Free vibration characteristics of functionally graded spherical torus based on first-order shear deformation theory
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摘要: 提出一种半解析法分析了一般边界条件下中等厚度功能梯度球环结构的自由振动特性。基于一阶剪切变形理论推导了中等厚度功能梯度球环结构公式,其中位移函数用改进傅里叶级数表示以消除边界的不连续性,并利用弹簧参数法来模拟一般边界条件;利用里兹法求解得到功能梯度球环结构的固有频率;在收敛性分析的基础上,将本文结果与有限元法、试验数据和文献数据进行了对比,并探讨相关参数的影响。研究表明,本文提出的方法收敛性好,求解精度高;功能梯度球环结构频率参数随厚度和剪切修正系数的增大而增大。Abstract: A semi-analytical method to investigate the free vibration characteristics of moderately thick functionally graded material(FGM)spherical torus structures with general boundary conditions was proposed. The theoretical formulas were derived by applying the first-order shear deformation theory, in which the displacement admissible functions were expressed by Improved Fourier Series to eliminate the discontinuity of the boundary. The general boundary conditions of the functionally graded spherical torus structure were simulated by different spring parameters. The natural frequencies of functionally graded spherical torus were obtained by Ritz method. The data in this paper were compared with those obtained by finite element method, experiment and literatures based on convergence analysis, and the influences of correlation parameter were studied. The results show that the proposed method has advantages of good convergence and high accuracy. The frequency parameter of functionally graded spherical torus structures increases with the increase of thickness and shear correction factors.
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