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