A comprehensive methodology to obtain electrical analogues of linear mechanical systems

Abstract

Electrical analogues of linear mechanical systems have traditionally been obtained using a set of rules that can potentially be tedious when applied to complex systems. In addition, such rules do not cover all the possibilities of mechanical systems including rotational and translational generalized coordinates. The present work establishes a comprehensive and systematic methodology for obtaining the electrical analogue of any mechanical system modelled by rigid bodies, springs, and dampers. The method is simple and straightforward. First, the dynamic equations of the mechanical system are derived into matrix form. These equations are then translated to the electrical domain by means of the electromechanical analogy and, finally, the electrical circuit is obtained by direct inspection of the matrices. In addition, the method can deal with a combination of translational and rotational coordinates in the definition of the mechanical model. To support the proposed method, and beyond the planar vehicle models found in the literature, the electrical analogue of a linear 3D 7-DOF full car model is presented in this work.