非多项式框架下带弹性地基的功能分级碳纳米管增强复合梁的静态、屈曲和自由振动响应

Abhijeet Babar, Rosalin Sahoo
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摘要

本文研究了位于帕斯捷尔纳克弹性地基上的功能分级碳纳米管增强复合材料(FG-CNTRC)梁的静力、屈曲和自由振动分析。该分析采用了基于秒函数的剪切变形理论(SFSDT)。该理论满足梁顶部和底部表面的无牵引边界条件,因此无需剪切修正系数。汉密尔顿原理用于确定支配微分方程和边界条件,而纳维耶求解技术则用于确定闭式解。分析方法用于研究 FG-CNTRC 梁的挠度、应力、临界屈曲载荷和固有频率,该梁位于包括剪力层和温克勒弹簧在内的帕斯捷尔纳克弹性地基上。为确定 FG-CNTRC 梁的材料特性,采用了混合物规则。本研究采用了均匀分布(UD-梁)、FG-X 梁、FG-O 梁和 FG-V 梁等不同的 CNT 配筋分布形式。考虑到不同的跨度厚度比、碳纳米管的体积分数和分布、温克勒弹簧和剪切层常数因子,所有的结构响应均可预测。与其他现有理论相比,本理论能准确预测 FG-CNTRC 梁的结构响应。此外,还包括一些新结果,作为新研究的基准解决方案。
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Static, buckling, and free vibration responses of functionally graded carbon nanotube-reinforced composite beams with elastic foundation in non-polynomial framework
In this work, the static, buckling, and free vibration analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam resting on a Pasternak elastic foundation are studied. The secant function-based shear deformation theory (SFSDT) is used for this analysis. This theory fulfills the traction-free boundary conditions at the top and bottom surfaces of the beam, hence there is no need for a shear correction factor. Hamilton’s principle is used to determine the governing differential equations and boundary conditions whereas Navier’s solution technique is used for determining the closed-form solution. The analytical approach is used to examine the deflection, stresses, critical buckling load, and natural frequencies of the FG-CNTRC beam resting on the Pasternak elastic foundation including a shear layer and Winkler springs. To determine the material characteristics of FG-CNTRC beams, the Rule of the mixture is used. Uniform distribution (UD-beam), FG-X beam, FG-O beam, and FG-V beam are the different forms of CNT reinforcement distribution that are used in this study. Considering different span thickness ratios, the volume fraction and distribution of CNT, the Winkler spring, and the shear layer constant factors, all the structural responses are predicted. It is also observed that the present theory predicts the structural responses of the FG-CNTRC beam accurately when compared to other existing theories. A few new results are also included as the benchmark solutions for the new research.
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