任意形状功能梯度板的自由振动分析
Free Vibration Analysis of Functional Gradient Mindlin Plate of Arbitrary Shape
DOI: 10.12677/OJAV.2019.71004, PDF,  被引量   
作者: 玉云艳*, 朱 翔, 李天匀：华中科技大学船舶与海洋工程学院，湖北 武汉;船舶与海洋水动力湖北省重点实验室，湖北 武汉;高新船舶与深海开发装备协同创新中心，上海；郭文杰：华中科技大学船舶与海洋工程学院，湖北 武汉;华东交通大学，铁路环境振动与噪声教育部工程研究中心，江西 南昌
关键词: 任意形状；功能梯度；典型边界条件；Rayleigh-Ritz法；改进的傅里叶级数法；Arbitrary Shape； Functionally Graded； Typical Boundary Conditions； Rayleigh-Ritz Method； Improved Fourier Series Method
摘要: 本文基于改进的Rayleigh-Ritz法对任意形状功能梯度材料板的自由振动特性进行了分析。假设功能梯度板的材料沿厚度方向指数变化，用Mindlin板理论描述板的振动。引入改进的Rayleigh-Ritz法，利用改进的傅里叶级数作为位移容许函数，结合Mindlin板理论推导得到功能梯度板的能量泛函表达式，根据能量泛函变分原理得到了振动系统的特征方程，求解得到功能梯度板的振动固有频率。通过与文献中功能梯度板的固有频率值对比，验证了本文方法的收敛性与准确性。然后分别对三角形板和圆形板的固有频率进行了求解，表明本文方法的通用性。然后通过算例分析讨论了功能梯度板的梯度指数、边界条件及板厚等参数对固有频率的影响。
Abstract: In this paper, the free vibration characteristics of functionally graded plates in arbitrary shape were studied based on the improved Rayleigh Ritz method. Assuming that the material of the functional-ly graded plate changes exponentially along the thickness direction, the vibration of the plate is described by Mindlin plate theory and the improved Fourier series is used as the displacement tolerance function. The energy functional expressions of the functionally graded plate are derived and the natural frequency is obtained by solving them. The convergence and accuracy of the proposed method are verified by compared with the existing literature. Then the proposed method was applied to the triangular and circular plates respectively, in which the versatility of the proposed method was showing. Finally the influences of gradient index, boundary condition and thickness of the functionally graded plate on the free vibration are discussed.
文章引用：玉云艳, 朱翔, 李天匀, 郭文杰. 任意形状功能梯度板的自由振动分析[J]. 声学与振动, 2019, 7(1): 28-40. https://doi.org/10.12677/OJAV.2019.71004

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