Nonlinear vibration of rotating pre-deformed blade with thermal gradient

Abstract

In this paper, the nonlinear dynamic behavior is investigated for a rotating pre-deformed pretwisted blade subjected to harmonic gas pressure. The pre-deformation curve produced by thermal gradient is derived. A novel nonlinear vibration system is established by considering the influence of pre-deformation. The combination of the Lagrange principle and the assumed modes method is utilized to obtain the motion equations, and then the equations are transformed into a dimensionless form through introducing a set of dimensionless parameters. For the purpose of ensuring high precision in determination of the internal resonance condition, the equations of motion are discretized by adequate trial functions. An eigenvalue analysis is conducted on the corresponding linear system to obtain the natural frequencies and examine the possibility of the 2:1 internal resonance. The method of multiple scales is developed to solve the resulting multi-degree-offreedom nonlinear ordinary differential equations. A numerical integration by means of Runge-Kutta is performed to establish the validity of the derived formulations. The evolution of frequency response curves with the rotating speed is observed. The influences of the thermal gradient, gas pressure and damping coefficient on the resonant dynamics of the system are investigated in detail. For the purpose of comparison, another distribution profile of pre-deformation, which is frequently used in previous literature, is also examined. It could be found that not only the amplitude but also the distribution of the initial deflection could influence the steadystate nonlinear response of the pre-deformed blade. A series of interesting nonlinear dynamic phenomena are discovered from the results.

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to 1 : 1 : 1 Simultaneous Resonance

“…Te authors found that the mutual friction had a great efect of mitigating the vibration when the normal forces were beneath radial and axial forces' excitation limits. Zhang and Li [6] studied the dynamics of a predeformed rotating blade subjected to gaseous pressure of harmonic type. Using Lagrange's equations, they obtained the equations of motion and normalized them through dimensionless parameters.…”

Nonlinear Vibrations of Rotating Pretwisted Composite Blade Reinforced by Functionally Graded Graphene Platelets Under Combined Aerodynamic Load and Air Flow in Tip Clearance

“…Yao et al [31] employed a pre-twisted, presetting and thin walled rotating beam model to analyzed 2:1 internal resonance and primary resonance of the compressor blade. Zhang and Li [32] studied the nonlinear vibrations of the rotating blade. Wang et al…”

Nonlinear Dynamics of the High-Speed Rotating Plate

“…Shariyat et al [18] performed the nonlinear dynamic analysis of rectangular composite plates. Zhang and Li [19] adopted the Lagrangian method to acquire dynamic equations of motion for the pretwist and predeformed rotating cantilever plate subjected to the harmonic aerodynamic force. Mendonça et al [20] considered internal damping in the shaft to study dynamic behaviors of the rotors mounted on composite shafts.…”

“…Substituting 23into (17), (18), (19), (20), and (21), we obtain the dimensionless governing equations of motion for the blade.…”