分数三参数流体模型黏弹性材料的阻尼性能分析

Damping property of viscoelastic materials described by fractional derivative three-parameter fluid

在一个应力循环中,黏弹材料阻尼特性主要体现在耗散柔量的相关项。在经典三参数黏弹性模型的基础上,采用Abel粘壶单元替代传统的牛顿粘壶单元,建立分数导数黏弹性三参数流体模型及其本构方程,并在频域内对反映黏弹性材料阻尼性能的复柔量、内摩擦角、阻尼比值等参量进行讨论。结果表明:分数微分算子的阶数能明显影响服从分数阶三参数流体模型黏弹性材料的储能柔量和损耗柔量的变化曲线,其耗散率会随着分数阶数的减小发生显著上升,而材料的内摩擦角曲线在不同的分数阶数下,随频率几乎不发生改变。

In a stress cycle of viscoelastic materials,the damping properties are mainly reflected by the related terms of dissipative compliance.Based on the classic three-parameter viscoelastic model,the Abel sticky cell is used to replace the traditional Newtonian viscous cell.The constitutive equation of the viscoelastic three-parameter fluid model with fractional derivative is founded and the damping performance of the viscoelastic material is studied.Parameters such as complex compliance,friction angle,and damping ratio are analyzed in the frequency domain.Conclusion:The order of the different fractional operators can significantly affect the energy and loss compliance of the viscoelastic material obeying the fractional three-parameter fluid model,and its dissipation rate curves will increase significantly when the fractional order decreases.The friction angle of the material is almost unchanged with frequency under different fractional orders.