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 引用本文: 王延庆 郭星辉 梁宏琨 李健 金乘武. 凸肩叶片的非线性振动特性与运动分岔[J]. 力学学报, 2011, 43(4): 755-764.
Wang Yanqing Guo Xinghui Liang Hongkun Li Jian Jin Chengwu. Nonlinear vibratory characteristics and bifurcations of shrouded blades[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 755-764.
 Citation: Wang Yanqing Guo Xinghui Liang Hongkun Li Jian Jin Chengwu. Nonlinear vibratory characteristics and bifurcations of shrouded blades[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 755-764.

Nonlinear vibratory characteristics and bifurcations of shrouded blades

• 摘要: 以凸肩叶片作为研究模型, 建立了考虑凸肩摩擦力, 几何大变形与阻尼的非线性振动方程.采用Galerkin法对振动方程离散化, 应用平均法对离散后模态方程组的非线性响应进行解析分析, 得到了非线性幅频特性曲线, 与数值解比较验证了解析解, 并讨论了系统周期解的稳定性. 用非线性振动理论详细研究了平均方程组的运动分岔现象, 揭示了平均方程组周期解的变化过程及其具有的非线性动力学性质. 解析结果表明, 凸肩之间的摩擦对系统第二阶非线性振动特性影响很大. 由于凸肩之间摩擦力方向的不断改变, 系统第二阶非线性幅频特性曲线不连续, 出现两个共振频域. 随着时间的推移, 系统振动的幅值会以T/ 4为周期在两个频域的幅频曲线上来回跳动, 这会使叶片的振动响应大幅降低.

Abstract: A shrouded blade is investigated in this paper. The nonlinear equation of vibration isobtained in consideration of frictions between two shrouds, damping and geometriclarge-deformation. The system is discretized by Galerkin's method. The averaging method isapplied to study the nonlinear response of the discrete modal equations, and nonlinearfrequency-response curves are gained. It can be found that the results obtained by the averagingmethod agree well with those from numerical simulation. The stability of periodic solutions of thesystem is also investigated. The bifurcation phenomenon of the averaged equations is studied indetail by the theory of nonlinear vibrations. The results show the change process and nonlineardynamic characteristics of the periodic solutions of averaged equations. The analytical results inthis study indicate that the frictions between two neighboring shrouds have great effect on thenonlinear resonance characteristics of the second order of this system. For the continuous changeof friction directions between two neighboring shrouds, the frequency-response curve of thesecond order becomes incontinuous and two different resonant frequency domains occur. As timepasses, the vibrational amplitude of the system will jump from one frequency-response curve tothe other between the two frequency domains in periods of T/4 continually, resulting in thevibrational response of the blade falls greatly.

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