The Equivalent Linearization Method with a Weighted Averaging for Analyzing of Nonlinear Vibrating Systems

Abstract

IN THIS PAPER, THE EQUIVALENT LINEARIZATION METHOD (ELM) WITH A WEIGHTED AVERAGING, WHICH IS PROPOSED BY ANH (ANH, 2015), IS APPLIED TO ANALYSE SOME VIBRATING SYSTEMS WITH NONLINEARITIES. THE STRONGLY NONLINEAR DUFFING OSCILLATOR WITH THIRD, FIFTH, AND SEVENTH POWERS OF THE AMPLITUDE, THE OTHER STRONGLY NONLINEAR OSCILLATORS AND THE CUBIC DUFFING WITH DISCONTINUITY ARE CONSIDERATED. THE RESULTS OBTAINED VIA THIS METHOD ARE COMPARED WITH THE ONES ACHIEVED BY THE MIN-MAX APPROACH (MMA), THE MODIFIED LINDSTEDT – POINCARE METHOD (MLPM), THE PARAMETER – EXPANSION METHOD (PEM), THE HOMOTOPY PERTURBATION METHOD (HPM) AND 4TH ODER RUNGE-KUTTA METHOD. THE OBTAINED RESULTS DEMONSTRATE THAT THIS METHOD IS VERY CONVENIENT FOR SOLVING NONLINEAR EQUATIONS AND ALSO CAN BE SUCCESSFULLY EXERTED TO A LOT OF PRACTICAL ENGINEERING AND PHYSICAL PROBLEMS.