A continuous model for the cellular beams was proposed from the perspective of the energy equivalence. The energy functional model of cellular beams was established in accordance with the Plate-Beam theory concept, where the nominal warping constant, uniform torsional rigidity, rotation moment of inertia were given out. 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 concentrated torque were theoretically and numerically analyzed, which proved the positive applicability of the continuous models established with accordance to the Plate-Beam theory. The torsional free vibration analysis process and derivation steps for the cellular beams with circular opening provided a replicable reference for the other opening type ones.
HUANG Bin, ZHANG Wenfu.
Torsional free vibration of circular opening I-section cellular beams[J]. Journal of Vibration and Shock, 2024, 43(6): 329-335
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 贾连光，金路．蜂窝式钢结构的力学性能[M]．北京：中国建筑工业出版社，2015．
JIA Lianguang，JIN Lu．Mechanical properties of honeycomb steel structures [M]．Beijing：China Construction Industry Press， 2015．
[2] 蒋上．正八边形孔蜂窝梁的挠度计算研究[D]．长沙：湖南大学，2011．
JIANG Shang．Study on deflection calculation of honeycomb beams with regular octagon holes[D]．Changsha：Hunan University，2011.
[3]罗烈，罗晓霖．蜂窝梁设计规范的比较研究[J]．建筑钢结构进展，2005，02： 43-47．
LUO Lie, LUO Xiaolin．Comparative study on design specifications for honeycomb beams [J]．Progress in Building Steel Structures，2005，02：43-47．
[4] MENKULASI F， MOEN C D，EATHERTON M R， KURUPPUARACH C D．Investigation of web post compression buckling limit state and stiffener requirements in castellated beam [J]． Engineering Journal American Institute of Steel Construction 2017，54 (1) 21-43．
[5] ERDAL F，SAKA M P． Ultimate load carrying capacity of optimally designed steel cellular beams [J]． Journal of Constructional Steel Research，2013，80，355-368.
[6] ELLOBODY E．Nonlinear analysis of cellular steel beams under combined buckling modes[J]． Thin-Walled Structure．2013， 52， 66-79．
[7] NSEIR J， LO M． Lateral torsional buckling of cellular steel beams. Proceedings of the Annual Stability Conference. Grapevine ：Structural Stability Research Council，2012.
[8] BOISSONADE N, NSEIR J, LO M. Design of cellular beams against lateral torsional buckling [J]．Structure Build，2014，167：436-44．
[9] LIU M, GUO K, WANG P, LOU C, ZHANG Y． Simplified method for prediction of elastic-plastic buckling strength of web-post panel castellated steel beams[J]． Steel Composite Structure. 2017，25 (6) ， 671-684．
[10] WANG P J， GUO K R，LIU M， ZHANG L．Shear buckling strengths of web-posts in a castellated steel beam with hexagonal web openings[J]．Journal of Disaster Prevention & Mitigation Engineering，2016，121，173-184.
[11] TSAVDARIDIS K D, MELLO C D．Web buckling study of the behavior and strength of perforated steel beams with different novel web opening shapes[J]．Journal of Disaster Prevention & Mitigation Engineering， 2011．67 (10) ：1605-1620.
[12] GRILO L F， FAKURY R H， CASTRO A， VERISSIMO S．Design procedure for the web-post buckling of steel cellular beams[J]．Journal of Disaster Prevention & Mitigation Engineering，2018，148，525-541．
[13] PANEDPOJAMAN P, THEPCHATRI T, LIMKATANYU S． Novel design equations for shear strength of local web-post buckling in cellular beams [J]．Thin-Walled Structure， 2014，76，92-104．
[14]李凯，何书韬，吴国民，毛艺达，李天匀．基于能量泛函的开口矩形板自由振动特性分析[J]．振动与冲击，2017，36(11)：161-165．
LI Kai， HE Shutao， WU Guomin， MAO Yida， LI Tianyun．The free vibration characteristics analysis of rectangular plate with central opening using energy functional method[J]．Journal of vibration and shock，2017，36(11)：161-165．
[15]牛国华，王钢峰，王剑．组合 L 型变截面梁的自由振动特性分析[J]．振动与冲击，2022，41(5)：228-234．
NIU Guohua， WANG Gangfeng， WANG Jian．Analysis of free vibration characteristics of composite L-shaped variable cross-section beam J]．Journal of vibration and shock，2022，41(5)：228-234．
[16] 井洁，毛晓晔，丁虎，陈立群．轴向力作用下过屈曲Timoshenko 梁与 Euler-Bernouli 梁的自由振动特性对比[J]．振动与冲击，2022，41(24) ：33-40．
JING Jie，MAO Xiaoye DINGHu， CHEN Liqun．Comparison of free vibration characteristics between post buckling Timoshenko beam and Euler Bernouli beam under axial force[J]．Journal of vibration and shock，2022，41(5)：228-234.
[17] 陈庆远，李 静，方鹏亚，裴世勋，刘双燕，苏毅．扭转弹簧约束复合材料层压梁的自由振动[J]．振动与冲击，2023，42(13) ：170-176.
CHEN Qingyuan，LI Jing，FANG Pengya，PEI Shixun，LIU Shuangyan，SU Yi．Free transverse vibration of composite laminated beam restrained by torsion springs[J]．Journal of vibration and shock，2023，42(13) ：170-176.
[18] VLASOV V Z．Thin-Walled Elastic Beams[M]． Israel Program for Scientific Translations，Jerusalem，1961.
[19] ZHANG W F．Plate-beam Theory for Thin-Walled Structures，Research Report，Northeast Petroleum University， Daqing，China，2015.
[20] ZHANG W F．Energy variational model and its analytical solutions for the elastic flexural-torsional buckling of I-beams with concrete-filled steel tubular flanges, in: Proceedings of the 8th International Symposium on Steel Structures[C]//. Korea, 2015, 1100-1108．
[21] 张文福，严威，刘迎春．基于板-梁理论的集中荷载下带侧向弹性支撑矩形钢管混凝土翼缘工字形梁的弯扭屈曲分析 [J]． 建筑钢结构进展， 2021， 23，61-70．
ZHANG Wenfu，YAN Wei，LIU Yingchun．Lateral torsional buckling analysis of rectangular steel tube concrete flange I-shaped beams with lateral elastic support under concentrated load based on plate beam theory [J]. Progress in Building Steel Structures，2021， 23， 61-70．
[22] 张文福．钢结构平面外稳定理论[M]．武汉：武汉理工大学出版社，2019．
ZHANG Wenfu．Out of plane stability theory of steel structures [M]. Wuhan: Wuhan University of Technology Press，2019．
[23] ZHANG W F，Gardner L， Wadee M A， Zhang Minghao．Analytical solutions for the inelastic lateral‑torsional buckling of I‑Beams under pure bending via Plate‑Beam theory[J]．International Journal of Steel Structures，2018．
[24] BECQUE J．The Interaction of Local and Overall Buckling of Cold-Formed Stainless Steel Columns [D]．The University of Sydney Australia，2008.
[25] HUANG B， ZHANG W F．Local-overall interactive buckling of high strength steel welded I-section columns under axial compression[J]． Thin-walled structure，2020， 157：106964．
PDF(1172 KB)
