基于双折线抗力模型的空爆荷载梁式构件振动位移研究

耿少波; 陈佳龙; 赵洲; 牛艳伟

doi:10.11883/bzycj-2021-0524

基于双折线抗力模型的空爆荷载梁式构件振动位移研究

doi: 10.11883/bzycj-2021-0524

耿少波^{1, 2,},
陈佳龙¹,
赵洲¹,
牛艳伟^2, ,

1.
中北大学理学院土木工程学科部，山西太原 030051
2.
长安大学公路大型结构安全教育部工程研究中心，陕西西安 710064

基金项目: 国家自然科学基金（51408558）；旧桥检测与加固技术交通运输行业重点实验室（长安大学）开放基金(300102212516)

详细信息

作者简介:
耿少波（1982－　），男，博士，副教授，gengshaobo@nuc.edu.cn

通讯作者:
牛艳伟（1981－　），男，博士，副教授，niuyanwei@chd.edu.cn

中图分类号: O383.2
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- 被引次数: 0
出版历程
- 收稿日期: 2021-12-21
- 修回日期: 2022-07-08
- 网络出版日期: 2022-08-10
- 刊出日期: 2022-10-31

A study on vibration displacements of beam members under air blast loading based on the bilinear resistance model

GENG Shaobo^{1, 2
,},
CHEN Jialong¹,
ZHAO Zhou¹,
NIU Yanwei^{2
, ,}

1.
Department of Civil Engineering, School of Science, North University of China, Taiyuan 030051, Shanxi, China
2.
Research Center of Highway Large Structure Engineering on Safety, Ministry of Education, Chang’an University, Xi’an 710064, Shaanxi, China

摘要

摘要: 为研究双折线抗力模型对空爆荷载梁式构件振动位移的影响，提出了柔性、刚性两类梁式构件正向弹塑性振动及回弹阶段弹塑性振动的分析法。应用等效单自由度法建立了各阶段振动方程并依据不同的初始条件推导出了各阶段的理论解。采用此理论解和代表性塑性强化系数，开展了双折线抗力模型中不同塑性强化程度对两类梁式构件正向弹塑性振动及回弹阶段弹塑性振动位移的典型工况验证。研究结果表明：基于双折线抗力模型位移理论解的适用范围更广；随着双折线抗力模型塑性强化系数的增大，两类梁式构件的最大弹塑性位移、残余变形均逐渐减小，且残余变形降低程度高于最大弹塑性位移；塑性强化系数增大到一定程度，梁式构件回弹阶段将出现塑性振动位移，进一步降低残余变形，无塑性回弹位移的理想弹塑性抗力模型会高估空爆荷载下梁式构件的残余变形。
- 双折线抗力模型 /
- 空爆荷载 /
- 弹塑性位移 /
- 残余变形
Abstract: In order to study the influence of bilinear resistance model on the vibration displacement of beam members under air blast loading, both the theoretical elast-plastic displacement solutions of the flexible and rigid members in forward and rebound stages were deduced, respectively. According to the relationship between blast duration and elastic duration from static position to maximum elastic displacement for members, the vibration situations could be divided into elastic forced vibration, elastic free vibration, plastic forced vibration, plastic free vibration, elastic rebound and plastic rebound. The equivalent single degree of freedom method was used to establish the vibration equations of each stage and the theoretical solutions of each stage were derived for different initial conditions. The method of the general solution plus the special solution was applied to solve each differential equation. Based on the theoretical solutions and the representative plastic strengthening coefficient, the elastoplastic vibration displacements of two types of beam members under different plastic strengthening degrees in the bilinear resistance model were verified under typical calculation cases. The corresponding complete vibration curves were finished for comparative analysis. The influence of the degree of plastic strengthening on the vibration representative value was analyzed. The results show that the displacement theoretical solution based on the bilinear resistance model has a wider range of application. With the increase of plastic strengthening coefficient of the bilinear resistance model, the maximum elastic-plastic displacement and residual deformation of the two types of beam members decrease gradually, and the reduction degree of residual deformation is higher than that of the maximum elastic-plastic displacement. When the plastic strengthening coefficient increases to a certain extent, the plastic vibration displacement will appear in the rebound stage of the beam members, further reducing the residual deformation. Compared with the bilinear resistance model, the elastic-perfectly plastic resistance overestimates the residual deformation of beam members under air blast loading.
- bilinear resistance model /
- air blast loading /
- elastic-plastic displacement /
- residual deformation

HTML全文

图 1 双折线抗力模型等效单自由度体系

Figure 1. Equivalent single-degree-of-freedom system of the bilinear resistance model

下载: 全尺寸图片幻灯片

图 2 柔性构件（ωt_i=0.2）弹塑性振动时程曲线

Figure 2. Time history curves of elastoplastic vibration for flexible members (ωt_i=0.2)

下载: 全尺寸图片幻灯片

图 3 刚性构件（ωt_i=2.0）弹塑性振动时程曲线

Figure 3. Time history curves of elastoplastic vibration for rigid members (ωt_i=2.0)

下载: 全尺寸图片幻灯片

图 4 塑性回弹状态与塑性强化系数的关系

Figure 4. Relationship between plastic rebound state and plastic hardening coefficient

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表 1 相对于理想弹塑性抗力模型的差异性结果

Table 1. Difference results relative to ideal elastoplastic resistance model

α	柔性构件				刚性构件
	β=2		β=5		β=2		β=5
	γ_β/%	γ_r/%	γ_β/%	γ_r/%	γ_β/%	γ_r/%	γ_β/%	γ_r/%
0.01	−0.5	−1.4	−1.2	−2.5	−0.5	−1.5	−1.2	−2.6
0.05	−1.0	−6.9	−5.2	−12.7	−1.5	−7.1	−5.6	−13.0
0.10	−2.0	−13.6	−9.4	−31.1	−2.5	−13.9	−10.0	−30.5
0.20	−3.5	−30.1	−15.6	−60.7	−4.0	−30.4	−16.6	−61.2

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