本文選題：修正偶應(yīng)力理論　切入點(diǎn)：功能梯度材料　出處：《沈陽航空航天大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：本文基于一種新的各向異性修正偶應(yīng)力理論建立了碳納米管增強(qiáng)復(fù)合材料功能梯度板的自由振動(dòng)以及靜力模型。模型能夠描述尺度效應(yīng),且僅包含一個(gè)尺度參數(shù),因而非常便于工程應(yīng)用。基于三階剪切變形理論和哈密頓原理推演了板的運(yùn)動(dòng)微分方程和相應(yīng)的邊界條件,并給出了板的平衡微分方程。以四邊簡支板為例給出了方板自振頻率和板中心撓度的解析解。討論了板的幾何尺寸、碳納米管體分比含量和分布方式等因素對板的自振頻率和板中心撓度的影響。分析結(jié)果表明本文模型所預(yù)測的板的自振基頻總是高于經(jīng)典模型預(yù)測的結(jié)果,二者間的差異在板的幾何尺寸接近于尺度參數(shù)的值時(shí)非常明顯,且會(huì)隨著板的幾何尺寸的增大而逐漸消失。進(jìn)一步研究發(fā)現(xiàn),隨著碳納米管體積分?jǐn)?shù)的增加,板中心撓度減小,振動(dòng)頻率增加。表明碳納米管能夠提高結(jié)構(gòu)的剛度。另外,碳納米管的分布形式對板撓度和基頻有顯著影響。
[Abstract]:Based on a new anisotropic modified couple stress theory, the free vibration and static models of functionally gradient plates of carbon nanotube reinforced composites are established in this paper. The model can describe the scale effect and contain only one scale parameter. Based on the third-order shear deformation theory and Hamiltonian principle, the differential equations of motion of plates and the corresponding boundary conditions are derived. The equilibrium differential equation of the plate is given. The analytical solutions of the natural vibration frequency and the central deflection of the square plate are given by taking the simply supported plate with four sides as an example. The geometric dimensions of the plate are discussed. The effect of the content and distribution of carbon nanotubes on the frequency of the plate and the deflection of the plate center is studied. The results show that the base frequency of the plate predicted by this model is always higher than that predicted by the classical model. The difference between the two is very obvious when the geometric dimension of the plate is close to the value of the scale parameter, and will gradually disappear with the increase of the geometric size of the plate. Further study shows that with the increase of the volume fraction of carbon nanotubes, the central deflection of the plate decreases. The increase of vibration frequency shows that carbon nanotubes can improve the stiffness of the structure. In addition, the distribution of carbon nanotubes has a significant effect on the deflection and fundamental frequency of the plate.
【學(xué)位授予單位】：沈陽航空航天大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TB33

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本文編號：1587037