| Summary: | In this article, the dynamic behavior of nonlinear autonomous system modeled by 4-th order ordinary differential equations is considered. Based on the pioneer work of Krylov-Bogoliubov-Mitropolskii (KBM), a modified KBM method is applied to achieve analytical solutions. Two different cases such as non-resonant and resonant conditions are studied in the presence of quadratic nonlinearities. The utility of the proposed method is justified by numerical result which is generated by Runge-Kutta fourth-order procedure. The analytical solution in each case shows an excellence agreement with numerical results. Keywords: KBM method, Autonomous system, Nonlinearity, Internal resonance
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