基于动力缩聚法的变物性功能梯度梁热模态分析

发布时间：2018-06-03 06:49

本文选题：FGM梁 + 动力缩聚法　；参考：《河北工程大学》2017年硕士论文

【摘要】：在任何结构体系中,大到几百米甚至几十千米不等的桥梁体系,小到只有几毫米的车辆防撞梁,梁结构都是结构中不可或缺的重要构件之一。目前,功能梯度材料(Functionally Graded Material,简称FGM)凭借其优良的耐热冲击、耐腐蚀、抗氧化以及耐磨性能,备受研究者的青睐。为了满足不同结构对梁特殊性能的要求,FGM梁的研究探索俨然已成为当今梁结构的一个发展趋势。本文基于小变形几何非线性理论和动力缩聚法对变物性Al 1100和ZrO_2两种材料组成的FGM梁进行热模态分析。首先根据有限元法推导FEM梁的有限元方程,再通过动力缩聚法减小计算量;然后将动力缩聚得到的结果分别和有限元法结果以及解析法精确解进行误差分析,证明本文中采用的动力缩聚法的正确性以及计算精度;最后,分析了不同组分分布系数、孔隙率控制参数对变物性FGM梁在不同温度以及不同位移边界条件下固有频率的变化规律。本文中主要探究了组分、孔隙率、以及位移边界条件和温度对梁固有频率的影响。温度一定时,随着组分参数的增大,FGM梁的固有频率也增大,这是由于随着组分参数的增大,梁中ZrO_2的成分随之增大,从而增大了梁的刚度;随着孔隙率控制系数的增大,FGM梁的固有频率随之增大,说明孔隙率控制系数对密度的敏感程度比对刚度的敏感程度高。组分参数和孔隙率控制系数一定时,梁固有频率均随温度的升高呈下降趋势,这是因为梁内热应力减小了梁的刚度,导致其固有频率的下降。本文对FGM梁的热模态分析为FGM梁的动力学分析提供了理论基础,为FGM梁的工程应用提供了参考价值。
[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.
【学位授予单位】：河北工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU323.3

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