Power Series -Aftertreatment Technique for Nonlinear Cubic Duffing and Double-Well Duffing Oscillators

Modeling of large amplitude of structures such as slender, flexible cantilever beam and fluid-structure resting on nonlinear elastic foundations or subjected to stretching effects often lead to strongly nonlinear models of Duffing equations which are not amendable to exact analytical methods. In this work, explicit analytical solutions to the large amplitude nonlinear oscillation systems of cubic Duffing and double-well Duffing oscillators are provided using power series-after treatment technique. The developed analytical solutions are valid for both small and large amplitudes of oscillation. The accuracy and explicitness of the analytical solutions are carried out to establish the validity of the method. Good agreements are established between the solution of the new method and established exact analytical solution. The developed analytical solutions in this work can serve as a starting point for a better understanding of the relationship between the physical quantities of the problems as it provides continuous physical insights into the problems than pure numerical or computation methods.