本文選題：功能梯度材料 + 圓板�。� 參考：《蘭州理工大學(xué)》2017年碩士論文

【摘要】：功能梯度材料是近年來新發(fā)明的一種新型復(fù)合材料,由其制成的構(gòu)件在高溫環(huán)境中具有區(qū)別于一般材料的優(yōu)越力學(xué)性能,它是通過對(duì)兩種及以上金屬或陶瓷材料的合理搭配而成。由于其物理性能的優(yōu)越性,常被用在需承受高溫環(huán)境的航空航天、核工業(yè)和化工領(lǐng)域等。因此功能梯度材料板的力學(xué)特性已成為工程應(yīng)用領(lǐng)域中重點(diǎn)研究的活躍課題。本論文分別研究普通功能梯度材料板和Winkler彈性地基上功能梯度材料板在考慮面內(nèi)振動(dòng)時(shí)的動(dòng)態(tài)力學(xué)行為特性。包括以下幾方面:1.FGM圓板考慮面內(nèi)振動(dòng)的動(dòng)態(tài)響應(yīng)首先采用Voigt等模型來模擬功能梯度材料圓板沿板的厚度方向變化的材料梯度,并假設(shè)其變化形式為冪函數(shù)的形式。基于經(jīng)典板理論,同時(shí)考慮橫向振動(dòng)和面內(nèi)振動(dòng),并使用Hamilton原理及變分法推導(dǎo)出軸對(duì)稱情況下功能梯度材料圓薄板動(dòng)態(tài)響應(yīng)的運(yùn)動(dòng)微分方程。并將控制方程無量綱化以方便求解,用打靶法對(duì)其進(jìn)行數(shù)值求解。將方程退化為一般均質(zhì)板,求解其固有頻率,得到了與相關(guān)文獻(xiàn)非常接近的結(jié)果。求解某兩種材料構(gòu)成的功能梯度材料作為算例,對(duì)其得到的數(shù)值結(jié)果進(jìn)行圖像化后直觀的分析討論,研究考慮面內(nèi)振動(dòng)會(huì)對(duì)FGM圓板的振動(dòng)產(chǎn)生的影響。2.Winkler彈性地基上FGM圓板考慮面內(nèi)振動(dòng)的動(dòng)態(tài)響應(yīng)從Winkler彈性地基上FGM板的振動(dòng)入手,考慮面內(nèi)振動(dòng),研究周邊固定和周邊不可移簡(jiǎn)支兩種邊界條件下功能梯度圓板的動(dòng)態(tài)響應(yīng)問題。應(yīng)用經(jīng)典板理論,并考慮小撓度問題,忽略轉(zhuǎn)動(dòng)慣性力矩,導(dǎo)出Winkler地基上FGM圓板在軸對(duì)稱情況下振動(dòng)的控制方程,假設(shè)FGM圓板的振動(dòng)形式為諧響應(yīng)形式,將比較難求解的偏微分控制方程變成常微分方程。本文僅研究周邊固定和周邊不可移簡(jiǎn)支的情形,應(yīng)用打靶法求解FGM圓薄板振動(dòng)問題的解。通過數(shù)值結(jié)果分析彈性地基參數(shù)及面內(nèi)振動(dòng)對(duì)FGM圓板振動(dòng)的影響。本文得到的結(jié)論對(duì)FGM圓板振動(dòng)特性的研究有積極的推進(jìn)作用,對(duì)于FGM板今后在工程實(shí)際應(yīng)用中更為精確的估計(jì)誤差也具有指導(dǎo)意義。
[Abstract]:Functionally graded material (FGM) is a new type of composite material newly invented in recent years. The components made of FGM have superior mechanical properties different from those of general materials in high temperature environment. It is made by matching two or more metal or ceramic materials. Because of its superiority in physical properties, it is often used in aerospace, nuclear industry and chemical industry which need to withstand high temperature environment. Therefore, the mechanical properties of functionally graded material plates (FGM) have become an active subject in the field of engineering application. In this paper, the dynamic mechanical behavior of FGM plates on Winkler elastic foundation and FGM plates on Winkler elastic foundation considering in-plane vibration are studied respectively. The dynamic response of FGM circular plates considering in-plane vibration is described as follows. Firstly, Voigt model is used to simulate the material gradient of FGM circular plates along the thickness of the plate, and the change form is assumed to be a power function. Based on the classical plate theory and considering both transverse and in-plane vibrations, the differential equations of motion of circular thin plates with functionally graded materials under axisymmetric conditions are derived by using Hamilton principle and variational method. The control equation is dimensionless to be solved conveniently, and the numerical method is used to solve the problem. The equation is degenerated into a general homogeneous plate and its natural frequency is solved. The results are very close to those of the related literatures. The functionally graded material composed of two kinds of materials is solved as an example, and the numerical results obtained are analyzed and discussed intuitively after image. The effect of in-plane vibration on the vibration of FGM circular plate is studied. 2. The dynamic response of FGM circular plate considering in-plane vibration on Winkler elastic foundation is studied starting with the vibration of FGM plate on Winkler elastic foundation, and the in-plane vibration is considered. The dynamic response of functionally graded circular plates under two boundary conditions, namely peripheral fixed and immovable simply supported, is studied. By applying classical plate theory and considering the problem of small deflection and ignoring the moment of inertia of rotation, the governing equation of vibration of FGM circular plate on Winkler foundation under axisymmetric condition is derived. The vibration form of FGM circular plate is assumed to be a harmonic response form. The more difficult partial differential governing equations are transformed into ordinary differential equations. In this paper, the problem of FGM circular thin plate vibration is solved by means of shooting method. The effects of elastic foundation parameters and in-plane vibration on the vibration of FGM circular plate are analyzed by numerical results. The conclusions obtained in this paper have a positive effect on the study of the vibration characteristics of FGM circular plates, and also have a guiding significance for the more accurate estimation errors of FGM plates in practical engineering applications in the future.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TB33

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 張靖華;潘雙超;李世榮;;熱沖擊下功能梯度圓板的動(dòng)力屈曲[J];應(yīng)用力學(xué)學(xué)報(bào);2015年06期

2 滕兆春;蒲育;;溫度影響下FGM圓環(huán)板的面內(nèi)自由振動(dòng)分析[J];振動(dòng)與沖擊;2015年09期

3 曹蕾蕾;裴建中;陳疆;張濤;;功能梯度材料熱應(yīng)力研究進(jìn)展[J];材料導(dǎo)報(bào);2014年23期

4 蒲育;滕兆春;房曉林;;圓環(huán)板面內(nèi)自由振動(dòng)的DQM求解[J];振動(dòng)與沖擊;2013年24期

5 吳曉;黃，

本文編號(hào)：2035928