Comments on the Application of Homotopy Analysis Method for Investigating Nonlinear Oscillations

Abstract

Homotopy analysis method (HAM) claimed to be an efficient for obtaining the periodic solution for a nonlinear oscillatory Duffing equation of motion. An endeavor is made here to look at its competence by considering the Helmholtz equation of motion. The Helmholtz equation of motion having non-odd restoring force function and the behavior of oscillations are to be unlike for the same magnitude of positive and negative amplitudes. This problem corresponds to the case of nonlinear asymmetric oscillations. Large discrepancy is noticed in the results for the case of large amplitude vibrations. The Homotopy analysis method is not capable to differentiate the non-periodic solution of the Helmholtz equation of motion.