Transition to chaos and escape phenomenon in two degrees of freedom   oscillator with a kinematic excitation
  We study the dynamics of a two-degrees-of-freedom (two DOF) nonlinear oscillator representing a quartercar model excited by a road roughness profile. Modelling the road profile by means of a harmonic function we derive the Melnikov criterion for a system transition to chaos or escape. The analytically obtained estimations are confirmed by numerical simulations. To analyze the transient vibrations we used recurrences. 
Marek Borowiec and Grzegorz Litak
nlin.CD