The Resonance of Septic Nonlinearity of the Forced and Damped Duffing Oscillator

Lubna Naz Arain, Imran Qasim Memon, Asghar Ali Maitlo, Muhammad Afzal Soomro, Sanaullah Dehraj, Rajab Ali Malookani, Asif Mehmood Awan

Abstract

The aim of this paper is to study the dynamics of a nonlinear damped Duffing oscillator under the influence of weak and strong harmonically time-varying external excitation. The mathematical Duffing oscillator is represented by a nonhomogeneous second-order ordinary differential equation with a seventh degree of nonlinearity. The approximate analytical solution of the governing equation is obtained in terms of amplitude and frequency responses via the application of a two timescale perturbation method. The two timescale perturbation method is used to find (un)steady state solution of the Duffing oscillator for weakly and strongly external harmonic excitation. It is found that the amplitude response decays as time increases due to the presence of damping in the system. In addition, the forcing and septic nonlinearity parameters are found to be dominated by the nonlinearity and amplitude of the system.

 

Keywords: damped duffing oscillator, external excitation, two timescale perturbation method, resonance.

 

https://doi.org/10.55463/issn.1674-2974.50.6.9


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