Internal Resonances of a Rotating Pre-deformed Blade Under a Harmonic Gas Pressure

This study presents the main similarities and differences among a series of resonance responses of a rotating blade under harmonic excitation, considering pre-deformation effects. The possibilities of 10 different types of resonances (such as primary resonances, sub-harmonic resonances, super-harmonic resonances, and even combination resonances) are determined via the theoretical analysis. The response curves and the stability ranges are compared for different types of resonances, respectively. A set of interesting findings are concluded in this study. The quadratic nonlinear terms, which are introduced by the pre-deformation field caused by the thermal gradient, not only introduce the rich phenomena through 2:1 internal resonance but also have dramatic effects on the dynamic response in the case of 3:1 internal resonance. The double jumping and saturation phenomena can be only found in the 2:1 internal resonances. For some of the resonance cases, the frequency response curves or stable regions are quite similar to each other.