Abstract A systematically stepwise analysis (SSA) is presented for the free vibration analysis of rotating functionally graded (FG) turbo-machinery blades with linear and non-linear variable thickness operating in thermal environment. The governing equations are extracted by deployment of principle of the virtual work and Hamilton’s principle in the context of first-order shear deformation plate theory (FSDT) and the two-dimensional kinematics of the rotating blades. The nonlinear terms of the strain tensor are taking into account to insert the resulted stresses obtained from a pseudo-static analysis. Also, the inertia and Coriolis forces are included in the second step of the vibrational analysis. Eventually, the isogeometric analysis (IGA) as a powerful numerical approach is employed to discretize the resulted governing equations. To exhibit the reliability and efficacy of the IGA, a comprehensive comparative study on the predicted natural frequencies and mode shapes of the FG blades is performed compared with the available solutions in published literatures as well as finite element analysis using ANSYS. In order to assist scientists and engineers during the design, the complicated frequency loci veering behavior and the associated mode shifting phenomena are investigated with precisely predicting the coupling between the in-plane, out of plane and torsional vibration.

中文翻译：

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在热环境下以任意交错角具有可变厚度的旋转功能梯度叶片的等几何步进振动行为

摘要 提出了一种系统的逐步分析（SSA），用于在热环境中运行的具有线性和非线性可变厚度的旋转功能梯度（FG）涡轮机械叶片的自由振动分析。在一阶剪切变形板理论（FSDT）和旋转叶片的二维运动学的背景下，通过部署虚功原理和哈密顿原理，提取控制方程。考虑应变张量的非线性项以插入从伪静态分析获得的结果应力。此外，惯性力和科里奥利力包含在振动分析的第二步中。最后，等几何分析（IGA）作为一种强大的数值方法被用来离散化得到的控制方程。为了展示 IGA 的可靠性和有效性，将 FG 叶片的预测固有频率和模式形状与已发表文献中的可用解决方案以及使用 ANSYS 进行的有限元分析进行了综合比较研究。为了在设计过程中为科学家和工程师提供帮助，我们研究了复杂的频率定位行为和相关的模式转移现象，并精确预测了平面内、平面外和扭转振动之间的耦合。