Nonlinear dynamic behavior of rotating blade with breathing crack

This study aims at investigating the nonlinear dynamic behavior of rotating blade with transverse crack.A novel nonlinear rotating cracked blade model(NRCBM),which contains the spinning softening,centrifugal stiffening,Coriolis force,and crack closing effects,is developed based on continuous beam theory and strain energy release rate method.The rotating blade is considered as a cantilever beam fixed on the rigid hub with high rotating speed,and the crack is deemed to be open and close continuously in a trigonometric function way with the blade vibration.It is verified by the comparison with a finite element-based contact crack model and bilinear model that the proposed NRCBM can well capture the dynamic characteristics of the rotating blade with breathing crack.The dynamic behavior of rotating cracked blade is then investigated with NRCBM,and the nonlinear damage indicator(NDI)is introduced to characterize the nonlinearity caused by blade crack.The results show that NDI is a distinguishable indicator for the severity level estimation of the crack in rotating blade.It is found that severe crack(i.e.,a closer crack position to blade root as well as larger crack depth)is expected to heavily reduce the stiffness of rotating blade and apparently result in a lower resonant frequency.Meanwhile,the super-harmonic resonances are verified to be distinguishable indicators for diagnosing the crack existence,and the third-order super-harmonic resonances can serve as an indicator for the presence of severe crack since it only distinctly appears when the crack is severe.

Subharmonic and Combination Resonance of Rotating Pre-deformed Blades Subjected to High Gas Pressure

The present paper deals with the investigation of dynamic responses of a rotating pre-deformed blade in four cases of resonance,including two subharmonic resonances and two combination resonances.The dimensionless gas excitation amplitude is assumed to share the same order with the dimensionless vibration displacement.Four cases of resonance are confirmed by examining the secular terms.The theoretical analysis framework is established for each resonance case based on the method of multiple scales.The original dynamic system is integrated numerically by the Runge–Kutta method.The frequency components and phases obtained from fast Fourier transform of the numerical response are used to verify the theoretical results.For the purpose of contrast,modulation equations are also integrated numerically.In all four resonance cases,the theoretical results agree well with the numerical simulation.Parameter studies are conducted to clarify the effects of system parameters on the perturbation curves.Various results are obtained for the rotating blade.A quasi-saturation phenomenon occurs in both combination resonances of summed type and difference type,and the corresponding limit value of the second-mode response can be reduced by decreasing the external detuning parameter.The quasi-saturation phenomenon of rotating blade only appears with high gas pressure.The subharmonic resonance of second mode and the combination resonance of summed type are hard to excite in practice compared with the other two cases.

Nonlinear transient responses of rotating twisted FGM cylindrical panels

This paper develops a new structure dynamic model to investigate nonlinear transient responses of the rotating blade made of functionally graded material(FGM). The rotating blade is simplified as a rotating FGM cylindrical panel with a presetting angle and a twist angle. The geometric nonlinearity effects are taken into account in the strain-displacement relationships, which are derived by Green strain tensor. Based on the first-order piston theory and the first-order shear deformation theory, the equations of motion for the rotating twisted FGM cylindrical panel are acquired by means of Hamilton principle and Galerkin method.Backward Differentiation Formula(BDF) and Runge-Kutta Algorithm are used to solve the nonlinear equations of motion for the system. The effects of four pulse load conditions on the system subjected to the internal pulse load or the external pulse load are fully discussed. A detailed parametric analysis is performed by considering the effects of the rotating speed, volume fraction index and temperature.