结构阻尼与材料阻尼的关系

Relationship between structural damping and material damping

针对固体材料在弹性阶段的内阻尼,采用材料粘弹性本构关系,通过有限单元法建立了考虑剪切变形影响的杆单元阻尼矩阵,得到了材料拉压粘滞系数和剪切粘滞系数之间的关系。我们可以通过实验测试材料的损耗因子或粘滞阻尼系数(材料阻尼),像结构质量矩阵、刚度矩阵一样通过比较确切的计算得到弹性阶段结构内阻尼的阻尼矩阵(结构阻尼),而且此阻尼矩阵既基于材料阻尼实验测试,又便于数学处理,且物理意义明确。其次,本文分析了材料阻尼对结构阻尼比影响,得到了材料损耗因子与结构模态阻尼比间的关系,并通过10层钢筋混凝土剪切型框架结构进一步给出了具体的数值结果。

The paper mainly studies the linear inner-damping relationship of solid material and structures. First of all, based on the constitution relationship of viscoelastic material and finite element methods, the damping matrixes of structural elements considering the effect of shear deformation are deduced and also the relation between the viscous coefficient and shear viscous coefficient is discovered. Therefore, through the measurement for loss tangent or the viscous coefficient of material, the damping matrix of structures can be established accurately and also conveniently similar to the mass and stiffness matrixes of structures with clear physical meaning. And, the influence of material damping on structural damping is analyzed and the relationship of the loss tangent of material and the damping ratios of structural modes is obtained. The numerical results for the relationship of the loss tangent of material and the damping ratios of structural modes are given for a shear-type reinforced concrete frame with ten stories.