Title

Nonlinear Response of a Beam Under Distributed Moving Contact Load

Document Type

Article

Publication Date

3-2006

Publication Source

Communications in Nonlinear Science and Numerical Simulation

Volume

11

Issue

2

Inclusive pages

203-232

DOI

10.1016/j.cnsns.2004.08.002

Publisher

Elsevier BV

Place of Publication

Netherlands

ISBN/ISSN

10075704

Abstract

In this paper, the nonlinear behavior of a one-dimensional model of the disc brake pad is examined. The contact normal force between the disc brake pad lining and rotor is represented by a second order polynomial of the relative displacement between the two elastic bodies. The frictional force due to the sliding motion of the rotor against the stationary pad is modeled as a distributed follower-type axial load with time-dependent terms. By Galerkin discretization, the equation governing the transverse motion of the beam model is reduced to a set of extended Duffing system with quasi-periodically modulated excitations. Retaining the first two vibration modes in the governing equations, frequency response curves are obtained by applying a two-dimensional spectral balance method. For the first time, it is predicted that nonlinearity resulting from the contact mechanics between the disc brake pad lining and rotor can lead to a possible irregular motion (chaotic vibration) of the pad in the neighborhood of simple and parametric resonance. This chaotic behavior is identified and quantitatively measured by examining the Poincaré maps, Fourier spectra, and Lyapunov exponents. It is also found that these chaotic motions emerge as a result of successive Hopf bifurcations characterized by the torus breakdown and torus doubling routes as the excitation frequency varies. Various aspects of the numerical difficulties in the solution of the nonlinear equations are also discussed.

Keywords

Disc brake noise, Chaotic motion, Nonlinear Leipholz beam

Disciplines

Engineering

This document is currently not available here.

  Contact Author

Share

COinS
 
 

Link to Original Published Item

http://dx.doi.org/10.1016/j.cnsns.2004.08.002