Abstract
The Lagrange’s equation remains the most used method by researchers to determine the finite element motion equations in the case of elasto-dynamic analysis of a multibody system (MBS). However, applying this method requires the calculation of the kinetic energy of an element and then a series of differentiations that involve a great computational effort. The last decade has shown an increased interest of researchers in the study of multibody systems (MBS) using alternative analytical methods, aiming to simplify the description of the model and the solution of the systems of obtained equations. The method of Kane’s equations is one possibility to do this and, in the paper, we applied this method in the study of a MBS applying finite element analysis (FEA). The number of operations involved is lower than in the case of Lagrange’s equations and Kane’s equations are little used previously in conjunction with the finite element method (FEM). Results are obtained regardless of the type of finite element used. The shape functions will determine the final form of the matrix coefficients in the equations. The results are applied in the case of a planar mechanism with two degrees of freedom.
Highlights
The dynamic analysis of a multibody system (MBS) with elastic elements requires, as a first step, time response of a single finite element, obtained via the equations of motion
Analytical mechanics offers a large number of formalisms for determining the equations of motion
Because there are many parameters that can vary, integrating the equations of motion of the mechanism, considering all the rigid elements is difficult and will lead to results far from reality. This is due to the fact that a number of factors such as joints that appear in the joints, the engine couple, and the frictions that occur in the joints which cannot be accurately determined
Summary
Department of Mechanical Engineering, Transilvania University of Bras, ov, B-dul Eroilor, 20, 500036 Bras, ov, Romania Technical Sciences Academy of Romania, B-dul Dacia, 26, 030167 Bucharest, Romania Department of Mechanical Systems Engineering, Faculty of Machine Building, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania Department of Mathematics, Transilvania University of Bras, ov, B-dul Eroilor, 20, 500036 Bras, ov, Romania;
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