凸肩叶片的非线性振动特性与运动分岔

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