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Bifurcation Behavior and Attractors in Vehicle Dynamics

Hochlenert D., Von Wagner U., Hornig S.

Machine Dynamics Problems

2009

Vol. 33, No. 2

57-73

Nonlinear self-excited systems in vehicle dynamics are discussed using the examples of squealing automotive disk brakes and the stability behavior of a railway wheelset. Both systems show self-excited vibrations for specific operation states. The self-excited vibrations are due to friction forces between pad and disk in the case of the automotive disk and due to contact forces in the case of the railway wheelset respectively. The analysis of the nonlinear equations of motion shows that the trivial solution looses stability either through a sub- or through a supercritical Hopf bifurcation depending on the system's parameters. In the case of a subcritical Hopf bifurcation two stable solutions coexist and the initial conditions determine which solution emerges. The properties of the nonlinear systems such as critical velocities, limit cycle amplitudes and attractors of coexisting solutions are calculated using center manifold reduction and normal form theory.

Application of Center Manifold in Mechanical Systems

Grzędziński J.

Machine Dynamics Problems

2001

Vol. 25, No. 3/4

79-95

In the paper the method of of center manifold reduction for mechanical systems described by integro-differential equations is briefly presented and applied to the limit cycle calculations of a three-dimensional thin airfoil placed in an incompressible flow. Limit cycle oscillations are caused by a cubic structural restoring force corresponding to theaileron rotation. It is emphasized, that the formal power series expansions used in the method of center manifold reduction may diverge and cause the method not to give satisfactory results for any mechanical system. An example is presented, when the method of center manifold reduction cannot even qualitatively predict the occurrence of a stable limit cycle and the use of other methods is necessary.