本文選題：FGM梁 + 動(dòng)力縮聚法　； 參考：《河北工程大學(xué)》2017年碩士論文

【摘要】：在任何結(jié)構(gòu)體系中,大到幾百米甚至幾十千米不等的橋梁體系,小到只有幾毫米的車輛防撞梁,梁結(jié)構(gòu)都是結(jié)構(gòu)中不可或缺的重要構(gòu)件之一。目前,功能梯度材料(Functionally Graded Material,簡稱FGM)憑借其優(yōu)良的耐熱沖擊、耐腐蝕、抗氧化以及耐磨性能,備受研究者的青睞。為了滿足不同結(jié)構(gòu)對梁特殊性能的要求,FGM梁的研究探索儼然已成為當(dāng)今梁結(jié)構(gòu)的一個(gè)發(fā)展趨勢。本文基于小變形幾何非線性理論和動(dòng)力縮聚法對變物性Al 1100和ZrO_2兩種材料組成的FGM梁進(jìn)行熱模態(tài)分析。首先根據(jù)有限元法推導(dǎo)FEM梁的有限元方程,再通過動(dòng)力縮聚法減小計(jì)算量;然后將動(dòng)力縮聚得到的結(jié)果分別和有限元法結(jié)果以及解析法精確解進(jìn)行誤差分析,證明本文中采用的動(dòng)力縮聚法的正確性以及計(jì)算精度;最后,分析了不同組分分布系數(shù)、孔隙率控制參數(shù)對變物性FGM梁在不同溫度以及不同位移邊界條件下固有頻率的變化規(guī)律。本文中主要探究了組分、孔隙率、以及位移邊界條件和溫度對梁固有頻率的影響。溫度一定時(shí),隨著組分參數(shù)的增大,FGM梁的固有頻率也增大,這是由于隨著組分參數(shù)的增大,梁中ZrO_2的成分隨之增大,從而增大了梁的剛度;隨著孔隙率控制系數(shù)的增大,FGM梁的固有頻率隨之增大,說明孔隙率控制系數(shù)對密度的敏感程度比對剛度的敏感程度高。組分參數(shù)和孔隙率控制系數(shù)一定時(shí),梁固有頻率均隨溫度的升高呈下降趨勢,這是因?yàn)榱簝?nèi)熱應(yīng)力減小了梁的剛度,導(dǎo)致其固有頻率的下降。本文對FGM梁的熱模態(tài)分析為FGM梁的動(dòng)力學(xué)分析提供了理論基礎(chǔ),為FGM梁的工程應(yīng)用提供了參考價(jià)值。
[Abstract]:In any structural system, bridge systems ranging from hundreds of meters to tens of kilometers, small to only a few millimeters of anti-collision beam, beam structure is one of the indispensable important components in the structure. At present, functionally Graded material (FGM) is favored by researchers for its excellent heat shock, corrosion resistance, oxidation resistance and wear resistance. In order to meet the requirements of different structures for the special performance of beams, the research and exploration of FGM beams has become a developing trend of beam structures nowadays. Based on the geometric nonlinear theory of small deformation and the dynamic condensation method, the thermal modal analysis of FGM beams with variable physical properties of Al 1100 and ZrO_2 is carried out in this paper. Firstly, the finite element equation of FEM beam is derived according to the finite element method, and then the calculation amount is reduced by dynamic condensation method, and then the error analysis of the result obtained by dynamic condensation is carried out respectively with the result of finite element method and the exact solution of the analytical method. It is proved that the dynamic condensation method used in this paper is correct and accurate. Finally, the distribution coefficients of different components are analyzed. The variation of natural frequencies of FGM beams with variable physical properties under different temperature and displacement boundary conditions is affected by porosity control parameters. In this paper, the effects of components, porosity, displacement boundary conditions and temperature on the natural frequencies of beams are investigated. When the temperature is constant, the natural frequency of the beam increases with the increase of the component parameters, which is due to the increase of the component parameter and the increase of the ZrO_2 component in the beam, thus increasing the stiffness of the beam. With the increase of porosity control coefficient, the natural frequency of FGM beam increases, which indicates that porosity control coefficient is more sensitive to density than to stiffness. When the component parameters and porosity control coefficient are constant, the natural frequency of beam decreases with the increase of temperature, which is because the thermal stress decreases the stiffness of the beam, which leads to the decrease of the natural frequency. The thermal mode analysis of FGM beam provides a theoretical basis for the dynamic analysis of FGM beam and a reference value for the engineering application of FGM beam.
【學(xué)位授予單位】：河北工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TU323.3

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