An approximate analytical technique is presented for handling strongly nonlinear oscillators with generalized rational power restoring force in the presence of damping based on the He’s homotopy perturbation and the extended form of the Krylov-Bogoliubov- Mitropolskii (KBM) methods. Approximate results are compared with the corresponding numerical (considered to be exact) results of the dynamical systems graphically. The comparison of the obtained results verifies its correctness and effectiveness. Our results show acceptable understanding with those solutions obtained by the well-known fourth order Runge-Kutta method for several significant damping. Thus, the proposed technique might play an important role for solving those nonlinear dynamical systems having rational power restoring force of the displacement.
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