【摘要】：功能梯度材料(Functionally graded materials,FGMs)作為一種新型材料,廣泛應(yīng)用于眾多的工程領(lǐng)域。其主要的原理是通過改變材料的組份,從而改變材料參數(shù)的變化規(guī)律,最終改變結(jié)構(gòu)的某些特性如強(qiáng)度、耐熱和振動特性等�；谶@一原理,我們可以根據(jù)實際需要,通過基于分析和計算的設(shè)計,生產(chǎn)和制備出具有獨(dú)特優(yōu)點的材料。本文首先簡單回顧了FGMs研究的歷史,側(cè)重于FGMs板的振動特性分析和板中波的傳播問題。然后,結(jié)合典型應(yīng)用簡單地介紹了固體結(jié)構(gòu)中的幾種常見的彈性波。這些彈性波的特性分析一直是近些年來的熱點問題,在工程領(lǐng)域也有著很多重要應(yīng)用。我們以石英晶體諧振器在生產(chǎn)加工時或長期在惡劣環(huán)境中工作引起的表面分層或破壞為對象,將由此造成的材料性能演化等效為FGMs板,并假設(shè)梯度函數(shù)為材料參數(shù)沿板的厚度方向的任意連續(xù)函數(shù)變化。在分析和計算板的厚度剪切振動特性時,我們對偏微分方程的某些因子使用了Fourier變換,得到了板厚度剪切振動的頻率方程。最后,我們給出了具體的數(shù)值算例來分析和說明FGMs板厚度剪切振動的頻率特性。我們首先將功能梯度形式假設(shè)為厚度方向的對稱形式,材料的屬性可以表示為板的厚度方向余弦函數(shù)的形式,此時參數(shù)光滑且對稱變化。然后,我們將功能梯度形式擴(kuò)展到可包括沿厚度方向的對稱和不對稱函數(shù)的一般變化形式,材料的屬性現(xiàn)在可以表示為厚度方向余弦和正弦函數(shù)組合的一般三角函數(shù)形式,解的過程仍是基于包含正弦和余弦函數(shù)的傅里葉展開。我們分析并計算了這兩種情況下的FGMs板的厚度剪切振動,所得頻率的解,或者頻率相對于均勻板的基頻和高階泛音的偏差也可以用來估計板的材料性能變化模式。
[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.
【學(xué)位授予單位】：寧波大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TB34

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本文編號：2307518