The nonlinear vibration properties of a coilable mast will decide the prestress of cable and the vibration control of spacecraft.The vibration analysis of the coilable mast was figured in the prestress range which had been derived by geometrical exact analysis and buckling analysis.For small amplitude vibrations,the geometric nonlinearity caused by the loading effect of cable prestress was considered,then,by the eigenvalue iteration method,the natural modes and frequencies were obtained.After calculations in accordance with various cable prestresses,the "frequency-prestress-cable diameter" surface as a guide manual in design was acquired.For large amplitude vibrations,the dynamic response signal processing was used to extract the natural modes and frequencies.Where the dynamic responses were obtained by explicit integration and the signal processing was conducted by FFT and SSI/data method.It is also found,when inspecting the dynamic response signals,the cable has the ability to decrease the amplitude of large vibration rapidly by means of changing the state between tension and relaxation alternatively at a high frequency,which will contribute to the rebalance of energy distribution of the coilable mast.%盘绕式伸展臂非线性振动特性决定加劲索的预应力取值及航天器的振动控制,采用几何精确理论与屈曲分析理论推导出静力条件下加劲索预应力取值范围,在此范围对盘绕臂的非线性振动进行计算.针对小幅非线性振动,考虑加劲索预应力的加载作用引发P-A效应的影响,采用特征值迭代法求解不同预应力下模态及频率,得到使盘绕臂自振频率最大的预应力值,总结出设计用的加劲索“频率-预应力-直径”参考面.针对大幅非线性振动,采用动力时程信号处理法,基于显式动力学积分获取盘绕臂大幅振动时程信号,结合快速傅氏变换(FFT)和随机子空间(SSI/data)两种方法,基于MATLAB平台编制时程信号处理程序,用于提取大幅振动的频率及模态.在动力时程信号中发现加劲索在大幅振动中的高频交替张弛使盘绕臂能量分布迅速达到动态平衡,从而使盘绕臂振幅迅速衰减.最后制作盘绕臂模型进行模态试验,测试的结果与计算结果基本吻合.
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