悬挂建筑结构原型模型的随机振动优化

Stochastic vibration optimization of prototype model of suspended building structure

以随机振动为基础,将白噪声作为地面加速度激励,进行悬挂建筑结构原型模型的动力响应优化分析.研究了无约束(即不限制悬挂次结构阻尼比ξ2的上限值)条件下悬挂建筑主结构的最优调谐比fopt、次结构最优阻尼比ξ2,opt、主结构加速度响应方差χa1和主结构位移响应方差χx1等参数与悬挂质量比μ之间的关系,以及在约束(即限制ξ2的上限值)条件下,χa1和fopt与μ之间的关系.结果表明:对具有大悬挂质量比(μ≈1)的悬挂建筑的主结构加速度响应方差进行无约束优化分析时,可以近似假定ξ1=0来求解fopt和ξ2,opt;而对相对位移响应方差优化,采用该假定将带来显著的误差甚至是错误,无约束条件下,χa1随着μ的增大而不断改进.约束优化分析表明,ξ2的上限越大,则χa1和χx1均越小.为了保证悬挂建筑结构的整体动力稳定性,不需要对主结构设置阻尼器,但需要对悬挂次结构(悬挂楼层)设置阻尼器.

On the basis of stochastic theory,the optimization of dynamic responses of prototype model of suspended building structure was carried out using white noise as ground vibration input.The relationships between four parameters,i.e.the optimal tuning ratio of main structure of building structure fopt,the optimal damping ratio of auxiliary structure ξ2,opt,the acceleration response variance of main structure χa1 as well as the displacement response variance of main structure χx1,and the suspended mass ratio μ were analyzed in the case of the unconstrained optimization where the upper limit value of the damping ratio of auxiliary structure ξ2 is not limited.Moreover,the relationship between χa1 and μ as well as that between fopt and μ were analyzed in the case of constraint optimization where the upper limit value of ξ2 is limited.The results show that： the damping ratio of main structure can approximately be assumed as zero,i.e.ξ1=0,to solve foptand ξ2,opt in the case of the unconstrained optimization of acceleration response variance of main structure of suspended building with the inherent large suspended mass ratio（μ≈1）;however,this assumption could bring large error or even be a mistake in the case of the optimization of displacement response variance.Under the condition of unconstrained optimization,χa1 improves with the increase of μ.Moreover,under the condition of constraint optimization,the larger the upper limit value of ξ2 is,the smaller the χa1 and χx1 are.The dampers should not be installed in the main structure but it is needed in the auxiliary structure or in the suspended floors to ensure the global stability of suspended building structure under dynamic excitation.