组合梁等效阻尼比的两种计算方法及对比研究

Comparative study of two calculation methods for equivalent damping ratios of composite beams

为了确定钢-混凝土组合梁等效阻尼比的合理取值,提出组合梁各阶振型等效阻尼比的两种计算方法。基于复阻尼理论和各阶振型单个振动周期内阻尼耗能相等的原则,推导了组合梁各阶振型的等效阻尼比,在形式上为组合梁两种材料的阻尼比关于刚度的加权平均。基于共振状态下结构响应与阻尼比之间的关系,对组合梁各部分材料赋予Rayleigh阻尼和整体等效阻尼比,根据各阶模态变形情况施加对应简谐荷载激励,得到两种情况下组合梁的共振幅值,由此推导出组合梁的等效振型阻尼比。按照以上两种方法,对一根钢-混凝土组合梁进行数值计算,并对计算结果进行分析比较。结果表明:前者基于能量原理,较为合理地反映了组合梁的振动耗能特性,可以应用于不考虑界面滑移耗能时,组合梁各阶振型阻尼比的计算;后者求解思路较明确,但其基本假定与实际情况存在差异,且在计算中激励方式不易确定,故基于能量法的分析方法更有优势;阻尼的取值对组合梁动力响应的影响较大。

To simplify the dynamic analysis of composite beams,two calculation methods for equivalent damping ratios of the various vibration modes were presented.Based on complex damping theory and the principle of the equality of energy dissipation in single vibration cycle of each vibration mode,equivalent damping ratio was derived through the first method.It has the form of the weighted average of the damping ratios based on stiffness of the two elements of composite beams.Based on the relationship between structural response and damping ratios in resonance conditions,another expression of equivalent damping ratio was derived through the second method.Based on the two proposed calculation methods,numerical analysis was conducted and the results were compared.The conclusions of this paper are listed as follows: Based on the principle of energy,the first method reflects the characteristics of energy consumption of vibration reasonably.It could be used for the calculation of equivalent damping ratios of the various vibration modes when the slip on the interface of the composite beam could be neglected.The solution idea of the second method is clear,but divergences between its basic assumption and the actual situation and flaw in its incentive method exist.So,in terms of accuracy and applicability,the first method is more advantageous.In addition,the damping values have great impact on the dynamic response of composite beams.