Geometric degree of nonconservativity

Abstract

This paper deals with nonconservative mechanical systems subjected to nonconservative positional forces leading to nonsymmetric tangential stiffness matrices. The geometric degree of nonconservativity of such systems is then defined as the minimal number ℓ of kinematic constraints necessary to convert the initial system into a conservative one. Finding this number and describing the set of corresponding kinematic constraints is reduced to a linear algebra problem. This index ℓ of nonconservativity is the half of the rank of the skew-symmetric part Ka of the stiffness matrix K that is always an even number. The set of constraints is extracted from the eigenspaces of the symmetric matrix K2a. Several examples including the well-known Ziegler column illustrate the results.