A generalized modelling technique for linearized motions of mechanisms with flexible parts

Analysis and control of vibrations of agricultural machines to improve machine performance and vibration comfort of the operator is a major concern of manufacturers these days. In this paper, an analytical method to build the linearized equations of motion of an elastic tree structured mechanism, is presented. The method is based on the principle of virtual work resulting in a set of parameterized linear equations that are functions of the mechanical parameters and the geometry and the interconnection structure of different bodies in the mechanism. The rigid-body motions of the mechanical system are represented by Lagrangian generalized co-ordinates while elastic deformations are described by nodal co-ordinates from a finite element formulation. Explicit expressions for external distributed and concentrated forces and internal concentrated forces acting on the mechanism are given.