Periodic solution for a kind of nonlinear oscilations by a new asymptotic approach

• Autorzy: Ji-Huan He
• Języki publikacji: EN

Abstrakty

EN

This paper proposes a new asymptotic approach to search for the periodic solutions of a kind of nonlinear oscillations. In this method the iteration technique is coupled with the traditional perturbation techniques, yielding a powerful mathematical tool for solving strongly nonlinear equations. Some examples are given to illustrate its effectiveness, convenience and accuracy. Generally, the first iteration leads to a highly accurate approximate solution which is uniformly valid for the whole solution domain. The new asymptotic approach is named the iteration-perturbation method.

Słowa kluczowe

EN

asymptotic theory; nonlinear oscillations

PL

teoria asymptotyczna

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2002
• Tom: Vol.50, iss.1-2
• Strony: 35--42
• Opis fizyczny: Bibliogr. 8 poz., wykr.

Twórcy

autor

Ji-Huan He

• Shannghai Donghua University, No. 1882 Yan'an xi Lu Road, Shanghai 200051, China,

Bibliografia

• 1. J.H. HE, Treatment shocks in transonic aerodynamics in Meshless Methods, Part I Lagrange multiplier approach, Int. J. Turbo and Jet-Engines, 16, l, 19–26, 1999.
• 2. J.H. HE, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178, 257–262, 1999.
• 3. J.H. HE, Variational iteration method: a kind of nonlinear analytical technique: some examples, International Journal of Nonlinear Mechanics, 34, 4, 699–708, 1999.
• 4. J.H. HE, A new perturbation technique which is also valid for large parameters, Journal of Sound and Vibration, 229, 5, 1257–1263, 1999.
• 5. J.H. HE, Iteration perturbation method for strongly nonlinear oscillations, Journal of Vibration and Control, 7, 5, 631–642, 2001.
• 6. J.R. ACTON, P.T. SQUIRE, Solving Equations with Physical Understanding, Adam Hilger Ltd, Bristol and Boston 1985.
• 7. I. ANDRIANOV, J. AWREJCEWICZ, Construction of periodic solution to partial differential equations with nonlinear boundary conditions, International Journal of Nonlinear Sciences and Numerical Simulation, l, 4, 327–332, 2000.
• 8. J.H. HE, A review on some new recently developed nonlinear analytical techniques, International Journal of Nonlinear Sciences and Numerical Simulation, 1, 1, 51–70, 2000.