Relationship between the homotopy analysis method and harmonic balance method
首发时间:2009-02-09
Abstract:The relationship between the homotopy analysis method (HAM) and harmonic balance (HB) method is studied. The HAM is employed to obtain the periodic solutions of conservative and self-excited systems, respectively. Different from the usual procedures in the existing literature, the HAM is modified by retaining only several lower harmonics. It is proved that as long as the solution obtained by the modified approach is convergent, it must converge to one HB solution. The Duffing equation, the van der Pol equation and the flutter equation of a two-dimensional airfoil are taken as three illustrative examples to validate the proposed theory.
keywords: homotopy analysis method harmonic balance method relationship
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Relationship between the homotopy analysis method and harmonic balance method
摘要:The relationship between the homotopy analysis method (HAM) and harmonic balance (HB) method is studied. The HAM is employed to obtain the periodic solutions of conservative and self-excited systems, respectively. Different from the usual procedures in the existing literature, the HAM is modified by retaining only several lower harmonics. It is proved that as long as the solution obtained by the modified approach is convergent, it must converge to one HB solution. The Duffing equation, the van der Pol equation and the flutter equation of a two-dimensional airfoil are taken as three illustrative examples to validate the proposed theory.
关键词: homotopy analysis method;harmonic balance method;relationship
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