风荷载作用下复刚度阻尼 TMD 减振结构优化设计

摘要

利用复刚度阻尼进行减振的优化设计理论亟需发展。建立具有复刚度阻尼特征的调频质量阻尼器（TMD）减振结构的动力学方程，并基于定点理论提出了采用复刚度阻尼的 TMD 结构最优频率比和最优阻尼比确定方法。对具有复刚度阻尼特征的 TMD 减振结构在简谐激励和平稳随机激励下的稳态响应进行了分析。以主结构位移振幅最小为优化条件，推导 TMD 的阻尼和频率最优参数的理论公式。结果表明复刚度阻尼 TMD 的整体减振效果接近于黏滞阻尼减振结构，在相同质量比和一定频率范围内，复刚度阻尼比黏滞阻尼可能具有更好的减振效果。对 Davenport 风速谱下复刚度阻尼 TMD 减振结构的随机响应进行分析，结果表明 TMD 的减振效果要弱于白噪声作用下的结果，复刚度阻尼TMD 减振效果稍逊于黏滞阻尼的情况，但二者结果较接近。在应用 TMD 减振技术时，采用复刚度阻尼是一种有益的选择方案。%The study on the optimal design theory for vibration reduction structures with complex stiffness and damping is necessary.The dynamic equations for structures including tuned mass dampers (TMDs)with complex stiffness and damping were established.The method for determining their optimal frequency ratio and optimal damping ratio was presented based on the fixed point theory.The steady state responses of the such kind structures to harmonic excitation and stationary random excitation were analyzed,respectively.The theoretical formulas for the optimal damping and frequency were derived when the displacement amplitude minimization of the main structure was set as the optimal objective.The results showed that the overall vibration reduction effect of this kind of structures were close to that of structures with viscous damping,and the former is better in a certain frequency range with the same mass ratio.The random responses of this kind of structures under Davenport wind speed spectrum were analyzed.The results showed that the vibration reduction effect of TMDs with complex stiffness and damping is less than that under white noise excitation, the vibration reduction effect of the such kind structures is less than that of structures with viscous damping,but the difference is slight;so,if TMDs are applied in vibration control,adopting complex stiffness and damping is a profitable option.