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浙江大学学报(工学版)  2019, Vol. 53 Issue (3): 503-511    DOI: 10.3785/j.issn.1008-973X.2019.03.011
土木工程     
基于Zig-zag理论的波形钢腹板梁自由振动分析
胡霖远1(),陈伟球1,张治成2,徐荣桥2,*()
1. 浙江大学 航空航天学院,浙江 杭州 310027
2. 浙江大学 建筑工程学院,浙江 杭州 310058
Free vibration analysis of concrete beams with corrugated steel webs based on Zig-zag theory
Lin-yuan HU1(),Wei-qiu CHEN1,Zhi-cheng ZHANG2,Rong-qiao XU2,*()
1. School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China
2. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
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摘要:

根据波形钢腹板梁的特点,将波形钢腹板梁模拟为具有正交各向异性层的夹芯梁,并引入层间连续的Zig-zag位移假设和分层抛物线分布的横向切应力假设,基于混合能变分原理,建立波形钢腹板梁自由振动的Zig-zag理论. 该理论的横向切应力满足上、下表面为0以及层间连续条件,因此无需引入剪切修正系数. 导出波形钢腹板梁的频率方程,得到不同边界条件下的频率和振型. 与其他方法的对比表明该理论能够精确地预测波形钢腹板梁的动力学特性.

关键词: 波形钢腹板Zig-zag理论混合能变分原理自由振动频率振型    
Abstract:

Concrete beams with CSWs were idealized as sandwich beams with an orthotropic core, according to the characteristics of the corrugated steel web (CSW). The assumptions of a zig-zag displacement and a layer-wise parabolic distribution of the transverse shear stress were introduced to derive the governing equations for the free vibration of concrete beams with CSWs based on the variational principle of mixed energy. The transverse shear stress in the developed theory satisfied the traction-free condition at both top and bottom surfaces of the beam, as well as the continuity condition at the interfaces between adjacent layers. The shear correction factor is therefore not necessary. The frequency equation of the beam with CSWs was derived and solved analytically for the frequencies and corresponding mode shapes under various boundary conditions. Comparisons with other methods indicate that the present theory can accurately predict the dynamic behavior of such beams.

Key words: corrugated steel web    Zig-zag theory    variational principle of mixed energy    free vibration    frequency    mode shape
收稿日期: 2018-01-07 出版日期: 2019-03-04
CLC:  O 342  
通讯作者: 徐荣桥     E-mail: hulinyuan@zju.edu.cn;xurongqiao@zju.edu.cn
作者简介: 胡霖远(1993—),男,硕士生,从事组合梁理论研究. orcid.org/0000-0002-9453-2694. E-mail: hulinyuan@zju.edu.cn
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引用本文:

胡霖远,陈伟球,张治成,徐荣桥. 基于Zig-zag理论的波形钢腹板梁自由振动分析[J]. 浙江大学学报(工学版), 2019, 53(3): 503-511.

Lin-yuan HU,Wei-qiu CHEN,Zhi-cheng ZHANG,Rong-qiao XU. Free vibration analysis of concrete beams with corrugated steel webs based on Zig-zag theory. Journal of ZheJiang University (Engineering Science), 2019, 53(3): 503-511.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2019.03.011        http://www.zjujournals.com/eng/CN/Y2019/V53/I3/503

图 1  波形钢腹板(CSW)的几何形状
图 2  CSW梁的原始截面和等效截面
n f/Hz δ/% f/Hz δ/%
有限元 本文方法 经典梁理论
1 17.191 17.218 0.16 19.950 16.05
2 51.768 51.904 0.26 79.800 54.15
3 88.945 89.264 0.36 179.550 101.90
4 126.248 126.572 0.26 319.200 152.80
5 162.577 163.840 0.78 498.749 206.80
6 199.196 201.377 1.10 718.199 260.50
7 235.990 239.461 1.47 977.549 314.20
8 273.130 278.316 1.90 1 276.800 367.50
表 1  简支(SS)波形钢腹板(CSW)梁自振频率
n f/Hz δ/% f/Hz δ/%
有限元 本文方法 经典梁理论
1 27.665 27.708 0.16 45.224 63.47
2 58.502 58.737 0.40 124.663 113.10
3 93.965 94.475 0.54 244.388 160.10
4 130.414 131.375 0.74 403.989 209.80
5 167.346 168.981 0.98 603.490 260.60
6 204.474 207.107 1.29 842.891 312.20
7 241.953 245.946 1.65 1 122.180 363.80
8 279.834 286.625 2.07 1 441.400 415.10
表 2  两端固支(CC)波形钢腹板梁自振频率
n f/Hz δ/% f/Hz δ/%
有限元 本文方法 经典梁理论
1 22.435 22.473 0.17 31.166 38.91
2 55.357 55.537 0.33 100.997 82.45
3 91.464 91.880 0.46 210.723 130.40
4 128.171 128.980 0.63 360.348 181.10
5 164.940 166.390 0.88 549.874 233.40
6 201.835 204.220 1.18 779.299 286.10
7 238.937 242.671 1.56 1 048.61 338.90
8 276.454 281.931 1.98 1 357.84 391.20
表 3  固支-简支(CS)波形钢腹板梁自振频率
n f/Hz δ/% f/Hz δ/%
有限元 本文方法 经典梁理论
1 6.593 6.599 0.10 7.107 7.80
2 30.762 30.913 0.49 44.539 44.79
3 67.243 67.647 0.60 124.713 85.47
4 104.546 105.350 0.77 244.384 133.70
5 142.189 143.544 0.95 403.989 184.10
6 179.391 181.642 1.26 603.490 236.40
7 216.701 220.171 1.60 842.890 289.00
8 254.029 259.211 2.04 1 122.180 341.80
表 4  固支-自由(CF)波形钢腹板梁自振频率
图 3  波形钢腹板梁的前3阶振型模态
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