Nonlinear pseudo-force in “breathing” delamination to generate harmonics: A mechanism and application study

Maosen Cao, Zhongqing Su, Tongfa Deng, Wei Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)


Subject to coupled vibro-acoustic excitation, the opening–closing motion of a “breathing” delamination in a composite laminate can create nonlinear harmonics, i.e., higher and sideband harmonics, in its steady-state vibration responses. Nonlinear harmonics have attracted increasing attention in the field of nondestructive testing because they can be sensitive indicators of barely visible delamination that is difficult to detect by conventional linear approaches. Although vibro-acoustic modulation has been acknowledged as the cause of nonlinear harmonics, the intrinsic force in a delamination that generates harmonics is not yet clear. Addressing this problem, this study analytically formulates a novel concept of nonlinear pseudo-force (NPF) in “breathing” delamination of composite laminates, by which the mechanism for generating nonlinear harmonics by vibro-acoustic modulation can be explicitly expounded. In the application aspect, as the NPF in delamination can cause local changes in operating deflection shapes (ODSs), this study proposes a novel approach using ODSs at nonlinear harmonics for locating “breathing” delamination of composite laminates, which is superior to current approaches that can only manifest the occurrence of delamination by nonlinear harmonics. Numerical simulations using finite element method are used to validate the mechanism and explore the application potential of ODSs for locating delamination. In particular, an array of coupled vibro-acoustic excitation is proposed to avoid wave attenuation of acoustic excitations. Thereby, vibration and acoustics can interact in the “breathing” delamination to generate nonlinear harmonics.

Original languageEnglish
Article number106124
JournalInternational Journal of Mechanical Sciences
Publication statusPublished - 15 Feb 2021


  • Delamination localization
  • Nonlinear harmonic
  • Nonlinear pseudo-force
  • Operating deflection shape
  • Vibro-acoustic modulation
  • “Breathing” delamination

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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