xiàn)象及其模型研究[J];陶瓷工程;2000年06期

2 徐智謀,鄭家q，

本文編號(hào)：1960573