Dynamics of Mechanical Systems with Variable Mass
September 24, 2012 — September 28, 2012
Coordinators:
- Hans Irschik (University of Linz, Austria)
- Alexander K. Belyaev (Russian Academy of Sciences, St. Petersburg, Russia)
The fundamental equations of classical mechanics were originally formulated for situations where mass is conserved in the mechanical system under consideration. Mass is generally not conserved when a supply of mass is present, or when open systems with a flow of mass through their surface are to be considered. Mass of the mechanical system then is said to be variable. In such a situation, the general methodological approaches of mechanics have to be properly modified. In fluid mechanics, open systems are encountered when studying a non-material control volume. In solid mechanics, systems with a variable mass appear as the result of a problem-oriented modeling, e.g. when mass is expelled or captured by a structure or machine. This again leads to the treatment as an open system, or to the assumption that that mass is explicitly dependent on the position. In solid mechanics, as well as in fluid mechanics, it is often appropriate to model the exchange of mass between the system under consideration and the environmental world by means of a supply of mass in the interior. This is of particular interest in the continuum theory of mixtures, for which mass and other entities are exchanged between the various components.
It is the goal of the proposed course to present up-to-date and unifying formulations for treating the dynamics of different types of mechanical systems with variable mass. We start with an overview of the continuum mechanics relations of balance and jump for open systems, from which extended Lagrange and Hamiltonian formulations will be derived, as a basis of current numerical procedures. Corresponding approaches will be stated at the level of the analytical mechanics, with emphasis on systems with a position-dependent mass, and applications to offshore engineering, as well as at the level of structural mechanics. Special emphasis will be laid upon axially moving structures, like belts and chains, and on pipes with an axial flow of fluid. Constitutive relations appearing in the dynamics of mechanical systems with variable mass will be studied with particular reference to the modeling of multi-component mixtures. Damage of steel structures in the form of hydrogen embrittlement will be addressed in this context. The dynamics of machines with a variable mass will be treated in detail and, in this context, conservation laws and the stability of motion will be analyzed. Novel finite element formulations for open systems in coupled fluid and structural dynamics will be presented. Moreover, the course will provide mathematical models directly related to methods of automatic control, and therefore should be of interest in the fields of Civil and Mechanical Engineering, as well as in Mechatronics.
KEYWORDS: Variable Mass, Theory of Mixtures, Extended Lagrange, Formulation, Extended Hamiltonian Formulation.