Affiliations: School of Astronautics, Harbin Institute of
Technology, P.O. Box 137, Harbin 150001, China | School of Science, Harbin Engineering University,
Harbin 150001, China
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 amplitude-frequency curves.
