PERTURBATION SOLUTIONS OF FIFTH ORDER OSCILLATORY NONLINEAR SYSTEM WITH DAMPING EFFECTS

Nonlinear phenomena related to engineering problems arise in the nature of fifth degrees of freedom are oscillatory. The governing equations of such problems are fifth order nonlinear differential systems with damping effects. In this article the Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended to obtain the solution of fifth order weakly nonlinear oscillatory systems with damping effect and preferred result has been achieved. An example is agreed to illustrate the implementation of the presented method. The first order analytical approximate solutions obtained by the method illustrate a good agreement with those obtained via numerical method for the several damping effects.