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功能梯度材料板中具有纵向速度的广泛内部共振现象。

A widespread internal resonance phenomenon in functionally graded material plates with longitudinal speed.

作者信息

Zhang Y F, Liu J T

机构信息

College of Aerospace Engineering, Shenyang Aerospace University, Shenyang, 110136, China.

出版信息

Sci Rep. 2019 Feb 13;9(1):1907. doi: 10.1038/s41598-018-37921-9.

DOI:10.1038/s41598-018-37921-9
PMID:30760768
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC6374398/
Abstract

A widespread internal resonance phenomenon is detected in axially moving functionally graded material (FGM) rectangular plates. The geometrical nonlinearity is taken into account with the consideration of von Kármán nonlinear geometric equations. Using d'Alembert's principle, governing equation of the transverse motion is derived. The obtained equation is further discretized to ordinary differential equations using the Galerkin technique. The harmonic balance method is adopted to solve the above equations. Additionally, stability analysis of steady-state solutions is presented. Research shows that a one-to-one internal resonance phenomenon widely exists in a large range of constituent volume distribution in moving FGM plates. Moreover, it is found that this internal resonance phenomenon can easily happen even though the FGM plates are under extremely small external excitation or with very large damping.

摘要

在轴向运动的功能梯度材料（FGM）矩形板中检测到一种广泛存在的内共振现象。考虑冯·卡门非线性几何方程来计入几何非线性。利用达朗贝尔原理推导横向运动的控制方程。使用伽辽金技术将所得方程进一步离散为常微分方程。采用谐波平衡法求解上述方程。此外，还给出了稳态解的稳定性分析。研究表明，在运动的功能梯度材料板的大范围成分体积分布中广泛存在一对一的内共振现象。而且发现，即使功能梯度材料板受到极小的外部激励或具有很大的阻尼，这种内共振现象也很容易发生。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/6ebaed76309b/41598_2018_37921_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/2f0b813c91e9/41598_2018_37921_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/535786a1a308/41598_2018_37921_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/12ea9c2e45fd/41598_2018_37921_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/87f8f960bd61/41598_2018_37921_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/5945aafe0561/41598_2018_37921_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/77f9faed880b/41598_2018_37921_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/5cd195d5eed0/41598_2018_37921_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/c92699e297de/41598_2018_37921_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/243759bf72e3/41598_2018_37921_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/a9cead533f99/41598_2018_37921_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/6ebaed76309b/41598_2018_37921_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/2f0b813c91e9/41598_2018_37921_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/535786a1a308/41598_2018_37921_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/12ea9c2e45fd/41598_2018_37921_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/87f8f960bd61/41598_2018_37921_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/5945aafe0561/41598_2018_37921_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/77f9faed880b/41598_2018_37921_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/5cd195d5eed0/41598_2018_37921_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/c92699e297de/41598_2018_37921_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/243759bf72e3/41598_2018_37921_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/a9cead533f99/41598_2018_37921_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/892b/6374398/6ebaed76309b/41598_2018_37921_Fig11_HTML.jpg

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