NONLINEAR DYNAMIC RESPONSE OF PRE-DEFORMED BLADE WITH VARIABLE ROTATIONAL SPEED UNDER 2:1 INTERNAL RESONANCE

In the engineering practice, the rotating speed of turbine blade is not a constant value during many application scenarios, for example, during the start-up, the speed varying and the outage of engines, the input and output power of the rotor are out of balance, usually along with the generation of torsional vibration and resulting in velocity pulse. At the same time, the pre-deformation of the blades, caused by some factors including service environment and the installation imperfection, is often inevitable. Nonlinear dynamic behavior of pre-deformed blade with the varying rotating speed is studied in this paper. Considering the rotating speed is consisted of a constant speed and small perturbation, the dynamic governing equation is obtained by Lagrange principle. The partial differential equation is transformed into ordinary differential equation by using assumed mode method. For the sake of generality, a set of dimensionless parameters are introduced. The method of multiple scales is exploited to solve the excitation system. The average equation is derived in the case of 2:1 internal resonance. After that the steady-state response of the system is obtained. The influences of rotating speed, temperature gradient and damping on the dynamic behavior of the blade are studied in detail. Meanwhile, we clarify the effects of cubic nonlinear terms on the steady state response of the blade in the case of the 2:1 internal resonance. The original dynamic equation is integrated numerically in forward and backward frequency sweep direction to observe the jump phenomenon, and to verify the analytical solution. The results show that the changes of parameters have different influences on the dynamic behavior of blade. In the case of the 2:1 internal resonance, the cubic nonlinear terms have little influence on the dynamic response of the system. The analytical solutions are in good agreement with the numerical solutions.