Nonlinear Vibration Analysis of a Beam with Supporting of Dry Friction

Ren Yongsheng, Qin Huizheng, Xiong Shibo, Geng Maixiang
(Institute of measurement Technology, Shanxi Mining Institute, Taiyuan, 030024)
Zhao Zilong (£Øi'an Tiaotong University, Xi'an, 710049£©

£Ábstract: A study of nonlinear vibration of a beam with a boundary condition of axial dry friction is presented. The constitute relationships of dry friction are characterized by three possible states: stick-slip state, transient slip state, and stick state. The governing equation for the beam is developed by Hamilton's principle, along with the boundary condition of dry friction force. The nonlinear ordinary differential equations then are derived by the Galerkin method. HBM is used to obtain the fundamental resonance response, and the stability conditions of the steady state solution are determined. Numerical simulations are conducted by Turbo-C program. Various of typical frequency response plots for different values of friction force parameters are given.
Keywords: dry friction damping, elastic beam, nonlinear vibration.