Dynamic and resonance response analysis for a turbine blade with varying rotating speed

A coupling model between turbine blades with a varying rotating speed and oncoming vortices
is constructed, where the coupling of the structure and the fluid is simulated by the van
der Pol oscillation. Partial differential governing equations of motions for the coupled system
are obtained and discretized by using the Galerkin method. The 1:2 subharmonic resonance
and the 1:1 internal resonance are investigated with the multiple scale method and first-order
averaged equations are then derived. Nonlinear responses and bifurcation characteristics are
studied by a numerical integration method. Stability of bifurcation curves is determined
by utilizing the Routh-Hurwitz criterion. The effect of system parameters including the
detuning parameter, steady-state rotating speed, amplitude of periodic perturbation for the
rotating speed and freestream velocity on vibration responses are investigated.