Dynamics of the Vibro-Impact Nonlinear Damped and Forced Oscillator under the Influence of the Electromagnetic Actuation

The main objective of the present work is to find an approximate analytical solution for nonlinear differential equation vibro-impact oscillator under influence electromagnetic actuation near primary resonance. trigger regime due Hertzian contact. optimal auxiliary functions method (OAFM) utilized give problem. influences static normal load and resonance are completely studied. novelties proposed procedure presence some new adequate functions, introduction convergence-control parameters, original construction initial first iteration, freedom choose determining values parameters. All these led explicit accurate solution, which another novelty in paper. This technique very accurate, simple, effective, easy apply using only iteration. A second was perform analysis stability model multiple scales eigenvalues Jacobian matrix.