基于不同高阶剪切变形理论的Pasternak地基上FG-CNTRC梁自由振动及屈曲无网格分析

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (2) : 1-11.

论文

杨立军1，彭林欣2，陈卫3

作者信息 +

Free vibration and buckling analysis of functionally graded carbon nanotube-reinforced composite beams on Pasternak foundation under high-order shear deformation theory

YANG Lijun1，PENG Linxin2，CHEN Wei3

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文章历史 +

摘要

功能梯度碳纳米管增强复合材料(functionally graded carbon nanotube-reinforced composite, FG-CNTRC)作为新一代先进复合材料，因其优越的力学性能而被研究者们广泛关注。本文以Pasternak地基上FG-CNTRC梁为研究对象，基于不同高阶剪切变形理论，将一种具有插值特性的无网格法—稳定移动克里金插值(stabilized moving kriging interpolation, SMKI)应用于求解Pasternak地基上FG-CNTRC梁的自由振动及屈曲问题。基于稳定移动克里金插值和不同高阶剪切变形理论给出FG-CNTRC梁的位移场，利用Hamilton原理和最小势能原理分别推导了Pasternak地基上FG-CNTRC梁的自由振动和屈曲控制方程。采用MATLAB编制了相关程序，将本文解与解析解或文献解对比，证明了本文方法在计算Pasternak地基上FG-CNTRC梁自由振动与屈曲的有效性及准确性。文末还讨论了不同高阶剪切变形理论、地基系数、碳纳米管体积分数等对其自振频率和屈曲临界荷载的影响。

Abstract

As a new generation of advanced composites, functionally graded carbon nanotube reinforced composite (FG-CNTRC) has been widely concerned by researchers because of their excellent mechanical properties. In this paper, the FG-CNTRC beam on Pasternak foundation is taken as the research object. Based on different high-order shear deformation theories, a meshless method with interpolation characteristics, the stable moving Kriging interpolation (SMKI) is applied to solve the free vibration and buckling problems of FG-CNTRC beam on Pasternak foundation. Based on stable Kriging interpolation and different high-order shear deformation theory, the displacement field of FG-CNTRC beam is derived. The free vibration and buckling control equations of FG-CNTRC beam on Pasternak foundation are obtained by using Hamilton principle and minimum potential energy principle respectively. The relevant program is compiled by MATLAB. The comparison between the solution in this paper and the analytical solution or the literature solution proves the effectiveness and accuracy of this method in calculating the free vibration and buckling of FG-CNTRC beam on Pasternak foundation. At the end of the paper, the effects of different high-order shear deformation theory, foundation coefficient and carbon nanotube volume fraction on the natural frequency and buckling critical load are also discussed.

导出引用

杨立军1，彭林欣2，陈卫3. 基于不同高阶剪切变形理论的Pasternak地基上FG-CNTRC梁自由振动及屈曲无网格分析[J]. 振动与冲击, 2024, 43(2): 1-11

YANG Lijun1，PENG Linxin2，CHEN Wei3. Free vibration and buckling analysis of functionally graded carbon nanotube-reinforced composite beams on Pasternak foundation under high-order shear deformation theory[J]. Journal of Vibration and Shock, 2024, 43(2): 1-11

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