摆式悬吊调谐质量阻尼器基于慢变参数法的非线性优化研究

Nonlinear optimization of pendulum tuned mass damper based on slowly varying parameter method

大幅响应下,摆式悬吊调谐质量阻尼器(PTMD)表现出非线性,以往研究PTMD时,将摆角等效线性化高估了其振动控制性能。文章运用拉格朗日方程推导了非线性模型的运动方程,采用Krylov-Bogoliubov慢变参数法推导了考虑摆角高次非线性的频响函数,并对比不同激励幅值下非线性模型与等效线性模型的结构响应,对PTMD非线性模型基于H 2准则进行了参数优化,得到了不同激励幅值下PTMD的最优设计参数,最后采用最优设计参数对某超高层结构模型进行时程分析验证。结果表明,激励幅值越大,非线性对结构响应的影响越大,等效线性模型越失真;在大幅值激励下,与线性模型优化的结果相比,考虑非线性进行参数优化后PTMD的减震率可以提高约10%。因此,考虑非线性优化设计可以有效提高PTMD振动控制性能。

The pendulum tuned mass damper(PTMD)shows nonlinearity under large amplitude response,and the vibration control performance of PTMD was overestimated by equivalent linearization of rotation angle in previous studies.In this paper,the motion equation of nonlinear model is derived by the Lagrange equation and the Krylov-Bogoliubov slow-variation parameter method was adopted to derive the frequency response function of the nonlinear model considering the high order nonlinearity of the pendulum angle.The structural responses of nonlinear model and equivalent linear model under different excitation amplitudes are then compared.The parameters of the PTMD nonlinear model are optimized based on H_(2)criteria,and the optimal design parameters of PTMD under different excitation amplitudes were obtained.Further,the time-history analysis method was adopted to verify the optimal design parameters of a super high-rise structure model.The results show that the larger the excitation amplitude is,the greater the influence of nonlinearity on the structural response is,and the equivalent linear model is gradually distorted.Under a large excitation amplitude,compared with the results of linear model optimization,the damping rate of PTMD can be increased by 10%after parameter optimization considering nonlinearity.Considering nonlinear optimization design can effectively improve the vibration control performance of PTMD.