Bifurcation and nonlinear analysis of nonconservative interaction between rotor and blade row

• Non-conventional modal interaction is studied in a bladed rotating disk.
• Multiple scale perturbation method is used for driving the bifurcation equation.
• The equation can show the common characteristics of the eigenvalue interaction.
• Both blade and rotor damping should be increased to remove the instability.
• Subcritical and supercritical hope bifurcations can occur from the interaction.

It is well known that nonconventional modal interaction between the collective blade motion and rotor lateral whirling can cause instability at a specific speed range. The bifurcation and nonlinear analysis of this interaction are studied in this research for a rotating bladed disk with long blades. In order to obtain a qualitative and general conclusion, a simple model of rotor and blades is considered in which the disk is supposed to be rigid. The blades are considered as inverted pendulums. The bearings and blade stiffness are assumed to be nonlinear and symmetric. The nonlinear stiffness of the blades and bearings includes cubic Duffing terms. A multiple scale method is employed for obtaining the bifurcation equation. The frequency coalescence phenomenon is studied through the bifurcation equation. The effect of rotor and blade damping as well as rotating speed is investigated. The results highlight some interesting phenomena related to the eigenvalue interaction and the nonlinearity in the system. An approximation for the final asynchronous limit cycle is also obtained and compared with the numerical results.