瑞利阻尼物理本质及参数对动力响应的影响

Physical essence and influence of model parameters on dynamic response of Rayleigh damping

为了研究瑞利阻尼模型的物理意义及模型参数对动力响应的影响,基于虚功方程推导瑞利阻尼的质量相关部分和刚度相关部分,利用解析和数值方法对比分析不同瑞利阻尼系数下的一维黏弹性杆件的动力响应.结果表明,瑞利阻尼质量相关部分反映了外部环境因素对振动体系的能量耗散作用;刚度相关部分反映了材料对动力响应的阻滞作用,表现为应力不仅与应变有关,而且与应变率相关.一维黏弹性振动响应解析解和有限元数值解对比分析表明,常规有限单元软件应力计算时,没有考虑应变率的贡献,导致计算应力和实际应力存在差异,计算应力不满足力边界条件.有限元应力计算误差随着瑞利阻尼系数和激励频率的增加而提高.

The influences of the physical meaning and model parameters of the Rayleigh damping model on the dynamic response were analyzed.The mass-related and stiffness-related items of Rayleigh damping model were derived based on the virtual work equation.The vibration response of one-dimensional viscoelastic rod with different Rayleigh damping coefficient was analyzed comparatively via analytical and numerical methods.The energy dissipation phenomenon caused by external environments can be reflected by mass-related section,while material＇s blocking effects on dynamic response can be reflected by stiffness-related item.The blocking effects mentioned above indicate that strain rate should be included in stress calculation except the strain item.Analytical and numerical methods were employed to analyze the vibration response of one-dimensional viscoelasticity. The comparison results show that numerical solutions differ with analytical ones in stress calculation,and the former without considering the contribution of strain rate to stress calculation can＇t meet the force boundary condition.The errors of stress calculated by the finite element method increase with the rise of Rayleigh damping coefficient and the exciting frequency.