Geometric degree of nonconservativity: set of solutions for the linear case and extension to the differentiable non-linear case
Lerbet, J. ; Challamel, N. ; Nicot, F. ; Darve, F.
Type de document
Article de revue scientifique à comité de lecture
Affiliation de l'auteur
UNIVERSITE D'EVRY VAL D'ESSONNE IBISC FRA ; UNIVERSITE EUROPEENNE DE BRETAGNE FRA ; IRSTEA GRENOBLE UR ETGR FRA ; GRENOBLE INP UMR 5521 L3SR FRA
Résumé / Abstract
This paper deals with nonconservative mechanical systems as those subjected to nonconservative positional forces and leading to non-symmetric tangential stiffness matrices. In a previous work, the geometric degree of nonconservativity of such systems, defined as the minimal number l of kinematic constraints necessary to convert the initial system into a conservative one is found to be, in the linear framework, the half of the rank of the skew-symmetric part of the stiffness matrix. In the present paper, news results are reached. First, a more efficient solution of the initial linear problem is proposed. Second, always in the linear framework, the issue of describing the set of all corresponding kinematic constraints is given and reduced to the one of finding all the Lagrangian planes of a symplectic space. Third, the extension to the local non-linear case is solved. A four degree of freedom system exhibiting a maximal geometric degree of nonconservativity (s = 2) is used to illustrate our results. The issue of the global non-linear problem is not tackled. Throughout the paper, the issue of the effectiviness of the solution is systematically addressed.
Applied Mathematical Modelling, vol. 40, num. 11-12, p. 5930 - 5941