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Vibration analysis and transient response of a functionally graded piezoelectric curved beam with general boundary conditions

机译：具有一般边界条件的功能梯度压电弯曲梁的振动分析和瞬态响应

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摘要

The paper presents a unified solution for free and transient vibration analyses of a functionally graded piezoelectric curved beam with general boundary conditions within the framework of Timoshenko beam theory. The formulation is derived by means of the variational principle in conjunction with a modified Fourier series which consists of standard Fourier cosine series and supplemented functions. The mechanical and electrical properties of functionally graded piezoelectric materials (FGPMs) are assumed to vary continuously in the thickness direction and are estimated by Voigt's rule of mixture. The convergence, accuracy and reliability of the present formulation are demonstrated by comparing the present solutions with those from the literature and finite element analysis. Numerous results for FGPM beams with different boundary conditions, geometrical parameters as well as material distributions are given. Moreover, forced vibration of the FGPM beams subjected to dynamic loads and general boundary conditions are also investigated.
机译：本文在Timoshenko梁理论的框架内，为具有一般边界条件的功能梯度压电弯曲梁的自由振动和瞬态振动分析提供了统一的解决方案。该公式是通过变分原理结合修改后的傅立叶级数得出的，该傅立叶级数由标准傅立叶余弦级数和补充函数组成。假定功能梯度压电材料（FGPM）的机械和电气性能在厚度方向上连续变化，并根据Voigt混合定律进行估算。通过将本解决方案与来自文献和有限元分析的解决方案进行比较，证明了本配方的收敛性，准确性和可靠性。给出了具有不同边界条件，几何参数以及材料分布的FGPM梁的大量结果。此外，还研究了FGPM梁在动态载荷和一般边界条件下的强迫振动。

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