Traveling Wave Mode Characteristics of Rotating Functional Gradient Material Cylindrical Shell Structures With Elastic Boundary Constraints
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摘要: 对旋转功能梯度圆柱壳自由振动行波特性及边界约束影响进行了分析研究.将功能梯度材料的物理特性表示成沿壳体厚度方向指数变化的函数，基于Love壳体理论，将圆柱壳3个方向的振动位移场采用改进Fourier(傅立叶)级数方法展开, 进而改善位移函数在边界位置求导连续性，结合旋转圆柱壳结构能量原理描述与RayleighRitz法，推导旋转功能梯度圆柱壳自由振动特征方程.通过将计算结果与现有文献结果对比验证了该文模型的正确性与收敛性.随后，通过算例讨论分析了功能梯度材料特性参数、几何参数、边界条件及约束弹簧刚度对旋转功能梯度圆柱壳自由振动行波振动特性的影响.结果表明：边界条件在环向波数n较小或长径比L/R较小的情况下对行波特性影响较为明显；随着厚径比H/R的增大，边界条件的影响逐渐减小；边界约束弹簧对行波特性影响程度取决于模态阶数情况；功能梯度材料特性参数对前后行波频率的影响随着模态序数的增大而逐渐增大.Abstract: The traveling wave mode characteristics of rotating functional gradient material (FGM) cylindrical shells in free vibration and the effects of elastic boundary constraints were analyzed, in which the physical properties of FGM were expressed as exponential functions varying along the thickness direction. Based on Love’s shell theory, the vibration displacements in the 3 directions were constructed in the form of modified Fourier series to improve the derivative continuity of displacement functions on each boundary. Then the energy description and Rayleigh-Ritz method were combined to formulate the eigen-equations of rotating FGM cylindrical shells. Comparison between the current results and those from other approaches in previous literatures was made to verify the correctness and convergence of the present method. Subsequently, the effects of FGM properties, geometric parameters, boundary conditions and constraint stiffnesses on the traveling wave mode characteristics of rotating FGM cylindrical shells were studied in detail. From the computed results, it is clear that the boundary conditions have significant effects on the traveling wave mode characteristics, especially when the circumferential wave number or the length-to-radius ratio L/R of a shell is relatively small; while the influence of boundary conditions decreases gradually with the thickness-to-radius ratio H/R.Additionally, the effects of boundary constraint stiffnesses on the traveling wave mode characteristics are greatly dependent on the mode order of a rotating FGM cylindrical shell, the influence of FGM properties on the traveling wave mode characteristics increases with the mode order.
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