基于分数阶黏弹性模型的混凝土阻尼频率相关性研究

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

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,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(<3.0 Hz),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。

As a parameter reflecting characteristics of energy dissipation,damping has an important impact on structural response under dynamic load.Here,aiming at effects of cyclic load form on concrete material damping under forced vibration,combined with ordinary concrete test data and 152 groups of literature test results,the correlation between concrete material damping and load frequency was analyzed in detail.It was shown that within low frequency range(<3.0 Hz),damping of concrete material decreases nonlinearly with increase in load frequency,it is inconsistent with the calculation law of classical integer order viscoelastic model.Based on the fractional calculus theory,the derivative order of the classical integer order model was improved(0<derivative order<1).It was shown that the modified fractional order model can better reflect the non-positive correlation between concrete material damping and cyclic load frequency in low frequency range;derivative order being less than 0.12 indicates concrete having weak viscoelastic effect;the study can provide a new model selection and parametric reference for concrete dynamic performance analysis.