In order to obtain a highly accurate periodic solution for systems based on strongly quadratic nonlinear oscillators, an averaging method improved through the use of the Jacobian elliptic function is proposed. In the improved averaging method, the Jacobian elliptic sine function is incorporated as the generating solution. The stability criterion for the approximate solutions obtained by this method is also presented. The proposed method is then applied to several different typical nonlinear oscillators. The efficiency of the proposed method is demonstrated by comparing the computational results with those obtained by the shooting method and the conventional averaging method. It is confirmed that the proposed method provides a more accurate solution than the conventional averaging method, which uses a trigonometric function as the generating solution.
|Number of pages||8|
|Journal||Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C|
|Publication status||Published - Jan 2005|
All Science Journal Classification (ASJC) codes
- Mechanics of Materials
- Mechanical Engineering
- Industrial and Manufacturing Engineering