六参数实用黏弹性阻尼结构基于Davenport风谱风振响应的复模态法

A Complex Mode Method for Wind-Induced Responses of 6-Parameter Practical Viscoelastic Damping Energy Dissipation Structures Based on the Davenport Wind Speed Spectrum

针对六参数实用黏弹性阻尼耗能结构,基于Davenport风速谱系列响应问题进行了系统的研究.首先,利用六参数黏弹性阻尼器的微分型本构关系,建立了耗能结构基于Davenport风速谱激励下的运动方程;然后,运用复模态法将耗能结构的运动方程由二阶微分方程转化为一阶方程,获得了耗能结构系统对风振激励响应的频域解和功率谱密度函数表达式;最后,利用数学恒等式,基于随机振动理论获得了耗能结构系统在Davenport风速谱激励下的响应和阻尼器受力的解析解.该文方法不仅考虑了结构系统在风振激励作用下全振型展开的结果,表达式较现有结果更为简便,效率及精度更高,且适用于非经典阻尼结构.

Based on the Davenport wind speed spectrum,the responses of 6-parameter practical viscoelastic damping energy dissipation structures were studied systematically.Firstly,the differential constitutive relation of the 6-parameter viscoelastic damper was used to establish the motion equation of the energy dissipation structure under the Davenport wind spectrum excitation.Then,the motion equation was transformed from the 2nd-order differential equation to the 1st-order one by means of the complex mode method,and the frequency-domain solution and the power spectral density function expression of the energy dissipation structure system under wind excitation were obtained.Finally,based on the random vibration theory,the analytical solutions of the response of the energy dissipation structure system under the Davenport wind spectrum excitation and the force response of the damper,were obtained with the mathematical identity.This method not only contains the results of the all-vibration-mode expansion of the structure system under wind excitation,but also has more simple and efficient expressions than existing methods,and applies to nonclassical structures.