Natural vibration-induced parametric excitation in delaminated Kirchhoff plates

Research output: Contribution to journalArticle

13 Citations (Scopus)


This paper revisits the problem of free vibration of delaminated composite plates with Lévy type boundary conditions. The governing equations are derived for laminated Kirchhoff plates including through-width delamination. The plate is divided into two subplates in the plane of the delamination. The kinematic continuity of the undelaminated part is established by using the system of exact kinematic conditions. The free vibration analysis of orthotropic simply supported Lévy plates reveals that the delaminated parts are subjected to periodic normal and in-plane shear forces. This effect induces parametric excitation leading to the susceptibility of the plates to dynamic delamination buckling during the vibration. An important aspect is that depending on the vibration mode the internal forces have a two-dimensional distribution in the plane of the delamination. To solve the dynamic stability problem the finite element matrices of the delaminated parts are developed. The distribution of the internal forces in the direction of the delamination front was considered. The mode shapes including a half-wave along the width of the plate accompanied by delamination buckling are shown based on the subsequent superimposition of the buckling eigenshapes. The analysis reveals that the vibration phenomenon is amplitude dependent. Also, the phase plane portraits are created for some chosen cases showing some special trajectories.

Original languageEnglish
Pages (from-to)2337-2364
Number of pages28
JournalJournal of Composite Materials
Issue number17
Publication statusPublished - Jul 1 2016


  • Delamination
  • dynamic stability
  • finite element method
  • free vibration
  • harmonic balance
  • laminated plate theory
  • parametric excitation

ASJC Scopus subject areas

  • Ceramics and Composites
  • Mechanics of Materials
  • Mechanical Engineering
  • Materials Chemistry

Fingerprint Dive into the research topics of 'Natural vibration-induced parametric excitation in delaminated Kirchhoff plates'. Together they form a unique fingerprint.

  • Cite this