Strength of Materials

, Volume 27, Issue 3, pp 146–152 | Cite as

Resonance of second order in vibrations of a beam containing a transverse crack

  • N. P. Plakhtienko
  • S. A. Yasinskii
Scientific and Technical Section


The article deals with the resonance of n-th order in forced transverse vibrations of a beam containing a crack situated perpendicularly to the middle line of the beam over its entire width and having a certain depth. The Ostrogradsky — Hamilton and Ritz methods are used to construct a system of ordinary nonlinear differential equations describing the dynamic behavior of a cracking beam. By the method of averaging a system of differential equations with slow variables is constructed for determining the amplitude and phase characteristics in subharmonic resonance of second order. A formula is obtained correlating the parameter of crack depth with the second harmonic of the forced periodic vibration process. The results of modeling on a PC are presented.


Differential Equation Dynamic Behavior Nonlinear Differential Equation Slow Variable Transverse Vibration 
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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • N. P. Plakhtienko
    • 1
  • S. A. Yasinskii
    • 1
  1. 1.Institute of MechanicsAcademy of Sciences of the UkraineKievUkraine

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