A note on the analysis of nonlinear dynamics of elastic membranes by the finite element method

Oden, J. Tinsley; Key, J.E.; Fost, R. B.

doi:10.1016/0045-7949(74)90068-6

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2007

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Cited by 6 publications

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“…They include the perturbation methods such as the method of harmonic balance, method of multiple scales, method of averaging, and the Lindstedt-Poincare method [4]. In the numerical nonlinear analyses, the finite difference method [5] and finite element method [6,7] have been popularly used.…”

Section: Introductionmentioning

confidence: 99%

Spectral Analysis Method for Nonlinear Dynamic Systems

Lee

Kim

2007

KEM

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This paper introduces a FFT-based spectral analysis method (SAM) for the nonlinear dynamic systems whose dynamic behaviors can be represented by the ordinary nonlinear differential equations. To verify the proposed SDM, a damped Duffing's equation is considered as an example nonlinear problem, and the phase diagrams obtained by the present SAM are compared with those obtained by other solution methods such as the method of multiple scales and the Runge-Kutta method.

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Section: Introductionmentioning

confidence: 99%

Spectral Analysis Method for Nonlinear Dynamic Systems

Lee

Kim

2007

KEM

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References

1995

Nonlinear Oscillations

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(1974). The inverse scattering transform Fourier analysis for nonlinear problems. Stud Appl. Math.. 53,249-315.588 Adams, 0. E. and R. M. Evan-Iwanowski (1973 Agrawal, B. N. (1975). Nonstationary and nonlinear vibration analysis and its application.Agrawal, B. J., and R. M. Evan-lwanowski (1973). Resonances in nonstationary, nonlinear, Ahmad, J., and H. C. Lee (1975). Nonlinear acoustic response of a cylindrical shell. J.Ahuja, R., and R. C. Duffield (1975). Parametric instability of variable crosssection beams Aks, S., and R. Carhart (1970). Renormalized perturbation theory for the weakly nonlinear

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Time evolutional analysis of nonlinear structures

Casciaro

1975

Meccanica

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A note on the analysis of nonlinear dynamics of elastic membranes by the finite element method

Cited by 6 publications

References 3 publications

Spectral Analysis Method for Nonlinear Dynamic Systems

Spectral Analysis Method for Nonlinear Dynamic Systems

References

Time evolutional analysis of nonlinear structures

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