Abstract
In order to obtain a highly accurate periodic solution for systems based on a Duffing equation with snap-through spring, an averaging method, which has been improved through the use of the Jacobian elliptic function, is proposed. Solution by combined Jacobian elliptic delta and zeta function are used as the generating solution of this averaging method. The proposed method is applicable to periodic solution of half swing mode of snap-through spring system. The method's validity is verified by comparing the results obtained by applying the proposed method to typical nonlinear oscillators with the very accurate numerical solutions computed by the shooting method.
