Original Paper

Nonlinear Dynamics

, Volume 70, Issue 2, pp 1125-1133

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Transition to chaos and escape phenomenon in two-degrees-of-freedom oscillator with a kinematic excitation

  • Marek BorowiecAffiliated withDepartment of Applied Mechanics, Lublin University of Technology
  • , Grzegorz LitakAffiliated withDepartment of Applied Mechanics, Lublin University of Technology Email author 


We study the dynamics of a two-degrees-of-freedom (two-DOF) nonlinear oscillator representing a quarter-car model excited by a road roughness profile. Modeling 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.


Nonlinear oscillations Vehicle suspension Recurrence plot