VARIATIONAL ITERATION SOLUTIONS FOR NONLINEAR DIFFERENTIAL EQUATIONS OF DIFFERENT DAMPING MODELS IN OSCILLATIONS AND VIBRATIONS

M. H. Hojjati (Iran) and Hafez Tari (Iran)

Received October 26, 2007

Abstract

In this paper, different damping models of non-hysteretic dynamical systems arising in oscillations and vibrations are presented in which damping is accounted for by linear or nonlinear terms in the equation of motion and by an extra nonlinear differential equation. The Variational Iteration Method (VIM) is then used as a solver of the corresponding nonlinear equations and the results are compared by those obtained numerically. The comparison clearly shows very good agreement which validates the VIM’s results. This demonstrates the applicability of VIM on solving either linear or nonlinear differential equations without the restriction of sensitivity to the degree of the nonlinear terms.

Keywords and phrases: variational iteration method, vibration, oscillation, damping models, non-hysteretic dynamical systems.