Study on High Performance Averaging Method for a Strongly Nonlinear System. 1st Report, In Case that the Jacobian Elliptic Cosine Function is Used as a Generating Solution.

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  • 強非線形系に対する平均法の高性能化に関する研究　第１報　　ヤコビのｃｎ楕円関数を母解とする場合
  • キョウ ヒセンケイケイ ニ タイスル ヘイキンホウ ノ コウセイノウカ ニ カンスル ケンキュウ ダイ1ポウ ヤコビ ノ cn ダエン カンスウ オ ボカイ ト スル バアイ

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Abstract

The averaging method improved by using the Jacobian elliptic function is developed in order to obtain a highly accurate periodic solution for a strongly nonlinear system. The Jacobian elliptic cosine function (so-called cn function) is used as a generating solution for the harmonically excited Duffing-type equation with hardening spring and damping. The stability for approximate solution obtained by the present method is also discussed. By comparing with the very accurate numerical solutions obtained by applying the shooting method, it is confirmed that the present method gives more accurate solution than that obtained by the traditional averaging method using the trigonometric function. In addition, not only the fundamental amplitude but also the higher harmonic amplitudes of the solution obtained by the present method are in good agreement with those obtained by the shooting method.

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