AN ANALYTICAL APPROXIMATION TECHNIQUE FOR THE DUFFING OSCILLATOR BASED ON THE ENERGY BALANCE METHOD

Abstract

In this paper, an analytical approximation technique has been presented of obtaining higher-order approximate solutions for highly nonlinear Duffing oscillator based on the energy balance method (EBM).  Higher-order approximate natural frequencies have been obtained in a novel analytical way.  The accuracy of the solution method is evaluated within as error analysis.  It is highly remarkable that using the presented technique, the approximation solutions produces desired results even for large oscillation as compared with the exact ones.  Moreover, the solution method yields much better results than existing solutions after using a suitable truncation formula.  The presented technique is applied to well-known Duffing oscillator to illustrate its novelty, reliability and wider applicability.