圆孔工字型蜂窝梁扭转模态自由振动研究  

Torsional free vibration of circular opening I-section cellular beams

作　　者：黄斌 张文福[1] HUANG Bin;ZHANG Wenfu(School of Civil Engineering and Architecture,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]南京工程学院建筑工程学院,南京211167

出　　处：《振动与冲击》2024年第6期329-335,344,共8页Journal of Vibration and Shock

基　　金：南京工程学院创新基金面上项目(CKJB202204);国家自然基金面上项目(52178143;51578120;51178087)。

摘　　要：从能量等效角度,提出了一种圆孔工字型截面蜂窝梁连续型模型,应用新的薄壁构件扭转理论:板-梁理论,建立了构件扭转模态自由振动能量泛函模型,明确了圆孔工字型截面蜂窝梁名义约束扭转惯性矩(翘曲常数)、自由扭转常数、转动惯量。通过变分运算,获得了平衡微分方程模型。基于扭转模态试函数,推导了圆孔工字型截面蜂窝梁自由振动扭转模态振动圆频率,并与有限元结果对比校验理论模型预测精度。开展了悬臂圆孔工字型蜂窝梁受集中扭矩作用的端部截面转角理论分析与有限元计算,进一步检验了基于板-梁理论建立的蜂窝梁连续模型的适用性。应用板-梁理论对圆孔工字型截面蜂窝梁自由振动扭转的分析过程及推导步骤,为其他开孔类型工字型蜂窝梁扭转模态自由振动研究提供了直接参考。A continuous model for circular opening I-section cellular beams was proposed from the perspective of energy equivalence.The energy functional model of the cellular beams was established in accordance with the plate-beam theory concept,and the nominal warping constant,uniform torsional rigidity,rotation moment of inertia were defined.The equilibrium differential equation was derived based on the variational operation,the trial displacement function for which was postulated to yield the frequency of the torsional free vibration mode.The prediction accuracy of the theoretical results was examined against numerical results.Subsequently,the rotation of the terminal section of the cantilever cellular specimens with circular opening subjected to a concentrated torque was theoretically and numerically analyzed,which proves the positive applicability of the continuous model established in accordance with the plate-beam theory.The torsional free vibration analysis process and derivation steps for the cellular beams with circular opening provide a replicable reference for the other opening type beams.

关 键 词：圆孔工字型截面蜂窝梁 扭转自由振动 板-梁理论 蜂窝梁连续型模型 能量泛函模型 

分 类 号：TU392[建筑科学—结构工程]