Free-vibration acoustic resonance of a nonlinear elastic bar

Ryuichi Tarumi, Yoshihito Oshita

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.

Original languageEnglish
Pages (from-to)772-786
Number of pages15
JournalPhilosophical Magazine
Issue number5
Publication statusPublished - Feb 11 2011


  • calculus of variation
  • complex Fourier series
  • direct analysis by the Ritz method
  • free-vibration acoustic resonance
  • nonlinear elasticity

ASJC Scopus subject areas

  • Condensed Matter Physics


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