《nonlinear vibration characteristics of a flexible blade with friction damping due to tip-rub》.pdf

Shock and Vibration 18 (2011) 105–114 105 DOI 10.3233/SAV-2010-0600 IOS Press Nonlinear vibration characteristics of a flexible blade with friction damping due to tip-rub a,∗ a a a b Dengqing Cao , Xiaochun Gong , Dong Wei , Shiming Chu and Ligang Wang aSchool of Astronautics, Harbin Institute of Technology, P.O. Box 137, Harbin 150001, China bSchool of Science, Harbin Engineering University, Harbin 150001, China Received 10 February 2010 Revised 20 June 2010 Abstract. An approximate approach is proposed in this paper for analyzing the two-dimensional friction contact problem so as to compute the dynamic response of a structure constrained by friction interfaces due to tip-rub. The dynamical equation of motion for a rotational cantilever blade in a centrifugal force field is established. Flow-induced distributed periodic forces and the internal material damping in the blade are accounted for in the governing equation of motion. The Galerkin method is employed to obtain a three-degree-of-freedom oscillator with friction damping due to tip-rub. The combined motion of impact and friction due to tip-rub produced a piecewise linear vibration which is actually nonlinear. Thus, a complete vibration cycle is divided into successive intervals. The system possesses linear vibration characteristic during each of these intervals, which can be determined using analytical solution forms. Numerical simulation shows that the parameters such as gap of the tip and the rotational speed of the blades have significant effects on the dynamical responses of the system. Finally, the nonlinear vibration characteristics of the blade are investigated in terms of the Poincare graph, and the frequency spectrum of the responses and the am