Nonlinear vibratory characteristics and bifurcations of shrouded blades

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.