Analysis of Highly Nonlinear Oscillation System Using He's Max-Min Method and Comparison with Homotopy Analysis Method and Energy Balance Methods

Lars Bo Ibsen, Amin Barari, Amin Kimiaeifar

    Publikation: Bidrag til bog/antologi/rapport/konference proceedingBidrag til bog/antologiForskning

    Abstrakt

    Nonlinear functions are crucial points and terms in engineering problems and the solutions of many important physical problems are centered on finding accurate solutions to these functions. In this paper, a new method called max–min method has been presented for deriving accurate/approximate analytical solution to strong nonlinear oscillators. Furthermore, it is shown that a large class of linear or nonlinear differential equations can be solved without the tangible restriction of sensitivity to the degree of the nonlinear term, adding that the method is quite convenient due to reduction in size of calculations. Results obtained by max–min are compared with Homotopy Analysis Method (HAM), energy balance and numerical solution and it is shown that, simply one term is enough to obtain a highly accurate result in contrast to HAM with just one term in series solution. Finally, the phase plane to show the stability of systems is plotted and discussed.
    OriginalsprogEngelsk
    TitelProgram Review, July 2009 - June 2010 : Joint Research and Development: Innovative Foundation Solutions
    RedaktørerSøren A. Nielsen
    Antal sider16
    UdgivelsesstedAalborg
    ForlagMBD Offshore Power A/S and Aalborg University
    Publikationsdato2010
    StatusUdgivet - 2010

    Emneord

    • Min-Max Method
    • Nonlinear Oscillation
    • Duffing Equation
    • Homotopy Analysis Method
    • He's Energy Balance Method

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