功能梯度材料板的厚度剪切振动
发布时间：2018-11-03 10:27
【摘要】：功能梯度材料(Functionally graded materials,FGMs)作为一种新型材料,广泛应用于众多的工程领域。其主要的原理是通过改变材料的组份,从而改变材料参数的变化规律,最终改变结构的某些特性如强度、耐热和振动特性等。基于这一原理,我们可以根据实际需要,通过基于分析和计算的设计,生产和制备出具有独特优点的材料。本文首先简单回顾了FGMs研究的历史,侧重于FGMs板的振动特性分析和板中波的传播问题。然后,结合典型应用简单地介绍了固体结构中的几种常见的弹性波。这些弹性波的特性分析一直是近些年来的热点问题,在工程领域也有着很多重要应用。我们以石英晶体谐振器在生产加工时或长期在恶劣环境中工作引起的表面分层或破坏为对象,将由此造成的材料性能演化等效为FGMs板,并假设梯度函数为材料参数沿板的厚度方向的任意连续函数变化。在分析和计算板的厚度剪切振动特性时,我们对偏微分方程的某些因子使用了Fourier变换,得到了板厚度剪切振动的频率方程。最后,我们给出了具体的数值算例来分析和说明FGMs板厚度剪切振动的频率特性。我们首先将功能梯度形式假设为厚度方向的对称形式,材料的属性可以表示为板的厚度方向余弦函数的形式,此时参数光滑且对称变化。然后,我们将功能梯度形式扩展到可包括沿厚度方向的对称和不对称函数的一般变化形式,材料的属性现在可以表示为厚度方向余弦和正弦函数组合的一般三角函数形式,解的过程仍是基于包含正弦和余弦函数的傅里叶展开。我们分析并计算了这两种情况下的FGMs板的厚度剪切振动,所得频率的解,或者频率相对于均匀板的基频和高阶泛音的偏差也可以用来估计板的材料性能变化模式。
[Abstract]:As a new material, functionally graded material (Functionally graded materials,FGMs) has been widely used in many engineering fields. The main principle is to change the changing rules of material parameters by changing the composition of materials, and finally to change some characteristics of structure such as strength, heat resistance and vibration. Based on this principle, we can produce and prepare materials with unique advantages through the design based on analysis and calculation according to the actual needs. In this paper, the history of FGMs research is briefly reviewed, focusing on the analysis of the vibration characteristics of FGMs plates and the propagation of waves in the plates. Then, some common elastic waves in solid structures are briefly introduced in combination with typical applications. The characteristic analysis of these elastic waves has been a hot issue in recent years and has many important applications in the engineering field. We take the surface delamination or damage caused by the quartz crystal resonator during production and processing or working in the bad environment for a long time. The resulting material properties are equivalent to that of the FGMs plate. The gradient function is assumed to be an arbitrary continuous function of the material parameter along the thickness direction of the plate. In the analysis and calculation of thickness shear vibration characteristics of plate, we use Fourier transform to some factors of partial differential equation, and obtain the frequency equation of plate thickness shear vibration. Finally, a numerical example is given to analyze and explain the frequency characteristics of thickness shear vibration of FGMs plate. The functional gradient form is assumed to be a symmetric form in the thickness direction and the properties of the material can be expressed as the cosine function of the thickness direction of the plate. The parameters are smooth and symmetric. Then, we extend the functional gradient form to include the general variation form of symmetric and asymmetric functions along the thickness direction, and the properties of the material can now be expressed as a general trigonometric function form of the combination of the thickness direction cosine and sinusoidal function. The process of solution is still based on Fourier expansion with sine and cosine functions. We analyze and calculate the thickness shear vibration of the FGMs plate under these two conditions, the solution of the obtained frequency, or the deviation of the frequency relative to the fundamental frequency and the higher order overtone of the uniform plate, can also be used to estimate the material performance variation mode of the plate.
【学位授予单位】：宁波大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB34
本文编号：2307518
[Abstract]:As a new material, functionally graded material (Functionally graded materials,FGMs) has been widely used in many engineering fields. The main principle is to change the changing rules of material parameters by changing the composition of materials, and finally to change some characteristics of structure such as strength, heat resistance and vibration. Based on this principle, we can produce and prepare materials with unique advantages through the design based on analysis and calculation according to the actual needs. In this paper, the history of FGMs research is briefly reviewed, focusing on the analysis of the vibration characteristics of FGMs plates and the propagation of waves in the plates. Then, some common elastic waves in solid structures are briefly introduced in combination with typical applications. The characteristic analysis of these elastic waves has been a hot issue in recent years and has many important applications in the engineering field. We take the surface delamination or damage caused by the quartz crystal resonator during production and processing or working in the bad environment for a long time. The resulting material properties are equivalent to that of the FGMs plate. The gradient function is assumed to be an arbitrary continuous function of the material parameter along the thickness direction of the plate. In the analysis and calculation of thickness shear vibration characteristics of plate, we use Fourier transform to some factors of partial differential equation, and obtain the frequency equation of plate thickness shear vibration. Finally, a numerical example is given to analyze and explain the frequency characteristics of thickness shear vibration of FGMs plate. The functional gradient form is assumed to be a symmetric form in the thickness direction and the properties of the material can be expressed as the cosine function of the thickness direction of the plate. The parameters are smooth and symmetric. Then, we extend the functional gradient form to include the general variation form of symmetric and asymmetric functions along the thickness direction, and the properties of the material can now be expressed as a general trigonometric function form of the combination of the thickness direction cosine and sinusoidal function. The process of solution is still based on Fourier expansion with sine and cosine functions. We analyze and calculate the thickness shear vibration of the FGMs plate under these two conditions, the solution of the obtained frequency, or the deviation of the frequency relative to the fundamental frequency and the higher order overtone of the uniform plate, can also be used to estimate the material performance variation mode of the plate.
【学位授予单位】：宁波大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB34
【参考文献】
相关期刊论文 前2条
1 宿星亮;高原文;;一维功能梯度材料声子晶体弹性波带隙研究[J];功能材料;2010年S2期
2 杨娟;李星;;功能梯度压电带拼接半无限大压电材料中裂纹对SH波的散射问题[J];力学季刊;2010年04期
，本文编号：2307518
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