等效复阻尼模型的时域数值计算方法

Time-domain numerical calculation method of equivalent complex damping model

复阻尼时域运动方程通解含有发散子集,导致基于复阻尼模型的时域数值计算结果不能收敛。针对复阻尼模型的时域发散问题,分别在单变量粘弹性本构模型、双变量粘弹性本构模型的基础上,推导了相应的等效复阻尼模型,构建了频域上与复阻尼模型本构关系等效的时域运动方程,并利用高斯精细积分法推导了时域数值计算公式。数值计算结果表明:等效复阻尼模型的时域计算结果是稳定收敛的,可有效避免复阻尼运动方程时域数值解中的发散现象;基于单变量粘弹性本构模型的阻尼模型计算量少、计算精度较低,仅适用于简化的层模型结构;基于双变量粘弹性本构模型的阻尼模型计算过程较为复杂、计算精度更高,适用于更真实的杆系结构。

There is divergent subset in the general solution of complex damping time-domain motion equation.So,the time-domain numerical results are divergent based on complex damping model.For divergence problem of complex damping model,the new time-domain motion equation is constructed on the basis of the constitutive relation of viscoelastic materials.It is equivalent to constitutive relation of complex damping frequency-domain model,an equivalent damping model is proposed.The corresponding time-domain numerical calculation expressions are got by Gauss precise integration method.The cases show that the time-domain calculation results are stably convergent based on equivalent complex damping model.The time-domain divergent phenomenon of complex damping model is effectively avoided.The calculation time consumption of equivalent damping model is little based on single variable viscoelastic constitutive model,but its calculation precision is low.So,it is only applied to structures using simplified story model.The calculation process of equivalent damping model is relatively complex based on double variable viscoelastic constitutive model.Its calculation time consumption is large,but its calculation precision is high.It can be applied to complex skeletal structures.