广义Maxwell阻尼器高层结构随机风振响应解析法

Analytic method for random wind-induced response of high-rise structure with general Maxwell dampers

为解决设置广义Maxwell阻尼器的非定常耗能结构在随机风荷载作用下的随机响应采用传统方法比较繁琐及精度不高的问题,针对此类结构提出基于传递函数法的精确分析方法。首先,用微分积分混合方程组建立了结构的动力运动方程;其次用传递函数法及巴斯金相关函数的随机风振激励模型,获得了结构用第一振型表达的时域瞬态位移响应非扩阶解析解;然后,根据获得的解析解,运用随机振动方法获得了该类型耗能结构第一振型下的随机风振响应及楼层处等效静态风荷载设计取值的解析解,最后通过算例计算显示:设置阻尼器后结构的位移减少约36.7%,同时与数值方法计算结果完全吻合,证明了本文方法的优越性。由于采用巴斯金相关函数的随机风振激励模型,本文方法可以应用其他诸如地震、路面不平等激励下的振动响应。

An accurate analytic method based on transfer function is applied to solve the response of high-rise structures equipped with General Maxwell dampers under random wind load,while traditional methods are relatively complicated and low precision. Firstly,structural dynamic integral-differential response equations are established. Secondly,by using transfer function method,the exact solutions of structural transient response in time-domain are obtained by expanding the structural response with respect to the first mode. Thirdly,analytical solution of wind-induced structural randomresponse and equivalent static design wind load of high-rise structure with general Maxwell dampers are obtained by using random vibration method. Finally,a numerical example is provided to show that the displacement of the structure with dampers is reduced by about 36. 7% against that without dampers,and the results given by the proposed method are in good agreement with the numerical method,so the advantages of the method are proved. In addition,due to the adoption of Baskin correlation function of random wind vibration excitation model,the proposed method can be applied to excitation response induced by earthquake,random fluctuation of pavement or track,and so on.