【摘要】：功能梯度材料(Functionally graded materials,簡稱FGM)是一種新型的功能材料,兼顧了各組分材料自身的優(yōu)點,使得FGM在航空工業(yè)、電子、機(jī)械、核能等領(lǐng)域有十分廣闊應(yīng)用的前景。研究材料在不同環(huán)境中的固有頻率及頻率的變化趨勢是工程力學(xué)研究的重要內(nèi)容之一。本文針對中厚圓板模型,較為全面地研究,尤其是定量研究了FGM板在不同環(huán)境下的自由振動頻率以及頻率的變化趨勢,得到了一些有意義的結(jié)果,主要內(nèi)容包括以下幾個方面:1.功能梯度中厚圓板自由振動的控制方程的建立假設(shè)功能梯度材料的物性參數(shù)沿厚度按冪函數(shù)均勻變化,建立FGM板在熱環(huán)境下的物理模型�；谝浑A剪切板理論,給出在熱環(huán)境下中厚圓板自由振動的基本控制方程,由于不同于經(jīng)典板理論,分析中考慮了一階橫向剪切變形和材料的梯度性質(zhì)等因素對變形的影響。在小振幅和諧振動假設(shè)下,分別給出在常溫和熱環(huán)境下用振型函數(shù)表示的中厚圓板的控制方程,同時給出各種邊界下的邊界條件,并將控制方程和邊界條件無量綱化。2.功能梯度中厚板自由振動的數(shù)值分析重點研究了FGM中厚板在不同熱環(huán)境下自由振動響應(yīng),采用打靶法數(shù)值求解,獲得FGM中厚板前三階固有頻率與厚徑比之間的特征關(guān)系曲線,詳細(xì)分析和討論了功能梯度指數(shù)、溫度以及邊界條件對振動特性的影響。數(shù)值結(jié)果表明:在常溫狀態(tài)下不論是簡支板、固支板還是自由板,固有頻率都隨板的厚徑比、梯度指數(shù)的增加單調(diào)下降;在熱環(huán)境中,無論是均勻升溫還是非均勻升溫,三種邊界條件下各階頻率都會隨溫度的升高而下降,其中一階頻率具有明顯的非線性性;當(dāng)物性參數(shù)與溫度相關(guān)時,自由振動頻率的變化趨勢會因功能梯度指數(shù)的不同而發(fā)生復(fù)雜的變化。本文的成果將有助于人們進(jìn)一步認(rèn)識功能梯度材料結(jié)構(gòu)的振動特性,同時有助于進(jìn)一步完善基于Mindlin板理論的研究成果,為以后的研究者提供有效的數(shù)值參數(shù)和分析結(jié)果。
[Abstract]:Functionally graded material (Functionally graded materials,) is a new type of functional material, which takes into account the advantages of each component material itself, which makes FGM have a very broad application prospect in aviation industry, electronics, machinery, nuclear energy and other fields. It is one of the important contents of engineering mechanics to study the natural frequency and frequency change trend of materials in different environments. In this paper, the variation trend of free vibration frequency and frequency of FGM plate in different environments are studied comprehensively, especially in the model of medium thick circular plate, and some meaningful results are obtained. The main contents include the following aspects: 1. The establishment of governing equation for free vibration of thick circular plates with functional gradient; assuming that the physical parameters of functionally graded materials vary uniformly along the thickness of the power function, the physical model of FGM plates in thermal environment is established. Based on the first order shear plate theory, the basic governing equations of the free vibration of the thick circular plate in thermal environment are given. Different from the classical plate theory, the effects of the first order transverse shear deformation and the gradient properties of the material on the deformation are considered in the analysis. Under the assumption of small amplitude and harmonic vibration, the governing equations of medium thick circular plates represented by mode functions under normal temperature and thermal environment are given respectively. At the same time, the boundary conditions under various boundaries are given, and the governing equations and boundary conditions are dimensionless. 2. In this paper, the free vibration response of FGM plate under different thermal conditions is studied, and the characteristic curves between the first three natural frequencies and thickness to diameter ratio of FGM plate are obtained by means of shooting method. The effects of functional gradient index, temperature and boundary conditions on vibration characteristics are analyzed and discussed in detail. The numerical results show that the natural frequency decreases monotonously with the thickness to diameter ratio of the plate, whether it is a simply supported plate, a clamped plate or a free plate at room temperature. In the thermal environment, the frequency of each order will decrease with the increase of temperature under the three boundary conditions, no matter whether it is uniform or non-uniform, and the first order frequency has obvious nonlinearity. When the physical parameters are related to temperature, the variation trend of free vibration frequency will be complicated by the difference of functional gradient exponent. The results of this paper will help people to further understand the vibration characteristics of functionally graded material structures, and further improve the research results based on Mindlin plate theory, and provide effective numerical parameters and analysis results for future researchers.
【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

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