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.

[1]  Jintai Chung,et al.  Dynamic modeling and analysis of a spinning Rayleigh beam under deployment , 2016 .

[2]  J. Warminski,et al.  Saturation Control for a Rotating Thin-walled Composite Beam Structure , 2016 .

[3]  J. B. Yang,et al.  Dynamic modelling and control of a rotating Euler–Bernoulli beam , 2004 .

[4]  Jerzy Warminski,et al.  Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle , 2014 .

[5]  W. Zhang,et al.  Analysis on nonlinear oscillations and resonant responses of a compressor blade , 2014 .

[6]  Biswajit Basu,et al.  Dynamics and control of vibrations in wind turbines with variable rotor speed , 2013 .

[7]  E. de Langre,et al.  Coupling of Structure and Wake Oscillators in Vortex-Induced Vibrations , 2004 .

[8]  Kexiang Wei,et al.  Vibration control of variable speed/acceleration rotating beams using smart materials , 2006 .

[9]  J. Jędrysiak,et al.  Nonlinear vibrations of periodic beams , 2016 .

[10]  Alexander F. Vakakis,et al.  Suppression of limit cycle oscillations in the van der Pol oscillator by means of passive non‐linear energy sinks , 2006 .

[11]  M. Yao,et al.  Nonlinear vibrations of blade with varying rotating speed , 2012 .

[12]  E. Esmailzadeh,et al.  Non-linear vibration of variable speed rotating viscoelastic beams , 2010 .

[13]  Zhifeng Hao,et al.  Two-sided damping constraint control strategy for high-performance vibration isolation and end-stop impact protection , 2016 .

[14]  M. A. Barron-Meza.  Vibration Analysis Of a Self-Excited Elastic Beam , 2010 .

[15]  I. G. Currie,et al.  Lift-Oscillator Model of Vortex-Induced Vibration , 1970 .

[16]  Zhifeng Hao,et al.  The isolation characteristics of an archetypal dynamical model with stable-quasi-zero-stiffness , 2015 .

[17]  Max F. Platzer,et al.  On Vortex Formation in the Wake Flows of Transonic Turbine Blades and Oscillating Airfoils , 2006 .

[18]  D. Kammer,et al.  Effects of Nonconstant Spin Rate on the Vibration of a Rotating Beam , 1987 .

[19]  J. Balthazar,et al.  Homotopy analysis of a forced nonlinear beam model with quadratic and cubic nonlinearities , 2016 .

[20]  Mihir Sen,et al.  Synchronization of coupled self-excited elastic beams , 2009 .

[21]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[22]  Pascal Hémon,et al.  AN IMPROVEMENT OF THE TIME DELAYED QUASI-STEADY MODEL FOR THE OSCILLATIONS OF CIRCULAR CYLINDERS IN CROSS-FLOW , 1999 .

[23]  Qingjie Cao,et al.  Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices , 2016 .

[24]  Qingjie Cao,et al.  A three-degree-of-freedom model for vortex-induced vibrations of turbine blades , 2016 .

[25]  R. Ibrahim.  Book Reviews : Nonlinear Oscillations: A.H. Nayfeh and D.T. Mook John Wiley & Sons, New York, New York 1979, $38.50 , 1981 .

[26]  M. Wiercigroch,et al.  A Reduced Order Model for Vortex–Induced Vibration of a Vertical Offshore Riser in Lock–in , 2008 .

[27]  Qingjie Cao,et al.  Bifurcation analysis for vibrations of a turbine blade excited by air flows , 2016 .

[28]  Jintai Chung,et al.  Nonlinear modeling for dynamic analysis of a rotating cantilever beam , 2016 .

[29]  Haym Benaroya,et al.  An overview of modeling and experiments of vortex-induced vibration of circular cylinders , 2005 .