【摘要】：功能梯度材料(Functionally graded material,FGM)是一種新型的非均質(zhì)復(fù)合材料,它是把兩種或者幾種不同的材料按照材料組份依據(jù)一定的規(guī)律組合而成,達到可以消除兩種材料之間產(chǎn)生的物理性能突變和應(yīng)力集中的目的,可以集兩種材料優(yōu)點于一身,進而被廣泛的應(yīng)用于航空航天、醫(yī)療、機械、電子工程等領(lǐng)域。梁是實際工程中最為常見的一種結(jié)構(gòu)構(gòu)件,研究其在溫度載荷、機械載荷以及其它環(huán)境下的靜、動力學(xué)行為一直都是力學(xué)工作者的研究內(nèi)容之一。目前,對于功能梯度材料梁動態(tài)振動問題的研究大部分是在忽略縱向振動的情況下進行的。本文則在考慮縱向振動影響的情況下研究了功能梯度材料梁在機械載荷作用下的非線性動態(tài)力學(xué)行為,主要的工作內(nèi)容可以簡要的概括為以下兩個方面:1.功能梯度材料Euler梁在考慮縱向振動時的動力學(xué)行為分析�；诮�(jīng)典Euler梁理論,建立了功能梯度材料梁在橫向均布載荷作用下非線性振動的問題模型。利用變分原理推導(dǎo)出其在機械載荷作用下,考慮縱向振動時的幾何非線性動力學(xué)微分方程。運用打靶法對該方程和邊界條件構(gòu)成的邊值問題進行數(shù)值求解。首先研究了功能梯度材料Euler梁的非線性橫向振動問題,得到其橫向振動的固有頻率;接著在此基礎(chǔ)上研究了當考慮縱向振動的影響時功能梯度材料Euler梁的振動問題,并根據(jù)具體的材料參數(shù)討論了考慮縱向振動影響時梯度參數(shù)、長高比以及邊界條件等對FGM梁動力學(xué)特性的影響規(guī)律。結(jié)果表明,在考慮了縱向振動影響時,功能梯度材料Euler梁的頻率將有所降低,但是降低程度在可以接受的范圍之內(nèi)。2.功能梯度材料正弦剪切變形梁在考慮縱向振動時的動力學(xué)行為分析�；谡壹羟凶冃瘟豪碚�,建立了功能梯度材料正弦剪切梁振動的數(shù)學(xué)模型,利用變分原理推導(dǎo)出了其考慮縱向振動時的動力學(xué)微分方程。仍然采用打靶法對該微分方程和相應(yīng)的邊界條件組成的邊值問題進行數(shù)值求解,得到了功能梯度正弦剪切變形梁在考慮了縱向振動時的頻率。將計算結(jié)果與已有的文獻作對比,得到很好的吻合。接著對比了相同條件下第二章中Euler梁與本章正弦剪切的結(jié)果,表明在正弦剪切理論下,FGM梁的頻率偏低,這種梁模型較經(jīng)典梁模型更貼近實際。最后分析了不同長高比、邊界條件下FGM正弦剪切變形梁的動力學(xué)特性。
[Abstract]:Functionally graded material (Functionally graded material,FGM) is a new type of heterogeneous composite material, which combines two or more different materials according to a certain law of material composition. It can eliminate the sudden change of physical properties and stress concentration between two kinds of materials, and can combine the advantages of two kinds of materials, and then be widely used in aerospace, medical, mechanical, electronic engineering and other fields. Beam is one of the most common structural components in practical engineering. It is always one of the research contents of mechanics workers to study the static and dynamic behavior of beam under temperature load, mechanical load and other environments. At present, most of the researches on the dynamic vibration of functionally graded material beams are carried out under the condition of ignoring the longitudinal vibration. In this paper, the nonlinear dynamic mechanical behavior of functionally graded material beams under mechanical load is studied under the consideration of longitudinal vibration. The main work contents can be summarized as follows: 1. The dynamic behavior of Euler beams with functionally graded materials considering longitudinal vibration is analyzed. Based on the classical Euler beam theory, the nonlinear vibration model of functionally graded material beams under transverse uniform load is established. By using the variational principle, a geometric nonlinear dynamic differential equation considering longitudinal vibration is derived. The boundary value problem of the equation and boundary condition is solved numerically by shooting method. In this paper, the nonlinear transverse vibration of functionally graded material (Euler) beams is studied, and the natural frequencies of the transverse vibration are obtained, and then the vibration of Euler beams with functionally graded materials is studied when the effect of longitudinal vibration is considered. According to the material parameters, the effects of gradient parameters, ratio of length to height and boundary conditions on the dynamic characteristics of FGM beams are discussed. The results show that the frequency of functionally graded material Euler beams will be decreased when longitudinal vibration is taken into account, but the degree of reduction is within the acceptable range. The dynamic behavior of sinusoidal shear deformed beams with functionally graded materials considering longitudinal vibration is analyzed. Based on the theory of sinusoidal shear deformation beam, the mathematical model of sinusoidal shear beam vibration with functionally graded materials is established, and the dynamic differential equation considering longitudinal vibration is derived by using the variational principle. The boundary value problem composed of the differential equation and the corresponding boundary conditions is still numerically solved by the shooting method, and the frequency of the functionally gradient sinusoidal shear deformation beam is obtained when the longitudinal vibration is considered. The calculated results are in good agreement with the existing literatures. Then, the results of Euler beam and sinusoidal shear in chapter 2 under the same conditions are compared. The results show that the frequency of FGM beam is lower than that of classical beam model under sinusoidal shear theory, and this model is closer to practice than that of classical beam model. Finally, the dynamic characteristics of FGM sinusoidal shear deformation beam with different ratio of length to height and boundary condition are analyzed.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TB34

【參考文獻】

相關(guān)期刊論文 前10條

1 常學(xué)平;成志強;柳葆生;;高階剪切理論下梯度直梁在熱環(huán)境中的靜動態(tài)響應(yīng)分析[J];四川理工學(xué)院學(xué)報(自然科學(xué)版);2016年03期

2 王捷;;功能梯度材料梁結(jié)構(gòu)的穩(wěn)定性分析[J];甘肅科學(xué)學(xué)報;2016年01期

3 鄒冬林;劉翎;饒柱石;塔娜;;利用有限元法與打靶法的縱橫耦合軸系主共振分析[J];振動工程學(xué)報;2016年01期

4 趙亮;胡振東;;軸向運動功能梯度懸臂梁動力學(xué)分析[J];振動與沖擊;2016年02期

5 汪亞運;彭旭龍;陳得良;;軸向功能梯度變截面梁的自由振動研究[J];固體力學(xué)學(xué)報;2015年05期

6 李成;隨歲寒;楊昌錦;;受初應(yīng)力作用的軸向運動功能梯度梁的動力學(xué)分析[J];工程力學(xué);2015年10期

7 邢譽峰;梁昆;;梁縱向與橫向耦合非線性振動分析[J];北京航空航天大學(xué)學(xué)報;2015年08期

8 張馳;于耕;張碩;;功能梯度材料梁的非線性研究[J];科學(xué)技術(shù)與工程;2014年20期

9 張靜華;魏軍揚;;DQ法求解FGM Levinson梁的靜態(tài)彎曲問題[J];華東交通大學(xué)學(xué)報;2014年03期

10 趙鳳群;王忠民;路小平;;軸向運動功能梯度Timoshenko梁穩(wěn)定性分析[J];振動與沖擊;2014年02期

相關(guān)會議論文 前1條

1 高陽;王敏中;;梁理論的發(fā)展歷史及其方法論[A];第三屆全國力學(xué)史與方法論學(xué)術(shù)研討會論文集[C];2007年

相關(guān)碩士學(xué)位論文 前4條

1 李秋全;功能梯度板彎曲有限元分析[D];揚州大學(xué);2013年

2 劉麗威;彈性地基上功能梯度梁、板的動力學(xué)特性分析[D];南京航空航天大學(xué);2012年

3 黃永玉;橫向荷載下梁的靜、動力學(xué)特性研究[D];蘭州理工大學(xué);2011年

4 龔云;功能梯度材料梁彎曲、屈曲和自由振動分析[D];蘭州理工大學(xué);2009年

，

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