PERTURBATION SOLUTIONS OF FIFTH ORDER MORE CRITICALLY DAMPED NONLINEAR SYSTEMS WITH LARGE EQUAL EIGENVALUES

In this article, the Krylov-Bogoliubov-Mitropolskii (KBM) method, which is considered to be one of the most convenient and widely used methods of studying the transient behavior of nonlinear systems, is extended with a view to finding out the solutions of fifth order more critically damped nonlinear systems. The analytical approximate solutions of fifth more critically damped nonlinear systems are used, where the three larger eigenvalues are identical and the two others are different. In this study, it is recommended that the perturbation solutions obtained by the modified KBM method demonstrate good coincidence with the numerical solutions.