Application of Homotopy Analysis Method for Investigating Nonlinear Oscillations

Abstract

Homotopy Analysis Method (HAM) is a well organized method to get the periodic solution of Non-Linear Oscillatory Duffing Equation of Motion. By having a glance on Helmholtz Equation of Motion an attempt has been made to explore the proficiency of HAM. This research article explores on Helmholtz Equation of Motion possessing non-odd restoring force function. Moreover in this equation the behavior of oscillations is different for the same magnitude of +ve and -ve amplitudes. This phenomenon concerns with asymmetric oscillations which are nonlinear. In the case of large amplitude vibrations a greater amount of inconsistency has been noticed here. Furthermore the incapability of HAM in differentiating the non-periodic solution of Motion has been extensively discussed.