A special case of parametrically excited systems: Free vibration of delaminated composite beams

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37 Citations (Scopus)


The problem of free vibration of delaminated composite beams is revisited in this paper by showing the existence of parametric excitation, bifurcation and stability. Why and when the delaminated part buckles during the vibration? To answer this question, first a finite element model is developed for the uncracked beam portion using the theory of layered beams and the so-called system of exact kinematic conditions. Second, a transition element is developed to establish the kinematic connection and continuity among the delaminated and uncracked portions. Thirdly, the delaminated beam portions are modeled by simple layered beam elements. The coupling between the flexural and longitudinal vibration is taken into consideration in the delaminated part and therefore it is shown that this part is loaded by periodic normal forces during the free vibration of the system. The time dependent stiffness because of the normal forces does not influence the frequencies globally at all, however, locally delamination buckling can take place, as well. The bifurcation and stability of the delaminated parts are analyzed using the harmonic balance method and the critical forces in delaminated layered beams under dynamic stability are determined. The free vibration mode shapes in the state of instability are predicted based on the critical dynamic force and the condition of constant arc length of the delaminated parts. Finally the phase plane portraits of the motion of the midpoint in the delaminated region are presented giving a global view on the behavior of composite beams under harmonic vibration.

Original languageEnglish
Pages (from-to)82-105
Number of pages24
JournalEuropean Journal of Mechanics, A/Solids
Publication statusPublished - Jan 1 2015


  • Delamination
  • Free vibration
  • Parametric excitation

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

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