Use of the Whittaker Equations in FEA of Two-Dimensional Elastic Multibody Systems

Abstract

In a previous paper [1], methods for obtaining the equations of motion for an MBS system with elastic elements were presented, using the finite element method (FEM), for the case of planar systems, composed of elastic plates, where two-dimensional finite elements were used. In the present paper, the methods presented are extended for the case of scleronomic, holonomic systems, using Whittaker's equations. The results contribute to the development of the study of the field of multibody systems with elastic elements. This development is imposed by the increase in the performance of machines and mechanisms, which has led to an increase in the operating speeds and forces developed in these systems. The result was that the elasticity of the various elements of a mechanical system can significantly influence its behavior, and undesirable phenomena such as vibrations or loss of stability may appear. In the paper, a classical method from Analytical Mechanics is applied, in parallel with FFM, for the study of mechanical systems with certain particularities in plane motion. The main advantage offered by this approach is the reduction of the number of independent coordinates necessary to describe the motion of a finite element, ultimately resulting in the reduction of the number of differential equations describing the motion of the entire system.