带支撑广义Maxwell粘弹性阻尼耗能结构风振响应分析

Wind vibration response analysis of a generalized Maxwell viscoelastic damped energy dissipation structures with supports

工程中粘弹性阻尼器的安装通过支撑与结构进行连接,但在安装粘弹性阻尼器的耗能结构随机响应分析中,为了简化计算过程,将支撑的刚度看作无穷大或者忽略支撑刚度的影响。实际上,对支撑刚度的影响加以考虑更能符合工程实际。针对考虑支撑刚度影响的粘弹性阻尼耗能结构风振响应分析过程复杂的问题,提出了一种求解考虑支撑影响的广义Maxwell粘弹性阻尼耗能结构基于Davenport谱风振响应的简明解析解法。在广义Maxwell粘弹性阻尼器微分型本构模型基础上,给出了考虑支撑刚度的粘弹性阻尼器等效本构关系。将粘弹性阻尼器等效本构关系与结构运动方程联立,采用复模态法将其解耦,获得结构风振响应的统一表达式。将耗能结构在Davenport风速谱下的系列响应功率谱密度函数分解为频域响应函数与Davenport功率谱密度函数的乘积形式,基于随机振动理论中谱矩的定义,对响应功率谱密度函数积分后获得无积分项的系列响应谱矩表达式。在算例中通过与虚拟激励法计算结果对比,验证了所提解法的准确性,并分析了支撑刚度在耗能系统中的影响。

Viscoelastic dampers are connected to a structure by using supports during installation.In the analysis of the stochastic response of energy-consuming structures with viscoelastic dampers,the stiffness of the supports is often considered infinite or the influence of the support stiffness is often ignored in order to simplify the simulation process.In fact,it is more practical to consider the influence of brace stiffness.Aiming at the complicated process of wind-induced vibration response analysis of viscoelastic damping energy dissipation structures considering the influence of brace stiffness,a concise analytical solution based on Davenport spectrum for wind vibration response of generalized Maxwell viscoelastic damping energy dissipation structures considering brace stiffness is proposed.Based on the differential constitutive model of a generalized Maxwell viscoelastic damper,the equivalent constitutive relation of the viscoelastic damper considering support stiffness is presented.The equivalent constitutive relation of the viscoelastic damper is combined with the equation of the structural motion,and the complex mode method is used to decouple them,and the unified expression of the structural wind-induced response is obtained.The series response power spectral density function of the energy dissipation structure under Davenport wind speed spectrum is decomposed into the product form of frequency domain response function and Davenport power spectral density function.Based on the definition of spectral moment in random vibration theory,the expression of series response spectral moment without integral term is obtained after integrating the response power spectral density function.In the example,the accuracy of the proposed method is verified by comparing with the results of the virtual excitation method,and the influence of the support stiffness on the energy dissipation system is analyzed.