Abstract
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 language | English |
|---|---|
| Pages (from-to) | 772-786 |
| Number of pages | 15 |
| Journal | Philosophical Magazine |
| Volume | 91 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Feb 11 2011 |
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Keywords
- 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
Cite this
Free-vibration acoustic resonance of a nonlinear elastic bar. / Tarumi, Ryuichi; Oshita, Yoshihito.
In: Philosophical Magazine, Vol. 91, No. 5, 11.02.2011, p. 772-786.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Free-vibration acoustic resonance of a nonlinear elastic bar
AU - Tarumi, Ryuichi
AU - Oshita, Yoshihito
PY - 2011/2/11
Y1 - 2011/2/11
N2 - 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.
AB - 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.
KW - calculus of variation
KW - complex Fourier series
KW - direct analysis by the Ritz method
KW - free-vibration acoustic resonance
KW - nonlinear elasticity
UR - http://www.scopus.com/inward/record.url?scp=79551510449&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79551510449&partnerID=8YFLogxK
U2 - 10.1080/14786435.2010.530614
DO - 10.1080/14786435.2010.530614
M3 - Article
AN - SCOPUS:79551510449
VL - 91
SP - 772
EP - 786
JO - Philosophical Magazine
JF - Philosophical Magazine
SN - 1478-6435
IS - 5
ER -