单跨简支梁竖向振动的磁悬浮半主动控制

由于传统的隔振器需要足够的竖向刚度来支撑上部结构,因而不能隔离竖向振动。为了解决这一问题,本文提出一种新的隔振策略,即磁浮式半主动控制方法,并将这一方法应用于弹性梁弯曲振动的半主动控制。将均质弹性梁简化为一带集中质量的简支梁,导出了控制系统的运动方程,讨论了系统在平衡点的稳定性,应用推广的Runge-Kutta方法,得到了系统在随机地面输入下的加速度响应。结果表明：杆件的初始悬浮位置是磁浮式半主动控制系统的平衡点,且平衡点是L稳定的;磁浮式半主动隔振系统具有类似于软弹簧的性质,与普通的弹性简支梁相比,磁浮式半主动振动控制系统的振动频率较低,加速度响应明显减小,系统具有良好的竖向隔振性能。

Magnetic Levitation Semi-active Control of Vertical Vibration for a Simply Supported Beam

The isolation of vertical vibration is being an insurmountable problem for traditional due to that large stiffness is necessary for supporting upper structures. A new vibration isolation isolators strategy for overcoming this problem based on magnetic levitation semi-active control technique is proposed in this paper, and it has been applied to the semi-active control of bending vibration of a simply supported beam. The governing equation of the semi-active control system for the beam bending vibration is derived on the assumption that beam mass is lumped in the middle of the beam. The system stability at equilibrium points is studied and the extended Runge-Kutta formula is applied to solve the system subjected to random ground excitations. The acceleration response of the system is investigated. The results indicate that the initial suspension position is an equilibrium point of the system and it is L-stable. The magnetic levitation compo- nent is similar to a soft-spring device. The vibration frequency of the semi-active control system is lower than that of the common simply supported beam, and the acceleration response is obviously reduced. The system has an excellent quality in the isolation of vertical vibration.