Computer algebra approach for vibrational treatment process dynamics

Abstract

The mathematical model was composed for the studies of nonlinear vibratory process dynamics, and it was applied for an abrasive processing in a magnetic field. A semi-analytical approach, combining the features of analytical and numerical computations, was proposed. Separating the linear and nonlinear parts of equations of motion, the harmonic balance method and computer algebra were synthesized for obtaining the analytical solutions of nonlinear part, whereas the linear part was solved by the numerical methods. On the basis of this technique, the numeric investigation of abrasive treatment process dynamics was performed, regimes ensuring the most effective treatment process were determined. The process optimization was fulfilled using LPi search method maximizing the power of treatment process and the phase difference between the settled motion of abrasive particles and of components being treated.