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

Rezaul Karim | Zendy; Pinakee Dey | Zendy; SOMI AKTER | Zendy; Mohammad Asif Arefin | Zendy; Saikh Shahjahan Miah | Zendy

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

Author(s) -

Rezaul Karim,

Pinakee Dey,

SOMI AKTER,

Mohammad Asif Arefin,

Saikh Shahjahan Miah

Publication year - 2019

Publication title -

advances in mathematical sciences

Language(s) - English

Resource type - Journals

ISSN - 2664-598X

DOI - 10.37516/adv.math.sci.2020.0123

Subject(s) - harmonic balance , nonlinear system , differential (mechanical device) , harmonic , mathematics , control theory (sociology) , differential equation , mechanical system , restoring force , process (computing) , mathematical analysis , physics , classical mechanics , computer science , control (management) , quantum mechanics , artificial intelligence , thermodynamics , operating system

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.

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