Free vibration analysis of FGM non-coplanar plate assemblies with arbitrary boundary conditions through a novel analytic method

IF 6.6 1区工程技术 Q1 ENGINEERING, CIVIL

Thin-Walled Structures Pub Date : 2025-09-09 DOI:10.1016/j.tws.2025.113958

Kun Xie , Yaqi Tian , Cong Zhang , Meixia Chen

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引用次数: 0

Abstract

A novel analytic model is proposed for free vibration analysis of FGM non-coplanar plate assemblies with arbitrary boundary conditions. To establish the governing equation, the titled structures are firstly decomposed to several independent rectangular plates. The first-order shear deformation theory (FSDT) and the superposition method are employed, and both out-of-plane and in-plane displacements and forces are simultaneously expressed as some unknowns. Then, continuity conditions at coupling edges are utilized to assemble all plates, and displacements at other edges are restrained by artificial springs. By virtue of the orthonormal properties of trigonometric functions, continuity and boundary conditions become a series of algebraic equations, which are integrated to form the final governing equation. To evaluate the accuracy and application, natural frequencies of four different models are compared, and present results agree well with ones of the literature, finite element method and modal testing. Furthermore, influences of material parameters, elastic boundary conditions and discontinuity conditions are carried out. The results reveal that major differences between FGM and homogenous L-shaped plates are natural frequencies and mode shapes keep unchanged. The increase of coupling angle can efficiently increase natural frequencies as the coplanar plate becomes non-coplanar L-shaped one, and natural frequencies slightly change as the nonzero coupling angle further increases. Three discontinuity conditions including the coupling angle, coupling location and thickness can obviously affect natural frequencies of L-shaped plates.

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用一种新的解析方法分析任意边界条件下FGM非共面板组件的自由振动

提出了一种新的分析任意边界条件下FGM非共面板组件自由振动的解析模型。为了建立控制方程，首先将标题结构分解为几个独立的矩形板。采用一阶剪切变形理论（FSDT）和叠加法，将面外和面内位移和力同时表示为未知量。然后，利用耦合边缘的连续性条件将所有板装配在一起，其他边缘的位移由人工弹簧约束。利用三角函数的正交性，连续性和边界条件成为一系列代数方程，这些方程被积分形成最终的控制方程。为了评价模型的精度和应用，比较了四种不同模型的固有频率，所得结果与文献、有限元法和模态试验结果吻合较好。此外，还研究了材料参数、弹性边界条件和不连续条件的影响。结果表明，FGM板与均匀l型板的主要区别在于固有频率和模态振型不变。随着耦合角的增大，共面板变为非共面l型板时，固有频率有效提高，而随着非零耦合角的进一步增大，固有频率变化不大。耦合角度、耦合位置和厚度等3种不连续条件对l型板的固有频率有明显影响。

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来源期刊

Thin-Walled Structures 工程技术-工程：土木

CiteScore

9.60

自引率

20.30%

发文量

801

审稿时长

66 days

期刊介绍： Thin-walled structures comprises an important and growing proportion of engineering construction with areas of application becoming increasingly diverse, ranging from aircraft, bridges, ships and oil rigs to storage vessels, industrial buildings and warehouses. Many factors, including cost and weight economy, new materials and processes and the growth of powerful methods of analysis have contributed to this growth, and led to the need for a journal which concentrates specifically on structures in which problems arise due to the thinness of the walls. This field includes cold– formed sections, plate and shell structures, reinforced plastics structures and aluminium structures, and is of importance in many branches of engineering. The primary criterion for consideration of papers in Thin–Walled Structures is that they must be concerned with thin–walled structures or the basic problems inherent in thin–walled structures. Provided this criterion is satisfied no restriction is placed on the type of construction, material or field of application. Papers on theory, experiment, design, etc., are published and it is expected that many papers will contain aspects of all three.