中文摘要：

主要研究非线性饱和控制减振系统中由于内共振频率偏差引起的减振频带的漂移问题,在该减振系统中考虑时滞对振动系统减振频带漂移以及减振频带宽度的影响,从而利用时滞来控制系统减振频带的漂移问题.采用多尺度方法得到了主共振和1：2内共振同时发生时系统运动方程的解析解.研究结果表明,对原始的无时滞减振系统,由于内共振频率偏差的存在,使得系统的减振频带向主共振点上、下两个方向漂移,并且内共振频率偏差的绝对值越大减振频带漂移的程度也越大,使得减振频带的分布不合理,造成主共振点附近减振效果明显下降.然而,根据内共振频率偏差的变化,适当调节系统中的时滞参数,可以消除减振频带的漂移,同时又能够增大减振频带的宽度.研究还表明,内共振频率偏差的绝对值越大时滞对消除减振频带漂移以及增大减振频带宽度的作用越显著.论文结论对于非线性振动系统的结构振动控制在定性和定量方面都具有参考价值.

英文摘要：

This paper analyzes the band shift caused by the deviation of internal resonance frequency of nonlinear saturation control system.The effects of delay on band shift and bandwidth are studied under consideration.Thus,the band shift can be controlled using an appropriate choice of the delay.The method of multiple scales is employed to obtain the analytical solutions when the primary resonance and 1：2 internal resonance occurs in the system simultaneously.From the examples illustrated,in the original system without delay,the frequency band shifts to the above and below of the primary resonance point caused by the deviation of internal resonance frequency.Moreover,the larger band shift is caused by the larger absolute value of deviation of internal resonance frequency.The performance of vibration suppression about the primary resonance point is reduced for the unreasonable distribution of frequency band.However,the band shift can be eliminated and the bandwidth can be enlarged using an appropriate choice of the delay according to the values of deviation of internal resonance frequency.The larger absolute value of deviation of internal resonance frequency,the more effects of the delay on the band shift and bandwidth will be.The conclusion of this paper provides qualitative and quantitative referenced value to control vibration in the nonlinear vibration system.