Theoretical calculation of circular-crested Lamb wave field in single- and multi-layer isotropic plates using the normal mode expansion method

Lingfang Li, Mohammad Faisal Haider, Hanfei Mei, Victor Giurgiutiu, Yong Xia

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


The guided wave technique is commonly used in the health monitoring of thin-walled structures because the guided waves can propagate far in the structures without much energy loss. However, understanding of the wave propagation in bounded layered structures is still lacking. In this study, the Lamb wave field of single- and multi-layer plates excited by surface-mounted piezoelectric wafer active sensors is theoretically analyzed using the normal mode expansion method, which is based on the elastodynamic reciprocity relation and utilizes the orthogonality relations of the Lamb wave modes. The mode participation factors of Lamb wave in single- and multi-layer isotropic plates are derived. The time domain responses are obtained through the inverse Fourier transform of the structural response spectrum, which is obtained by multiplying the transfer function with the excitation frequency spectrum. The developed normal mode expansion method is first applied to an aluminum single-layer plate. The obtained analytical tuning curves and out-of-plane velocity of the plate are in good agreement with the numerical and experimental results. Finally, the analytical wave responses of an aluminum–adhesive–steel triple-layer plate are verified through comparison with the finite element analysis and experiment. The proposed normal mode expansion method provides a reliable and accurate calculation of the wave field in single- and multi-layer plates.

Original languageEnglish
Pages (from-to)357-372
Number of pages16
JournalStructural Health Monitoring
Issue number2
Publication statusPublished - 1 Mar 2020


  • elastodynamic reciprocity relation
  • isotropic plates
  • Lamb wave
  • normal mode expansion
  • piezoelectric wafer active sensor
  • tuning curve

ASJC Scopus subject areas

  • Biophysics
  • Mechanical Engineering

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