APPROXIMATE SOLUTIONS OF DAMPED NON LINEAR SYSTEM WITH VARYING PARAMETER AND DAMPING FORCE-Reference-Cited by-同舟云学术

APPROXIMATE SOLUTIONS OF DAMPED NON LINEAR SYSTEM WITH VARYING PARAMETER AND DAMPING FORCE

Published:2019-11-03 Issue: Volume: Page:13-18
ISSN:2664-598X
Container-title:Advances in Mathematical Sciences
language:en
Short-container-title:Adv. Math. Sci.

Author:

KARIM REZAUL¹,DEY PINAKEE¹,AKTER SOMI¹,ASIF AREFIN MOHAMMAD²,SHAHJAHAN MIAH SAIKH¹

Affiliation:

1. Mawlana Bhashani Science and Technology University

2. Jashore University of Science & Technology

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.

Publisher

Knowvel Journals

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