FGM圆板考虑面内振动的动态响应

发布时间：2018-06-18 15:15

本文选题：功能梯度材料 + 圆板　；参考：《兰州理工大学》2017年硕士论文

【摘要】：功能梯度材料是近年来新发明的一种新型复合材料,由其制成的构件在高温环境中具有区别于一般材料的优越力学性能,它是通过对两种及以上金属或陶瓷材料的合理搭配而成。由于其物理性能的优越性,常被用在需承受高温环境的航空航天、核工业和化工领域等。因此功能梯度材料板的力学特性已成为工程应用领域中重点研究的活跃课题。本论文分别研究普通功能梯度材料板和Winkler弹性地基上功能梯度材料板在考虑面内振动时的动态力学行为特性。包括以下几方面:1.FGM圆板考虑面内振动的动态响应首先采用Voigt等模型来模拟功能梯度材料圆板沿板的厚度方向变化的材料梯度,并假设其变化形式为幂函数的形式。基于经典板理论,同时考虑横向振动和面内振动,并使用Hamilton原理及变分法推导出轴对称情况下功能梯度材料圆薄板动态响应的运动微分方程。并将控制方程无量纲化以方便求解,用打靶法对其进行数值求解。将方程退化为一般均质板,求解其固有频率,得到了与相关文献非常接近的结果。求解某两种材料构成的功能梯度材料作为算例,对其得到的数值结果进行图像化后直观的分析讨论,研究考虑面内振动会对FGM圆板的振动产生的影响。2.Winkler弹性地基上FGM圆板考虑面内振动的动态响应从Winkler弹性地基上FGM板的振动入手,考虑面内振动,研究周边固定和周边不可移简支两种边界条件下功能梯度圆板的动态响应问题。应用经典板理论,并考虑小挠度问题,忽略转动惯性力矩,导出Winkler地基上FGM圆板在轴对称情况下振动的控制方程,假设FGM圆板的振动形式为谐响应形式,将比较难求解的偏微分控制方程变成常微分方程。本文仅研究周边固定和周边不可移简支的情形,应用打靶法求解FGM圆薄板振动问题的解。通过数值结果分析弹性地基参数及面内振动对FGM圆板振动的影响。本文得到的结论对FGM圆板振动特性的研究有积极的推进作用,对于FGM板今后在工程实际应用中更为精确的估计误差也具有指导意义。
[Abstract]:Functionally graded material (FGM) is a new type of composite material newly invented in recent years. The components made of FGM have superior mechanical properties different from those of general materials in high temperature environment. It is made by matching two or more metal or ceramic materials. Because of its superiority in physical properties, it is often used in aerospace, nuclear industry and chemical industry which need to withstand high temperature environment. Therefore, the mechanical properties of functionally graded material plates (FGM) have become an active subject in the field of engineering application. In this paper, the dynamic mechanical behavior of FGM plates on Winkler elastic foundation and FGM plates on Winkler elastic foundation considering in-plane vibration are studied respectively. The dynamic response of FGM circular plates considering in-plane vibration is described as follows. Firstly, Voigt model is used to simulate the material gradient of FGM circular plates along the thickness of the plate, and the change form is assumed to be a power function. Based on the classical plate theory and considering both transverse and in-plane vibrations, the differential equations of motion of circular thin plates with functionally graded materials under axisymmetric conditions are derived by using Hamilton principle and variational method. The control equation is dimensionless to be solved conveniently, and the numerical method is used to solve the problem. The equation is degenerated into a general homogeneous plate and its natural frequency is solved. The results are very close to those of the related literatures. The functionally graded material composed of two kinds of materials is solved as an example, and the numerical results obtained are analyzed and discussed intuitively after image. The effect of in-plane vibration on the vibration of FGM circular plate is studied. 2. The dynamic response of FGM circular plate considering in-plane vibration on Winkler elastic foundation is studied starting with the vibration of FGM plate on Winkler elastic foundation, and the in-plane vibration is considered. The dynamic response of functionally graded circular plates under two boundary conditions, namely peripheral fixed and immovable simply supported, is studied. By applying classical plate theory and considering the problem of small deflection and ignoring the moment of inertia of rotation, the governing equation of vibration of FGM circular plate on Winkler foundation under axisymmetric condition is derived. The vibration form of FGM circular plate is assumed to be a harmonic response form. The more difficult partial differential governing equations are transformed into ordinary differential equations. In this paper, the problem of FGM circular thin plate vibration is solved by means of shooting method. The effects of elastic foundation parameters and in-plane vibration on the vibration of FGM circular plate are analyzed by numerical results. The conclusions obtained in this paper have a positive effect on the study of the vibration characteristics of FGM circular plates, and also have a guiding significance for the more accurate estimation errors of FGM plates in practical engineering applications in the future.
【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】：TB33

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