考虑纵向振动的功能梯度材料梁的非线性动力学行为分析
发布时间：2018-10-10 16:45
【摘要】：功能梯度材料(Functionally graded material,FGM)是一种新型的非均质复合材料,它是把两种或者几种不同的材料按照材料组份依据一定的规律组合而成,达到可以消除两种材料之间产生的物理性能突变和应力集中的目的,可以集两种材料优点于一身,进而被广泛的应用于航空航天、医疗、机械、电子工程等领域。梁是实际工程中最为常见的一种结构构件,研究其在温度载荷、机械载荷以及其它环境下的静、动力学行为一直都是力学工作者的研究内容之一。目前,对于功能梯度材料梁动态振动问题的研究大部分是在忽略纵向振动的情况下进行的。本文则在考虑纵向振动影响的情况下研究了功能梯度材料梁在机械载荷作用下的非线性动态力学行为,主要的工作内容可以简要的概括为以下两个方面:1.功能梯度材料Euler梁在考虑纵向振动时的动力学行为分析。基于经典Euler梁理论,建立了功能梯度材料梁在横向均布载荷作用下非线性振动的问题模型。利用变分原理推导出其在机械载荷作用下,考虑纵向振动时的几何非线性动力学微分方程。运用打靶法对该方程和边界条件构成的边值问题进行数值求解。首先研究了功能梯度材料Euler梁的非线性横向振动问题,得到其横向振动的固有频率;接着在此基础上研究了当考虑纵向振动的影响时功能梯度材料Euler梁的振动问题,并根据具体的材料参数讨论了考虑纵向振动影响时梯度参数、长高比以及边界条件等对FGM梁动力学特性的影响规律。结果表明,在考虑了纵向振动影响时,功能梯度材料Euler梁的频率将有所降低,但是降低程度在可以接受的范围之内。2.功能梯度材料正弦剪切变形梁在考虑纵向振动时的动力学行为分析。基于正弦剪切变形梁理论,建立了功能梯度材料正弦剪切梁振动的数学模型,利用变分原理推导出了其考虑纵向振动时的动力学微分方程。仍然采用打靶法对该微分方程和相应的边界条件组成的边值问题进行数值求解,得到了功能梯度正弦剪切变形梁在考虑了纵向振动时的频率。将计算结果与已有的文献作对比,得到很好的吻合。接着对比了相同条件下第二章中Euler梁与本章正弦剪切的结果,表明在正弦剪切理论下,FGM梁的频率偏低,这种梁模型较经典梁模型更贴近实际。最后分析了不同长高比、边界条件下FGM正弦剪切变形梁的动力学特性。
[Abstract]:Functionally graded material (Functionally graded material,FGM) is a new type of heterogeneous composite material, which combines two or more different materials according to a certain law of material composition. It can eliminate the sudden change of physical properties and stress concentration between two kinds of materials, and can combine the advantages of two kinds of materials, and then be widely used in aerospace, medical, mechanical, electronic engineering and other fields. Beam is one of the most common structural components in practical engineering. It is always one of the research contents of mechanics workers to study the static and dynamic behavior of beam under temperature load, mechanical load and other environments. At present, most of the researches on the dynamic vibration of functionally graded material beams are carried out under the condition of ignoring the longitudinal vibration. In this paper, the nonlinear dynamic mechanical behavior of functionally graded material beams under mechanical load is studied under the consideration of longitudinal vibration. The main work contents can be summarized as follows: 1. The dynamic behavior of Euler beams with functionally graded materials considering longitudinal vibration is analyzed. Based on the classical Euler beam theory, the nonlinear vibration model of functionally graded material beams under transverse uniform load is established. By using the variational principle, a geometric nonlinear dynamic differential equation considering longitudinal vibration is derived. The boundary value problem of the equation and boundary condition is solved numerically by shooting method. In this paper, the nonlinear transverse vibration of functionally graded material (Euler) beams is studied, and the natural frequencies of the transverse vibration are obtained, and then the vibration of Euler beams with functionally graded materials is studied when the effect of longitudinal vibration is considered. According to the material parameters, the effects of gradient parameters, ratio of length to height and boundary conditions on the dynamic characteristics of FGM beams are discussed. The results show that the frequency of functionally graded material Euler beams will be decreased when longitudinal vibration is taken into account, but the degree of reduction is within the acceptable range. The dynamic behavior of sinusoidal shear deformed beams with functionally graded materials considering longitudinal vibration is analyzed. Based on the theory of sinusoidal shear deformation beam, the mathematical model of sinusoidal shear beam vibration with functionally graded materials is established, and the dynamic differential equation considering longitudinal vibration is derived by using the variational principle. The boundary value problem composed of the differential equation and the corresponding boundary conditions is still numerically solved by the shooting method, and the frequency of the functionally gradient sinusoidal shear deformation beam is obtained when the longitudinal vibration is considered. The calculated results are in good agreement with the existing literatures. Then, the results of Euler beam and sinusoidal shear in chapter 2 under the same conditions are compared. The results show that the frequency of FGM beam is lower than that of classical beam model under sinusoidal shear theory, and this model is closer to practice than that of classical beam model. Finally, the dynamic characteristics of FGM sinusoidal shear deformation beam with different ratio of length to height and boundary condition are analyzed.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34
本文编号：2262523
[Abstract]:Functionally graded material (Functionally graded material,FGM) is a new type of heterogeneous composite material, which combines two or more different materials according to a certain law of material composition. It can eliminate the sudden change of physical properties and stress concentration between two kinds of materials, and can combine the advantages of two kinds of materials, and then be widely used in aerospace, medical, mechanical, electronic engineering and other fields. Beam is one of the most common structural components in practical engineering. It is always one of the research contents of mechanics workers to study the static and dynamic behavior of beam under temperature load, mechanical load and other environments. At present, most of the researches on the dynamic vibration of functionally graded material beams are carried out under the condition of ignoring the longitudinal vibration. In this paper, the nonlinear dynamic mechanical behavior of functionally graded material beams under mechanical load is studied under the consideration of longitudinal vibration. The main work contents can be summarized as follows: 1. The dynamic behavior of Euler beams with functionally graded materials considering longitudinal vibration is analyzed. Based on the classical Euler beam theory, the nonlinear vibration model of functionally graded material beams under transverse uniform load is established. By using the variational principle, a geometric nonlinear dynamic differential equation considering longitudinal vibration is derived. The boundary value problem of the equation and boundary condition is solved numerically by shooting method. In this paper, the nonlinear transverse vibration of functionally graded material (Euler) beams is studied, and the natural frequencies of the transverse vibration are obtained, and then the vibration of Euler beams with functionally graded materials is studied when the effect of longitudinal vibration is considered. According to the material parameters, the effects of gradient parameters, ratio of length to height and boundary conditions on the dynamic characteristics of FGM beams are discussed. The results show that the frequency of functionally graded material Euler beams will be decreased when longitudinal vibration is taken into account, but the degree of reduction is within the acceptable range. The dynamic behavior of sinusoidal shear deformed beams with functionally graded materials considering longitudinal vibration is analyzed. Based on the theory of sinusoidal shear deformation beam, the mathematical model of sinusoidal shear beam vibration with functionally graded materials is established, and the dynamic differential equation considering longitudinal vibration is derived by using the variational principle. The boundary value problem composed of the differential equation and the corresponding boundary conditions is still numerically solved by the shooting method, and the frequency of the functionally gradient sinusoidal shear deformation beam is obtained when the longitudinal vibration is considered. The calculated results are in good agreement with the existing literatures. Then, the results of Euler beam and sinusoidal shear in chapter 2 under the same conditions are compared. The results show that the frequency of FGM beam is lower than that of classical beam model under sinusoidal shear theory, and this model is closer to practice than that of classical beam model. Finally, the dynamic characteristics of FGM sinusoidal shear deformation beam with different ratio of length to height and boundary condition are analyzed.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34
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