• PDF / 1,469,096 Bytes
• 15 Pages / 595.276 x 790.866 pts Page_size
• 5 Downloads / 145 Views

DOWNLOAD

REPORT

---

ISSN 1860-2134

Subharmonic and Combination Resonance of Rotating Pre-deformed Blades Subjected to High Gas Pressure Bo Zhang1,2

Hu Ding3

Li-Qun Chen3

1

( School of Science, Chang’an University, Xi’an 710064, Shaanxi, China) (2 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200444, China) (3 School of Science, Harbin Institute of Technology, Shenzhen 518055, China)

Received 16 September 2019; revision received 29 March 2020; Accepted 6 April 2020 c The Chinese Society of Theoretical and Applied Mechanics 2020 

ABSTRACT 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 quasisaturation 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.

KEY WORDS Internal resonance, Subharmonic resonance, Combination resonance, Rotating blade, Stability

1. Introduction Rotating blades are present in many industry applications. The aircraft engine is one of the most important instances. Blade vibration failure due to resonance and flutter occupies a large proportion of the total engine failure. A better understanding of the resonance mechanism and dynamic behavior of rotating blades is helpful to reduce blade vibration failure. In the early studies [1–6] of this field, researchers presented numerous dynamic modeling methodologies of rotating blades and investigated the dynamic characteristics of such structures with only some classical effects taken into consideration in the framework of small-deformation theory. Afterwards, some researchers also paid their attention to some nonclassical effects on the dynamic characteristics 

Corresponding author. E-mail: [email protected]

ACTA MECHANICA SOLIDA SIN