Abstract In this paper, the free vibration characteristics of functionally graded double-beam system (FGDBS) elastically connected by an elastic layer with uniform elastic stiffness under arbitrary boundary conditions are investigated. It is assumption that the material distribution properties of the individual beams of FGDBS depends on different four-parameters. Timoshenko beam theory in which the effects of shear deformation and rotational inertia are considered is utilized to model the free vibration of FGDBS and displacement components can be obtained from the Haar wavelet series and their integral. Hamilton’s principle is applied to construct coupled governing equations and the virtual spring boundary technique is applied to generalize boundary conditions at four ends of FGDBS. The convergency and accuracy of the proposed method can be confirmed through the comparison results with previous literature and finite element method (FEM). A lot of new results have been proposed, such as the frequency characteristics of FGDBS under arbitrary boundary conditions which can be provided as reference data for future research.

中文翻译：

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Haar小波离散化功能梯度双梁系统自由振动分析

摘要 本文研究了由均匀弹性刚度的弹性层弹性连接的功能梯度双梁系统(FGDBS)在任意边界条件下的自由振动特性。假设 FGDBS 的各个梁的材料分布特性取决于不同的四参数。Timoshenko 梁理论考虑了剪切变形和转动惯量的影响，用于模拟 FGDBS 的自由振动，位移分量可以从 Haar 小波级数及其积分中获得。应用Hamilton原理构建耦合控制方程，应用虚拟弹簧边界技术对FGDBS四端的边界条件进行泛化。通过与以往文献和有限元法（FEM）的比较结果，可以证实所提方法的收敛性和准确性。提出了很多新的结果，例如任意边界条件下FGDBS的频率特性，可以作为未来研究的参考数据。