Open Access Open Access  Restricted Access Subscription or Fee Access

Analytical Solutions of Fourth Order Critically Damped Nonlinear Oscillatory Systems with Pairwise Equal Complex Eigenvalues

M. Abul Kawser, Md. Mizanur Rahman, Md. Mahafujur Rahaman

Abstract



In this paper, we have considered asymptotic solutions, when the four eigenvalues are pairwise equal and complex by modifying the Krylov-Bogoliubov-Mitropolskii (KBM) method, which is regarded as one of the most widely used method for studying the transient behavior of oscillating systems. We apply successfully the modified KBM method to obtain the solutions of fourth order critically damped oscillatory nonlinear systems. It is shown that the solutions obtained by the modified KBM method satisfactorily correspond to those obtained by the numerical method using Mathematica.

Keywords


KBM method, critically damped oscillatory system, nonlinearity, eigenvalues.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.