电磁惯性质量阻尼器对斜拉索的减振性能分析

Vibration reduction effect of EIMD on stay cable

为了验证电磁惯性质量阻尼器(electromagnetic inertial mass damper, EIMD)对斜拉索自由振动的减振效果,基于D’Alembert原理建立EIMD与斜拉索共同作用的非线性自由振动方程。在误差允许范围内忽略抗弯刚度,拉索自身纵向惯性力和阻尼力,以及外部动态荷载的情况下,研究平面内横向振动、平面外振动的拉索动位移。通过标准伽辽金(Galerkin)法简化振动方程,搭建Simulink动力仿真模型对拉索振动方程进行数值模拟计算,得出斜拉索跨中平面内外位移-时间曲线。通过对比拉索自由振动位移可以得出:安装EIMD后,斜拉索平面内振动位移相较于原索振动降低73.3%,平面外振动位移相较于原索振动降低72.5%。建立并求解斜拉索-EIMD线性自由振动方程,分析拉索垂度对阻尼器控制效果的影响程度。

Here, to verify vibration reduction effect of electromagnetic inertial mass damper(EIMD) on free vibration of stay cable, nonlinear free vibration equation of stay cable with EIMD was established based on D’Alembert principle. Neglecting bending stiffness, longitudinal inertia force and damping force of cable as well as external dynamic load within allowable error ranges, cable’s in-plane free transverse vibration and out of plane free vibration were studied. Galerkin method was used to simplify the cable free vibration equation, and SIMULINK dynamic simulation model was constructed with cable free vibration equation to simulate cable free vibrations with EIMD and without EIMD. Vibration displacement time history curves of in-plane and out-plane of cable mid span were obtained. By comparing cable free vibration displacement with EIMD and that without EIMD, it was shown that after installation of EIMD, in-plane vibration displacement of cable is reduced by 73.3% compared to that without EIMD, and out-plane vibration displacement of cable is reduced by 72.5% compared to that without EIMD. Finally, the linear free vibration equation of stay cable with EIMD was established and solved to analyze influence of cable sag on damper control effect.