Equivalent orthotropic elastic moduli identification method for laminated electrical steel sheets

Akira Saito*, Yasunari Nishikawa, Shintaro Yamasaki, Kikuo Fujita, Atsushi Kawamoto, Masakatsu Kuroishi, Hideo Nakai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


In this paper, a combined numerical-experimental methodology for the identification of elastic moduli of orthotropic media is presented. Special attention is given to the laminated electrical steel sheets, which are modeled as orthotropic media with nine independent engineering elastic moduli. The elastic moduli are determined specifically for use with finite element vibration analyses. We propose a three-step methodology based on a conventional nonlinear least squares fit between measured and computed natural frequencies. The methodology consists of: (1) successive augmentations of the objective function by increasing the number of modes, (2) initial condition updates, and (3) appropriate selection of the natural frequencies based on their sensitivities on the elastic moduli. Using the results of numerical experiments, it is shown that the proposed method achieves more accurate converged solution than a conventional approach. Finally, the proposed method is applied to measured natural frequencies and mode shapes of the laminated electrical steel sheets. It is shown that the method can successfully identify the orthotropic elastic moduli that can reproduce the measured natural frequencies and frequency response functions by using finite element analyses with a reasonable accuracy.

Original languageEnglish
Pages (from-to)607-628
Number of pages22
JournalMechanical Systems and Signal Processing
Publication statusPublished - 2016 May 1
Externally publishedYes


  • Electric machines
  • Electrical steel sheets
  • Inverse problem
  • Laminated composite plates
  • Optimization
  • Parameter-dependent eigenvalue problems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications


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