MODIFIED HOMOTOPY PERTURBATION METHOD BASED SOLUTION OF LINEARLY DAMPED DUFFING OSCILLATOR AND COMPARISON WITH SIMULATED SOLUTION*
By
Anunay K. Chaudhary1, Pankaj Narang2 and M. K. Das3
1Department of Physics, Sri Venkateswara College University of Delhi, South Campus
Benito Juarez Road, New Delhi, India 110021
2Department of Physics, Atma Ram Sanatan Dharm College University of Delhi, South Campus
Dhaula Kuan, New Delhi, India 110021
3Institute of Informatics & Communication, University of Delhi, South Campus
Benito Juarez Road, New Delhi, India 110021
Email: akchaudhary@svc.ac.in, pnarang@arsd.du.ac.in, dasmkd11@gmail.com
(Received: February 19, 2023; In format: March 02, 2023; Revised: September 04, 2023; Accepted: October 08, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53222
Abstract
The Dung oscillator provides a basis for studying nonlinear dynamics as its phase space trajectory is fairly complex and depends on the parameter of the system viz., initial amplitude, phase, frequency, linear damping coefficient and non-linearity parameter. In order to understand the complexity of the system, three variable effective expansions have been introduced in the usual homotopy perturbation framework to obtain the solution of damped Dung system which nds application in several areas in engineering sciences such as vibration of bars, plates and electronic circuits, etc. The necessity of the extended homotopy frame work has been further discussed for non-conservative system. Simulation results for different parameters of the systems, such as, linear damping coefficient (μ), amplitude (α) and nonlinearity parameter (ε) are compared with the corresponding results based on perturbative homotopy analysis up to third order by changing (i) the magnitude of linear damping coefficient (μ), (ii) the magnitude of the nonlinearity of the system (ε). Even though the simulated result matches satisfactorily with the perturbative solution over the entire evolutionary time scale, noticeable divergence and phase shift are observed only lately for increased value μ and ε, respectively.
2020 Mathematical Sciences Classification: 34D10: 34A34: 37M05: 70K60.
Keywords and Phrases: Dynamical system, Dung Oscillator, regular solution, Homotopy method, three control parameter expansion.