Abstract
The study of second-order damped nonlinear differential equations is important in the development of the theory of dynamical systems and the behavior of the solutions of the over-damped process depends on the behavior of damping forces. We aim to develop and represent a new approximate solution of a nonlinear differential system with damping force and an approximate solution of the damped nonlinear vibrating system with a varying parameter which is based on Krylov–Bogoliubov and Mitropolskii (KBM) Method and Harmonic Balance (HB) Method. By applying these methods we solve and also analyze the finding result of an example. Moreover, the solutions are obtained for different initial conditions, and figures are plotted accordingly where MATHEMATICA and C++ are used as a programming language.
Highlights
Following the extended Krylov-Bogoliubov-Mitropolskii (KBM) [1, 4, 5, 8] method, Bojadziev and Edwards [2] studied some dampedA significant approach, known as the expansion of the small parameter, oscillatory and non-oscillatory systems modeled by is used to investigate nonlinear oscillatory systems, which is erected upon the perturbation theory
An extension of the Krylov-Mitropolskii (KBM) method which is applied to study nonlinear Bogoliubov-Mitropolskii method and Harmonic Balance method oscillatory and non-oscillatory differential systems with small applied to systems of hyperbolic partial differential equations modeling nonlinearities
Krylov–Bogoliubov and Mitropolskii (KBM) [4] developed a perturbation method to determine an retardation effects is shown. This method was approximate solution of a second order nonlinear differential system developed by Krylov and Bogoliubov to find out the periodic solutions described by of second order nonlinear differential systems with small nonlinearities
Summary
Following the extended Krylov-Bogoliubov-Mitropolskii (KBM) [1, 4, 5, 8] method, Bojadziev and Edwards [2] studied some dampedA significant approach, known as the expansion of the small parameter, oscillatory and non-oscillatory systems modeled by is used to investigate nonlinear oscillatory systems, which is erected upon the perturbation theory. Following the extended Krylov-Bogoliubov-Mitropolskii (KBM) [1, 4, 5, 8] method, Bojadziev and Edwards [2] studied some damped. This theory was used as a basis for one of the widely known methods called the Krylov-Bogoliubov- where c( ) and ( ) are positive. Physical processes with damping and slowly varying parameters The applicability of this technique or the study of similar systems involving. KBM [4] developed a perturbation method to determine an retardation effects is shown In the beginning, this method was approximate solution of a second order nonlinear differential system developed by Krylov and Bogoliubov to find out the periodic solutions described by of second order nonlinear differential systems with small nonlinearities. Popov extended it to damped x 02x f (x, x ),
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