Analytical Approach to a Two-Module Vibro-Impact System

  • Pawel FritzkowskiEmail author
  • Roman Starosta
  • Jan Awrejcewicz
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 228)


A mechanical system composed of two weakly coupled vibro-impact modules under harmonic excitation is considered. The mathematical model of the system is presented in a non-dimensional form. The analytical approach based on the combination of the multiple scales method and the saw-tooth function is employed. The periodic responses of the system with two impacts per cycle near 1:1 resonance are studied. The results have semi-analytical character. Stability of the periodic motions is evaluated. In the unstable case, occurrence of a different response regime is shown: the strongly modulated response. The analytical predictions are compared with purely numerical results.


Vibro-impact systems Nonlinear energy sink Multiple scales method Saw-tooth function 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Pawel Fritzkowski
    • 1
    Email author
  • Roman Starosta
    • 1
  • Jan Awrejcewicz
    • 2
  1. 1.Institute of Applied Mechanics, Poznan University of TechnologyPoznańPoland
  2. 2.Department of Automatics and BiomechanicsTechnical University of ŁódźŁódźPoland

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