含多裂纹（群）钢筋混凝土梁的自由振动研究

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (19) : 109-114.

论文

陈得良1,2，汪亚运3，吝国胜3，邱泽彬3，雷伟3

作者信息 +

Free vibration of a RC beam with multi-crack

CHEN Deliang1,2, WANG Yayun3, LIN Guosheng3, QIU Zebin3, LEI Wei3

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文章历史 +

摘要

基于Euler-Bernoulli梁理论，利用Hamilton变分原理，在考虑纵向钢筋对裂纹约束效应以及裂纹区应力集中效应的基础上，建立了含多裂纹（群）钢筋混凝土梁模型，然后通过Taylor级数展开的数值方法，得到了含多裂纹（群）钢筋混凝土简支梁的动力学特征方程。并利用数值分析，研究了裂纹深度、裂纹密集度以及钢筋约束效应对钢筋混凝土梁固有频率的影响。研究表明，含裂纹混凝土梁在考虑钢筋约束效应的影响下，其固有频率大于不考虑钢筋约束效应时的固有频率，且随着裂纹深度的扩展、裂纹数目的增加以及裂纹（群）位置的变化都会对钢筋混凝土梁结构的固有频率产生影响。

Abstract

Based on Euler-Bernoulli beam theory, using Hamilton variational principle, the dynamic model of a reinforced concrete (RC) beam with multi-crack was established considering constraint effect of longitudinal steel bars on cracks and stress concentration effect in crack zone. The vibration characteristic equation for a simple supported RC beam with multi-crack was derived with Taylor series expansion numerical method. Using numerical analysis, influences of crack depth, crack density and steel bars’ constraint effect on natural frequencies of the RC beam were studied. The results showed that natural frequencies of the cracked RC beam considering steel bars’ constraint effect are larger than its ones not considering steel bars’ constraint effect; crack depth extending, increase in crack density and variation of crack position all affect natural frequencies of the cracked RC beam.

导出引用

陈得良1,2，汪亚运3，吝国胜3，邱泽彬3，雷伟3. 含多裂纹（群）钢筋混凝土梁的自由振动研究[J]. 振动与冲击, 2019, 38(19): 109-114

CHEN Deliang1,2, WANG Yayun3, LIN Guosheng3, QIU Zebin3, LEI Wei3. Free vibration of a RC beam with multi-crack[J]. Journal of Vibration and Shock, 2019, 38(19): 109-114

参考文献

[1] 王丹生, 朱宏平. 基于弯曲弹簧模型的裂纹混凝土梁动力特性分析[J]. 世界地震工程. 2006, 22(1): 45-48.
Wang Dan-Sheng，Zhu Hong-Ping. Dynamic characteristics of concrete beam s with a crack based on a bending spring model[J]. World Earthquake Engineering. 2006, 22(1): 45~48.
[2] E. Hamed, Y. Frostig . Free vibrations of cracked prestressed concrete beams. Engineering Structures .2004.26(11): 1611~1621
[3] Zsolt Huszár. Vibrations of cracked reinforced and prestressed concrete beams. Architecture and Civil Engineering .2008, 6( 2):155 ~164.
[4] 罗青松. 含裂缝的预应力钢筋混凝土梁固有频率的有限元分析[J]. 华中科技大学学报(城市科学版), 2006, 23(z2): 83~85.
Luo Qing-Song. Finite Element Analysis on prestressed reinforced concrete beam with crack[J]. Journal of HUST(urban Science Edition），2006，23(z2)：83-85.
[5] 易伟建, 段素萍. 带裂缝钢筋混凝土梁的非线性振动特征识别[J]. 振动与冲击, 2008, 27(3): 26~29/41.
Yi Wei-Jian, Duan Su-Ping. Identification of nonlinear dynamical characteristics of cracked reinforced concrete beam[J]. Journal of Vibration and Shock. 2008, 27(3): 26~29/41.
[6] Roberto Capozucca. A reflection on the application of vibration tests for the assessment of cracking in PRC/RC beams[J]. Engineering Structures. 2013, 48: 508~518.
[7] 李学平, 余志武. 含多处裂纹梁的振动分析[J]. 应用力学学报, 2007, 24(1): 66~68.
Li Xue-Ping, Yu Zhi-Wu. Vibration Analysis to Muttipl Cracked Cracked Beam[J]. Chinese Journal of Applied Mechanics, 2007, 24(1): 66~68.
[8] S. Christides, A.D.S. Barr. One-dimensional theory of cracked Bernoulli-Euler beams [J]. International Journal of Mechanical Sciences, 1984, 26(84): 639~648.
[9] D Chen, F Liu. Free Vibration of a Single-Edge Cracked RC Beam Strengthened with FRP[J]. Journal of Engineering Mechanics, 2014, 140(6): 682~694.
[10] M. H. H. Shen, C. Pierre. Free vibrations of beams with a single-edge crack [J]. Journal of sound and vibration. 1994, 170(2): 237~259.