Dergiler / Mathematical and Computational Applications / 2010 / Cilt: 15 - Sayı: 5

Nonlinear vibration analysis of a rigid rod on a circular surface via Hamiltonian approach

Sayfa
974–977
DOI
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Comparison of the obtained result with the exact one shows good agreement even for large amplitudes and strong nonlinearities.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This paper applies the Hamiltonian approach a nonlinear oscillator of a rigid rod on a circular surface without slipping, and its natural frequency is obtained.
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Temel Bulgular & Veri:This paper applies the Hamiltonian approach a nonlinear oscillator of a rigid rod on a circular surface without slipping, and its natural frequency is obtained.
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Sonuç & Katkı:Comparison of the obtained result with the exact one shows good agreement even for large amplitudes and strong nonlinearities.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

This paper applies the Hamiltonian approach a nonlinear oscillator of a rigid rod on a circular surface without slipping, and its natural frequency is obtained. Comparison of the obtained result with the exact one shows good agreement even for large amplitudes and strong nonlinearities.

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Bu Makaleye Atıf Yap

KHAN, Y., WU, Q., ASKARİ, H., SAADATNİA, Z., YAZDİ, M. K. (2010). Nonlinear vibration analysis of a rigid rod on a circular surface via Hamiltonian approach. Mathematical and Computational Applications, Cilt: 15 - Sayı: 5, 974–977. https://ajindex.com/articles/279962

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  1. J.H. He, An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering, Int. J. Mod. Phys. B, 22(2008) 3487-3578 [2] J.H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B, 20(2006) 1141-1199 [3] J.H.He, G.-C. Wu, F. Austin, The variational iteration method which should be followed, Nonlinear Sci. Lett. A. 1 (2010) 1–30. [4] H. Askari, M. Kalami Yazdi, Z. Saadatnia, Frequency Analysis of Nonlinear Oscillators with Rational Restoring Force via He’s Energy Balance Method and He’s Variational Approach, Nonlinear Sci. Lett. A. 1 (2010) 425-430. [5] L. Cveticanin, A New Modified-Elliptic-Harmonic-Balance Method and Its Application for Symmetric and Pure, Quadratic Oscillators, Nonlinear Science Letters A, 1(2010) 53-59 [6] J. Biazar, F. Mohammadi, Multi-Step Differential Transform Method for Nonlinear Oscillators, Nonlinear Science Letters A, 1(2010)391-397 [7] Y. Khan, An Effective Modification of the Laplace Decomposition Method for Nonlinear Equations,” International Journal of Nonlinear 285Sciences and Numerical Simulation, 10(11-12) (2009), 1373-1376. [8] Y. Khan, and Q. Wu, Homotopy Perturbation Transform Method for Nonlinear Equations Using He’s Polynomials,” Computers and Mathematics with Applications, (2010). [9] J.H.He, Hamiltonian approach to nonlinear oscillators, Phy. Lett. A. 374 (2010) 2312-2314. [10] E. W. Gaylord, Natural Frequencies of Two Nonlinear Systems Compared with the Pendulum, J. Appl. Mech. 146 (1959) 145–146 [11] S.S. Ganji, D.D. Ganji, A.G. Davodi, S. Karimpour, Analytical solution to nonlinear oscillation system of the motion of a rigid rod rocking back using max–min approach, Appl. Math. Modelling. 34 (2010) 2676–2684. [12] S. S. Ganji, D. D. Ganji, H. Babazadeh, N. Sadoughi, Application of amplitude–frequency formulation to nonlinear oscillation system of the motion of a rigid rod rocking back, Math. Meth. Appl. Sci. 33 (2010) 157–166. [13] J.H.He, Max-Min Approach to Nonlinear Oscillators, Int. J. Non-linear Sci. Numer. Simul. 9(2), (2008) 207–210. [14] J.H.He, An Improved Amplitude-frequency Formulation for Nonlinear Oscillators, Int. J. Non-linear Sci. Numer. Simul. 9(2), (2008) 211–212. [15] B. S. WU, C. W. LIM, L. H. HE, A New Method for Approximate Analytical Solutions to Nonlinear Oscillations of Nonnatural Systems, Nonlinear Dyn. 32 (2003) 1–13