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半跨径向均布荷载作用下功能梯度孔隙拱的面内参数共振行为研究

STUDY ON IN-PLANE PARAMETRIC RESONANCE BEHAVIOR OF FUNCTIONALLY GRADED POROUS ARCHES UNDER A HALF-SPAN RADIAL LOAD

投稿时间：2025-07-21 修订日期：2025-10-04

DOI：

英文关键词:Functionally graded porous materials Circular arches Parameter resonance Unstable regions, Differential quadrature method.

基金项目:国家自然科学基金（52308154、52508168）；广东省基础与应用基础研究基金（2022A1515111135、 2025A1515010407）

作者	单位	邮编
刘圆圆	广州科技贸易职业学院应急技术学院	511442
张紫祥	佛山大学土木与交通学院
刘璐璐	佛山大学土木与交通学院
畅金龙	广州科技贸易职业学院应急技术学院
黄永辉^*	广州大学风工程与工程振动研究中心	510006

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中文摘要:

本文主要探究了半跨径向荷载作用下功能梯度多孔材料圆弧拱的面内参数共振失稳行为。假设孔隙呈非均匀对称梯度分布，基于Halpin-Tsai微观力学模型预测了功能梯度孔隙材料的力学性能。随后，利用Hamilton原理建立了半跨径向荷载作用下功能梯度多孔材料拱的控制方程，联用微分求积法和鲍络金法获得了拱发生平面内参数共振的动力不稳定域。在此基础上开展了详尽的参数分析，通过数值仿真校验了数值结果的正确性。研究结果表明，发生参数共振的动力不稳定域同孔隙系数、拱的长细比、开口角和荷载分布范围显著相关。0.3% - 0.5%范围内，GPL的质量分数越大，功能梯度多孔材料拱的动力不稳定域越小。动力不稳定域的域宽随静荷载分量的增大而增大，当激励幅值一定，荷载作用范围越广，动力不稳定域的带宽越大。

英文摘要:

This paper investigates the in-plane parameter resonance of functionally graded porous arches under a half-span distributed radial load. The material properties of circular arches having a symmetric pore distribution pattern were predicted according to a Halpin-Tsai micromechanics model. Hamilton's principle was applied to establish the governing equations. The differential quadrature method (DQM) in conjunction with a Bolotin’s approach were adopted to solve them numerically. The unstable region corresponding to the in-plane parameter resonance of arches were then determined. In-depth parameter analyses were conducted subsequently. Numerical simulation was carried out to verify the accuracy of the presented results. Research results show that the unstable regions are affected by porosity coefficient, slenderness ratio, included angle, as well as the load distribution range significantly. Within the range of 0.3% to 0.5%, the increasing GPL mass fraction results in a continuous reduction in the area of the dynamic unstable region. The width of the dynamic unstable region increases with the increase of the static load component. When the excitation amplitude remains a constant, the wider the range of load action, the greater the bandwidth of the dynamic unstable region.

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