Engineering Transactions, 50, 1-2, pp. 35–42, 2002
10.24423/engtrans.506.2002

Periodic Solutions for a Kind of Nonlinear Oscillations by a New Asymptotic Approach

Ji-Huan He
Shanghai Donghua University
China

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.
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

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.

J.H. HE, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178, 257–262, 1999.

J.H. HE, Variational iteration method: a kind of nonlinear analytical technique: some examples, International Journal of Nonlinear Mechanics, 34, 4, 699–708, 1999.

J.H. HE, A new perturbation technique which is also valid for large parameters, Journal of Sound and Vibration, 229, 5, 1257–1263, 1999.

J.H. HE, Iteration perturbation method for strongly nonlinear oscillations, Journal of Vibration and Control, 7, 5, 631–642, 2001.

J.R. ACTON, P.T. SQUIRE, Solving Equations with Physical Understanding, Adam Hilger Ltd, Bristol and Boston 1985.

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.

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.




DOI: 10.24423/engtrans.506.2002