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

Abstract

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.

Active and Time Delay Controls on Vibrations of the Micro-Electro-Mechanical System (MEMS) Resonator

“…So, the reduction in the amplitude is about 93%. Numerical solution of the response equation represented in equation (19) have been discussed. Fig.…”

“…Wang et al [19] investigated the dynamic response and bifurcation characteristics of blades with varying rotating speed. The results of the paper showed the interaction of the fluid and the structure that the opposite varying trends for the amplitudes and phase angles with respect to the system parameters; indicate the energy transfer between the vibrations of the fluid and the structure.…”

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“…The cracks are related directly to the stiffness of the blade where they reduce the stiffness. Wang et al [6] presented a mathematical model of the turbine blades based on the coupling effect of the fluid and dynamic effect (vortices and the rotational speed). They found the nonlinear response and state of stability of the rotating blades, their results presented the frequencies and mode shapes under different configurations.…”

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“…Wang et al [12] investigated the dynamic response and bifurcation characteristics of blades with varying rotating speed. The results of the paper showed the interaction of the fluid and the structure that the opposite varying trends for the amplitudes and phase angles with respect to the system parameters indicate the energy transfer between the vibrations of the fluid and the structure.…”