基础竖向周期激励下GFRP圆弧拱面内动力稳定性实验研究

吴涛波; 刘爱荣

doi:10.6052/j.issn.1000-4750.2021.05.S044

基础竖向周期激励下GFRP圆弧拱面内动力稳定性实验研究

doi: 10.6052/j.issn.1000-4750.2021.05.S044

吴涛波,
刘爱荣^,

广州大学风工程与工程振动研究中心，广东，广州 510006

基金项目: 国家自然科学基金项目(51878188)；高等学校学科创新引智计划项目(111计划D21021)；广州市科技计划项目(20212200004)；中国工程院战略咨询重点项目(2021-XZ-37)

详细信息

作者简介:
吴涛波(1997−)，男，江西人，硕士生，主要从事新型桥梁结构的静动力稳定性研究(E-mail: 1014451495@qq.com)

通讯作者:
刘爱荣(1972−)，女，山西人，教授，博士，主任，主要从事新型桥梁结构静动力稳定性研究(E-mail: liuar@gzhu.edu.cn)

中图分类号: TU311.2
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- 被引次数: 0
出版历程
- 收稿日期: 2021-05-29
- 修回日期: 2022-03-09
- 网络出版日期: 2022-05-06
- 刊出日期: 2022-06-06

EXPERIMENTAL STUDY ON IN-PLANE DYNAMIC STABILITY OF GFRP CIRCULAR ARCH UNDER A VERTICAL HARMONIC BASE EXCITATION

WU Tao-bo,
LIU Ai-rong^,

Research Center for Wind Engineering and Engineering Vibration, Guangzhou University, Guangzhou, Guangdong 510006, China

摘要

摘要: 该文为探究铺层角度对基础竖向激励下GFRP圆弧拱平面内动力稳定性能的影响，开展了系统的实验研究。设计了6组不同铺层角度的圆弧拱试件，利用TIRA激振器模拟输出基础竖向周期激励，采用NDI三维动态采集仪采集圆弧拱的竖向动位移，根据测得拱的面内自由振动响应，分别通过快速傅里叶变换和自由衰减法获得拱的自振频率和阻尼比。通过扫频实测了GFRP拱的动力不稳定域边界，并与有限元计算结果进行对比，基本吻合。研究表明：当外部频率约为结构自身频率两倍时，结构会出现激烈的面内反对称振动现象，即为参数共振失稳；当激励加速度小于临界激发加速度时，拱处于定态振动；外激励大于临界激发加速度时，GFRP拱出现参数振动，并且随着加速度的增大，拱的振动愈发激烈；随着铺层角度的增大，拱的自振频率和临界激发加速度逐渐减小，阻尼比与不稳定域范围逐渐增大。
- GFRP圆弧拱 /
- 基础竖向激励 /
- 周期荷载 /
- 动力失稳 /
- 参数共振 /
- 铺层角度
Abstract: The purpose of this study is to investigate the dynamic stability of GFRP circular arches with different lay-up angles under vertical excitations. Thusly, a systematic experimental study is performed. Six groups of circular arches with different lamination are designed, the vertical periodic vibration of foundation was simulated by applying TIRA series vibrator. The vertical displacement of circular arch was collected by NDI 3D dynamic acquisition instrument. According to the displacement data, free vibration frequency and damping ratio of the arch are obtained by fast Fourier transform and free attenuation method. The boundary of dynamic instability region of GFRP arch was measured by frequency sweep. The experimental results were compared with the finite element results, and the results show that when the external load frequency is about 2 times of the natural frequency of the structure, the structure has an intense in-plane antisymmetric parametric resonance. When the excitation acceleration is less than the critical excitation acceleration, the structure will not be unstable. The greater is the acceleration of external excitation, the easier does the parameter resonance phenomenon occur. With the increase of the lamination angle, the structural frequency and critical excitation acceleration decreases, and the damping ratio and the range of instability region increase gradually.
- GFRP circular arch /
- vertical excitation of foundation /
- periodic load /
- dynamic instability /
- parametric resonance /
- layer angle

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图 1 拱脚夹具及加载装置

Figure 1. Support lofting and loading device

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图 2 有限元模型

Figure 2. Finite element model

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图 3 有限元位移时程图

Figure 3. Finite element displacement time history diagram

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图 4 自由振动曲线

Figure 4. Free vibration curve

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图 5 20%、50%、80%激发力下扫频图

Figure 5. Frequency sweep back and forth under 20%, 50%, 80% exciting force

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图 6 动力不稳定域有限元与实验对比图

Figure 6. Comparison between finite element and experimental dynamic instability domain

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图 7 不同铺层角的不稳定域对比图

Figure 7. Comparison of instability domain with different lamination angles

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表 1 基本力学性能数据

Table 1. Basic mechanical property data

弹性模量E₁/GPa	弹性模量E₂/GPa	剪切模量G₁₂/GPa	剪切模量G₂₃/GPa	泊松比μ₁₂	泊松比μ₂₃
32.632	7.451	2.879	1.698	0.3	0.4

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表 2 试件设计参数

Table 2. Design parameters of test piece

工况组	矢跨比	铺层数	跨径/ mm	截面高度/mm	截面宽度/mm	铺层设计
1	1/7	6	800	0.9	20	[0]₆
2	1/7	6	800	0.9	20	[±15]₃
3	1/7	6	800	0.9	20	[±30]₃
4	1/7	6	800	0.9	20	[±45]₃
5	1/7	6	800	0.9	20	[±60]₃
6	1/7	6	800	0.9	20	[±75]₃

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表 3 自振频率及模态测试结果

Table 3. Natural frequency and modal test results

分析方法	有限元法		OMA 分析		误差/(%)
分析方法	自振频率	理论一阶振型	自振频率	实测一阶振型	误差/(%)
[0]₆	14.55	面内反对称	14.55	面内反对称	0.00
[±15]₃	13.34	面内反对称	13.39	面内反对称	0.39
[±30]₃	10.50	面内反对称	10.41	面内反对称	−0.89
[±45]₃	7.83	面内反对称	7.41	面内反对称	−5.35
[±60]₃	6.89	面内反对称	7.03	面内反对称	2.00
[±75]₃	6.88	面内反对称	7.02	面内反对称	2.04

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表 4 阻尼比测试结果

Table 4. Test results of damping ratio

分析方法	自由衰减法阻尼比/(%)	OMA分析阻尼比/(%)	误差/(%)
[0]₆	0.3562	0.3621	1.63
[±15]₃	0.4168	0.4223	1.30
[±30]₃	0.5381	0.5584	3.64
[±45]₃	0.7453	0.7572	1.57
[±60]₃	0.7513	0.7674	2.09
[±75]₃	0.9142	0.9379	2.53

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表 5 有限元边界频率与实测边界频率对比

Table 5. Comparison with the measured critical frequency and finite element critical frequency

激振力大小/(%)	上边界			下边界
激振力大小/(%)	实验值/Hz	有限元值/Hz	误差/(%)	实验值/Hz	有限元值/Hz	误差/(%)
40	29.14	28.93	0.72	29.14	29.14	0.00
50	29.07	28.78	0.99	29.19	29.23	0.12
60	29.05	28.67	1.31	29.22	29.29	0.24
70	28.97	28.62	1.21	29.27	29.36	0.31
80	28.92	28.59	1.14	29.33	29.43	0.34
90	28.9	28.57	1.15	29.35	29.47	0.39

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参考文献(19)

[1]	陈海龙, 范华林, 金丰年. 爆炸荷载作用下地下拱结构动力分析[J]. 工程力学, 2013, 30(4): 169 − 174. doi: 10.6052/j.issn.1000-4750.2011.11.0760 Chen Hailong, Fan Hualin, Jin Fengnian. Forced vibration of underground clamped arch under blast load [J]. Engineering Mechanics, 2013, 30(4): 169 − 174. (in Chinese) doi: 10.6052/j.issn.1000-4750.2011.11.0760
[2]	钟子林, 刘爱荣. 基础竖向多频参数激励下圆弧拱平面内动力失稳研究[J]. 工程力学, 2022, 39(4): 53 − 64. doi: 10.6052/j.issn.1000-4750.2021.07.ST06 Zhong Zilin, liu Airong. Studies on in-plane dynamic instability of vertically and parametrically base multi-frequency excited circular arches [J]. Engineering Mechanics, 2022, 39(4): 53 − 64. (in Chinese) doi: 10.6052/j.issn.1000-4750.2021.07.ST06
[3]	Bolotin. Dynamic stability of elastic systems [M]. Beijing: Higher Education Press, 1960.
[4]	Humphrey J S. On the adequacy of energy criteria for dynamic buckling of arches [J]. AIAA J, 1966, 4: 921 − 923. doi: 10.2514/3.3568
[5]	Humphreys J S. On dynamic plastic deformation of shallow circular arches [J]. AIAA J, 1966, 4: 926 − 928. doi: 10.2514/3.3571
[6]	Simitses G J. Dynamic stability of suddenly loaded structures [M]. New York: Springer-Verlag, 1990.
[7]	王连华, 易壮鹏, 张辉. 周期荷载作用下几何缺陷拱的动力稳定性[J]. 湖南大学学报(自然科学版), 2007(11): 16 − 19. Wang Lianhua, Yi Zhuangpeng, Zhang Hui. Dynamic stability of arch with the geometrical imperfection subject to the periodic load [J]. Journal of Hunan University (Natural Science Edition), 2007(11): 16 − 19. (in Chinese)
[8]	Pi Y L, Bradford M A, Liang S G. Elasto-dynamic instability of shallow pin-ended steel arches under central step loading [J]. Advanced Steel Construction, 2009, 5(4): 465 − 322.
[9]	Pi Y L, Bradford M A, Qu W L. Energy approach for dynamic buckling of shallow fixed arches under step loading with infinite duration [J]. Structural Engineering and Mechanics, 2010, 35(5): 555 − 570. doi: 10.12989/sem.2010.35.5.555
[10]	Pi Y L, Bradford M A. Nonlinear dynamic buckling of pinned-fixed shallow arches [J]. Nonlinear Dynamics, 2013, 73(3): 1289 − 1306. doi: 10.1007/s11071-013-0863-2
[11]	Pi Y L, Bradford M A. In-plane stability of preloaded shallow arches against dynamic snap-through accounting for rotational end restraints [J]. Engineering Structures, 2013, 56: 1496 − 1510. doi: 10.1016/j.engstruct.2013.07.020
[12]	吴玉华. 大跨度钢管混凝土拱桥抗震性能及动力稳定研究[D]. 杭州: 浙江大学, 2009. Wu Yuhua. Study on seismic performance and dynamic stability of long span steel tube concrete arch bridge [D]. Hangzhou: Zhejiang University, 2009. (in Chinese)
[13]	Liu A, Lu H, Fu J, et al. Analytical and experimental studies on out-of-plane dynamic instability of shallow circular arch based on parametric resonance [J]. Nonlinear Dynamics, 2017, 87(1): 677 − 694. doi: 10.1007/s11071-016-3068-7
[14]	Liu A, Yang Z, Bradford M A, et al. Nonlinear dynamic buckling of fixed shallow arches under an arbitrary step radial point load [J]. Journal of Engineering Mechanics, 2018, 144(4): 04018012.
[15]	Liu A, Yang Z, Lu H, et al. Experimental and analytical investigation on the in-plane dynamic instability of arches owing to parametric resonance [J]. Journal of Vibration and Control, 2018, 24(19): 4419 − 4432. doi: 10.1177/1077546317726210
[16]	Zhong Z, Liu A, Pi Y L, et al. In-plane dynamic instability of a shallow circular arch under a vertical-periodic uniformly distributed load along the arch axis [J]. International Journal of Mechanical Sciences, 2020, 189: 105973. doi: 10.1016/j.ijmecsci.2020.
[17]	Zhong Z, Liu A, Fu J, et al. Analytical and experimental studies on out-of-plane dynamic parametric instability of a circular arch under a vertical harmonic base excitation [J]. Journal of Sound and Vibration, 2021, 500: 116011. doi: 10.1016/j.jsv.2021.116011
[18]	卢汉文. 圆弧拱平面外稳定性研究[D]. 广州: 广州大学, 2018. Lu Hanwen. Research out-of-plane buckling of circular arches [D]. Guangzhou: Guangzhou University, 2018. (in Chinese)
[19]	R·克拉夫, J·彭津. 结构动力学[M]. 2版. 北京: 高等教育出版社, 2006. Clough Ray W, Penzien Joseph. Dynamics of structures [M]. 2th ed. Beijing: Higher Education Press, 2006. (in Chinese)