减震结构采用Lyapunov方程的阻尼器优化配置方法

Optimization for the arrangement of added dampers of energy dissipation structures by using Lyapunov equation

基于Lyapunov方程实现了减震结构的阻尼器优化布置,并将该方法应用于具有偏心结构的减震优化设计中。将阻尼器的位置参数和力学参数引入到结构的运动方程中,并在状态空间中利用Lyapunov方程求解减震结构的随机地震响应;然后基于满应力设计方法对结构的附加阻尼进行重新设计,通过反复迭代达到各层位移的满应力分布,实现结构各层位移最大均方值的最小化;最后以6层无偏心的平面框架和3层偏心框架为例,采用上述方法实现了阻尼的最优布置,并与最小传递函数的优化方法进行了对比,验证了本文方法的可行性与有效性。该研究为减震结构阻尼器的优化配置提供了方法,有利于减震结构的工程应用和推广。

Based on Lyapunov equation,the damper optimization arrangement of the seismic structure is realized,and the method is applied to the shock-absorbing optimization design with eccentric structures.The position parameters and mechanical parameters of dampers are introduced into the structure′s equations of motion.Lyapunov is used to solve the random seismic response to the damping structures of state space.Then the additional damping is redesigned according to the fully stressed design algorithm.Fully stress of displacement on each story is reached iteratively for minimizing the maximum mean squared drift of each story.The optimal distribution of damping is solved by the above approach taking two examples:a 6-story shears frame and a 3-story eccentric frame.The results are compared with the method of minimizing transfer function to confirm the feasibility and effectiveness.The research provides a solution to the optimal distribution of dampers,which is beneficial to the engineering application and promotion of aseismic structures.