基于分数阶黏弹性模型的混凝土阻尼频率相关性研究

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (15) : 201-208.

论文

梅生启1,2,李韶华1,李鹏飞3,徐浩然2,张元昊2

作者信息 +

Fractional order viscoelastic model reflecting correlation between concrete material damping and load frequency based on multi-sample data

MEI Shengqi1,2, LI Shaohua1, LI Pengfei3, XU Haoran2, ZHANG Yuanhao2

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文章历史 +

摘要

阻尼作为反映耗能特征的参数，对动态荷载下结构响应有重要影响。针对强迫振动条件下循环荷载形式对混凝土材料阻尼的影响，本文结合普通混凝土试验数据并收集152组文献测试结果，详细分析了混凝土材料阻尼与荷载频率的相关性。发现在低频范围时（<3.0Hz），混凝土材料阻尼均随荷载频率增大呈非线性降低，与经典整数阶黏弹性模型计算规律不符。基于分数阶微积分理论对经典整数阶模型的导数阶数进行改进（0<导数阶数<1），发现修正后分数阶模型能够更好反映混凝土材料阻尼与循环荷载频率在低频时的非正相关性，导数阶数小于0.12，表明混凝土呈现弱黏弹性效应，为混凝土动态性能分析提供一种新的模型选择和参数参考。
关键词：混凝土阻尼；频率相关性；分数阶微积分；黏弹性理论

Abstract

As a parameter reflecting the energy dissipation characteristics of a structure, damping has an important effect on dynamic response analysis. For the damping frequency coherence of concrete under the condition of forced vibration, there is no unified conclusion. In this paper, the damping data of 152 groups of concrete materials are firstly analyzed. It is found that in the range <3.0Hz, the damping of concrete materials decreases nonlinearly with the increase of frequency, but the statistical results are discrete. Then the classical viscoelastic model and fractional viscoelastic model were used to analyze the frequency correlation of energy dissipation. In order to determine the effectiveness of fractional order model, the test data of ordinary concrete are further compared and analyzed. It is found that the experimental results show that the damping nonlinearity decreases with the increase of frequency, and the fractional-order model can better reflect the energy dissipation characteristics of concrete materials, which provides a reference for the application of fractional-order calculus in the dynamic performance analysis of concrete.
Keyword: Concrete material damping; Frequency correlation; Fractional calculus; Viscoelastic theory

导出引用

梅生启1,2,李韶华1,李鹏飞3,徐浩然2,张元昊2. 基于分数阶黏弹性模型的混凝土阻尼频率相关性研究[J]. 振动与冲击, 2022, 41(15): 201-208

MEI Shengqi1,2, LI Shaohua1, LI Pengfei3, XU Haoran2, ZHANG Yuanhao2. Fractional order viscoelastic model reflecting correlation between concrete material damping and load frequency based on multi-sample data[J]. Journal of Vibration and Shock, 2022, 41(15): 201-208

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