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Effect of porosity on free vibration and buckling of functionally graded porous beams with non-uniform cross-section

孔隙度对具有不均匀横截面的功能分级多孔梁的自由振动和屈曲行为的影响

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Abstract

The purpose of this work is to investigate the effect of porosity on free vibration and buckling behaviours of non-uniform cross-section functionally graded porous beams. The material properties are considered varied along the thickness direction while the cross-section is non-uniform along the length of the beam. Three different patterns including symmetric, non-symmetric and uniform have been considered as the porosity distribution. The classical beam theory and Hamilton’s principle are used to derive the governing equations of the problem and the derived formulations are solved using differential quadrature method. The obtained results were validated via both well-known and analytical reported solutions. The optimal discretization setting was determined via mesh independency study. Detailed parametric analyses are presented to get an insight into the effects of different mechanical parameters including porosity coefficient, slenderness ratio and varying cross-section on the fundamental frequency and critical buckling load. The results show that an increase in material porosity leads to a significant reduction in beam buckling capacity. However, the free vibration behaviour of beams completely depends on their porosity pattern. In addition, the symmetric distribution pattern has the best performance in the terms of beam buckling capacity and fundamental frequency.

摘要

本文旨在研究孔隙度对具有不均匀横截面的功能分级多孔梁的自由振动和屈曲行为的影响。一 般认为材料的性能沿厚度方向变化, 而梁的横截面沿其长度方向分布不均匀。三种不同的孔隙度分布 包括对称分布、非对称分布和均匀分布。利用经典的梁理论和Hamilton 原理推导出了问题的控制方 程, 并用微分求积法推导出公式。通过已知方法和分析解法对所得结果进行了验证。通过网格独立性 研究, 确定了最优离散化设置。利用详细的参数化分析研究了不同力学参数, 包括孔隙率系数、长径 比和变化截面对基频和临界屈曲载荷的影响。结果表明, 材料孔隙率的增加会导致梁的屈曲能力显著 降低。然而, 梁的自由振动行为完全取决于其孔隙度模式。此外, 孔隙呈对称分布的梁其屈曲能力和 基频性能最好。

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  1. Department of Civil Engineering, Bushehr Branch, Islamic Azad University, Bushehr, 7515895496, Iran

    Zeinab Bagheri, Alireza Fiouz & Mahmood Seraji

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Zeinab BAGHERI conducted the literature review, generated data, developed the codes, illustrated the results, and wrote the first draft of the manuscript. Alireza FIOUZ provided the concept and edited the draft of the manuscript. Mahmood SERAJI edited the draft of the manuscript.

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Zeinab BAGHERI, Alireza FIOUZ and Mahmood SERAJI declare that they have no conflict of interest.

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Bagheri, Z., Fiouz, A. & Seraji, M. Effect of porosity on free vibration and buckling of functionally graded porous beams with non-uniform cross-section. J. Cent. South Univ. 31, 841–857 (2024). https://doi.org/10.1007/s11771-023-5302-z

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