Mechanical circuits-based modelling for mechanical dynamics systems

Abstract

The mathematical model of mechanical systems can be obtained through conventional methodologies as free body diagram, Lagrange equations, and electromechanical analogies, among others. These methodologies contemplate the mechanical systems excited by force sources. However, the mechanical systems can be excited by displacement sources too where conventional methodologies fail or represent long-winded procedures. A methodology to cope with mechanical systems excited by displacement sources is introduced. This approach is based on the mechanical circuit representation, a scheme that allows that exposes the interconnections and interactions of the elements of the mechanical system. Some of the conventional methodologies cannot apply when displacement sources are present. If a comparison is established between the conventional methodologies that can work with displacement sources, the methodology developed in this work allows one to obtain the mathematical model of a system faster than using them. The mechanical circuit approach let calculate the forces that would provoke the displacement of each mechanical element in the system directly.