Abstract
In order to obtain a highly accurate periodic solution for systems based on Duffing equation with single-degree-of-freedom, an averaging method, which has been improved through the use of the Jacobian elliptic function, is proposed. Solution by combined Jacobian elliptic cosine and sine function are used as the generating solution of this averaging method. Numerical results of 3rd order subharmonic vibration and 3rd order higher harmonic vibration of forced Duffing oscillator are shown. By comparing with the very accurate numerical solution obtained by shooting method, it is confirmed that the present method is very effective in analyzing periodic solution of subharmonic and higher harmonic vibration.
