Nonlinear Dynamics Of The Blade With High Rotating Speed

Rotating blade has a wide range of application such as aero-engine blade, turbineblade and helicopter blade. To get better performance and take weight out of theengine, the blades are designed to be hollow. The aero-loading on the blades isperturbed super-sonic gas flow, so the effect of a perturbed rotating speed should beconsidered through the analysis. Since rotating blades usually produce large amplitudeof vibration, the system will show a complex nonlinear dynamical behavior, forexample, the limit cycle vibration, bifurcation, sub-harmonic superharmonicresonance, the amplitude jumps and even chaotic motion. Nonlinear vibration of largeamplitude and irregular chaotic vibration cause serious blade fatigue, buckling,fracture failure,resulting in flight accident, and even the plane crash. In this paper thenonlinear characteristics of the blade of the high-pressure compressor of theaero-engine are investigated.The blade, which is equipped with the background of giant aero-engine turbineblade, is modeled as a rotating thin-walled beam mounted at a rigid hub. Thegeometrical nonlinearity, centrifugal force and aero-loading are considered in themodeling process. The nonlinear governing equation is derived by Hamilton principle,and the averaged equation is obtained through Galerkin method and multiple scalesmethod. The numerical analysis is given based on the averaged equation of therotating blade. The content of this paper can be summarized as following chapters.(1) The blade is simplified as a rotating thin-walled Euler-Bernoulli beammounted at a rigid hub and the nonlinear dynamical equation is conducted. The airfluid fluctuation is introduced as cosine type perturbation. The nonlinear geometricaldeformation and the aerodynamic load determined by first-order piston theory areconsidered. A two-degree-of-freedom governing equation of the transverse vibrationsof the blade is derived by Hamilton principle and the Galerkin method.(2) Perturbation analysis by the method multiple scales, bifurcation and chaosanalysis are investigated for the case of1:1internal resonance. The averaged equationis obtained for the case of1:1internal resonance. The numerical simulation which theperturbed rotation is selected as controlling parameter contains bifurcation diagram,phase portrait, wave form and power spectrum. The results show that the systemexperiences periodic motions and chaotic motions alternatively.(3) Perturbation analysis including the method multiple scales, steady state andchaos analysis are investigated for the case of2:1internal resonance. The averagedequation of the transverse vibrations is obtained. Phase portrait, wave form and powerspectrum are given in the numerical simulation. Besides, a stability analysis isdelivered based on the frequency response curve of the system. (4) The dynamical equation for the model of the rotating blade with the sheardeformation is carried out. In addition to the two in-plane transverse displacements,the variables of the system contain two in-plane shear deformations. Afour-degree-of-freedom nonlinear governing equation of the rotating blade is derivedby the Hamilton principle and the Galerkin method.(5) Perturbation analysis by the method of multiple scales and the numericalanalysis are investigated for the blade system involving shear effects. For the case of2:1:1:2internal resonance, the eight-dimensional averaged equation is gained.Bifurcation diagram, phase portrait, wave form and power spectrum are shown in thenumerical simulations to investigate the nonlinear response of the system to the steadystate rotating speed.