Undamped Free Vibration Analysis of Functionally Graded Beams: A Dynamic Finite Element Approach

IF 12.2 1区 工程技术 Q1 MECHANICS Applied Mechanics Reviews Pub Date : 2022-10-07 DOI:10.3390/applmech3040070
A. Gee, S. M. Hashemi
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引用次数: 1

Abstract

A Dynamic Finite Element (DFE) method for coupled axial–flexural undamped free vibration analysis of functionally graded beams is developed and subsequently used to investigate the system’s natural frequencies and mode shapes. The formulation is based on the Euler–Bernoulli beam theory and material grading is assumed to follow a power law variation through the thickness direction. Using the closed-form solutions to the uncoupled segments of the system’s governing differential equations as the basis functions of approximation space, the dynamic, frequency-dependent, trigonometric interpolation functions are developed. The interpolation functions are used with the weighted residual method to develop the DFE of the system. The resulting nonlinear eigenvalue problem is then solved to determine the coupled natural frequencies. Example elements using DFE, Finite Element Method (FEM) and the Dynamic Stiffness Method (DSM) are implemented in MATLAB for testing, verification, and validation. Good agreement was observed and the DFE formulation exhibited superior convergence performance compared to the FEM.
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功能梯度梁无阻尼自由振动分析:一种动力有限元方法
提出了一种用于功能梯度梁轴-弯耦合无阻尼自由振动分析的动态有限元方法,并将其用于研究系统的固有频率和模态振型。该公式基于欧拉-伯努利梁理论,并假设材料分级在厚度方向上遵循幂律变化。利用系统控制微分方程不耦合段的封闭解作为近似空间的基函数,建立了动态的、频率相关的三角插值函数。利用插值函数和加权残差法建立了系统的DFE。然后求解得到的非线性特征值问题以确定耦合固有频率。在MATLAB中使用DFE、有限元法(FEM)和动刚度法(DSM)实现实例单元进行测试、验证和验证。与有限元法相比,DFE公式具有较好的收敛性能。
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来源期刊
CiteScore
28.20
自引率
0.70%
发文量
13
审稿时长
>12 weeks
期刊介绍: Applied Mechanics Reviews (AMR) is an international review journal that serves as a premier venue for dissemination of material across all subdisciplines of applied mechanics and engineering science, including fluid and solid mechanics, heat transfer, dynamics and vibration, and applications.AMR provides an archival repository for state-of-the-art and retrospective survey articles and reviews of research areas and curricular developments. The journal invites commentary on research and education policy in different countries. The journal also invites original tutorial and educational material in applied mechanics targeting non-specialist audiences, including undergraduate and K-12 students.
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