Homotopy Analysis Method for Large-Amplitude Free Vibrations of Strongly Nonlinear Generalized Duffing Oscillators

In this study, the homotopy analysis method (HAM) is used to solve the generalized Duffing equation. Both the frequencies and periodic solutions of the nonlinear Duffing equation can be explicitly and analytically formulated. Accuracy and validity of the proposed techniques are then verified by comparing the numerical results obtained based on the HAM and numerical integration method. Numerical simulations are extended for even very strong nonlinearities and very good correlations which achieved between the results. Besides, the optimal HAM approach is introduced to accelerate the convergence of solutions.