热环境中功能梯度中厚圆板的自由振动
发布时间：2018-12-09 20:24
【摘要】：功能梯度材料(Functionally graded materials,简称FGM)是一种新型的功能材料,兼顾了各组分材料自身的优点,使得FGM在航空工业、电子、机械、核能等领域有十分广阔应用的前景。研究材料在不同环境中的固有频率及频率的变化趋势是工程力学研究的重要内容之一。本文针对中厚圆板模型,较为全面地研究,尤其是定量研究了FGM板在不同环境下的自由振动频率以及频率的变化趋势,得到了一些有意义的结果,主要内容包括以下几个方面:1.功能梯度中厚圆板自由振动的控制方程的建立假设功能梯度材料的物性参数沿厚度按幂函数均匀变化,建立FGM板在热环境下的物理模型。基于一阶剪切板理论,给出在热环境下中厚圆板自由振动的基本控制方程,由于不同于经典板理论,分析中考虑了一阶横向剪切变形和材料的梯度性质等因素对变形的影响。在小振幅和谐振动假设下,分别给出在常温和热环境下用振型函数表示的中厚圆板的控制方程,同时给出各种边界下的边界条件,并将控制方程和边界条件无量纲化。2.功能梯度中厚板自由振动的数值分析重点研究了FGM中厚板在不同热环境下自由振动响应,采用打靶法数值求解,获得FGM中厚板前三阶固有频率与厚径比之间的特征关系曲线,详细分析和讨论了功能梯度指数、温度以及边界条件对振动特性的影响。数值结果表明:在常温状态下不论是简支板、固支板还是自由板,固有频率都随板的厚径比、梯度指数的增加单调下降;在热环境中,无论是均匀升温还是非均匀升温,三种边界条件下各阶频率都会随温度的升高而下降,其中一阶频率具有明显的非线性性;当物性参数与温度相关时,自由振动频率的变化趋势会因功能梯度指数的不同而发生复杂的变化。本文的成果将有助于人们进一步认识功能梯度材料结构的振动特性,同时有助于进一步完善基于Mindlin板理论的研究成果,为以后的研究者提供有效的数值参数和分析结果。
[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.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34
本文编号：2369978
[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.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34
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