By Hans Irschik, Alexander K. Belyaev
The booklet offers updated and unifying formulations for treating dynamics of alternative varieties of mechanical platforms with variable mass. the place to begin is assessment of the continuum mechanics kin of stability and bounce for open structures from which prolonged Lagrange and Hamiltonian formulations are derived. Corresponding methods are acknowledged on the point of analytical mechanics with emphasis on structures with a position-dependent mass and on the point of structural mechanics. designated emphasis is laid upon axially relocating constructions like belts and chains and on pipes with an axial circulate of fluid. Constitutive family within the dynamics of platforms with variable mass are studied with specific connection with modeling of multi-component combos. The dynamics of machines with a variable mass are handled intimately and conservation legislation and the soundness of movement may be analyzed. Novel finite aspect formulations for open platforms in coupled fluid and structural dynamics are presented.
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Extra resources for Dynamics of Mechanical Systems with Variable Mass
G. Tait. Treatise on Natural Philosophy. Clarendon Press, Oxford, 1867. W. Tomaszewski, P. -C. Geminard. The motion of a freely falling chain tip. American Journal of Physics, 74(9):776–783, 2006. A. A. Toupin. The classical ﬁeld theories. In S. Fl¨ ugge, editor, Prinzipien der Klassischen Mechanik und Feldtheorie, volume III/1 of Handbuch der Physik (Encyclopedia of Physics), pages 226–793. Springer-Verlag, Berlin G¨ottingen Heidelberg, 1960. W. Wong and K. Yasui. Falling chains. American Journal of Physics, 74 (6):490–496, 2006.
F. Ziegler. Mechanics of Solids and Fluids. Springer-Verlag, New York, second edition, 1998. Systems with mass explicitly dependent on position Celso Pupo Pesce ∗ and Leonardo Casetta † Escola Polit´ecnica, University of S˜ ao Paulo, S˜ ao Paulo, Brazil Abstract This chapter addresses an interesting type of variable mass systems. Those in which mass may be explicitly written as function of position. Two perspectives can be followed: systems with a material type of source, attached to particles continuously gaining or loosing mass and systems for which the variation of mass is of a “control volume type”, mass trespassing a control surface.
P. Pesce and L. Casetta false by the same authors, in a meritorious scientiﬁc attitude; see Wong et al (2007). The present chapter derives such an extended form of the Lagrange equation, through Lagrangean and Hamiltonian approaches. Illustrative and practical examples are addressed in two engineering ﬁelds, oﬀshore and civil engineering. In the ﬁrst category are included: (i) the reel laying operation of marine cables; (ii) the dynamics of a water column inside a free surface piercing open pipe (and the analogous moon pool problem) and (iii) the hydrodynamic impact of a solid body against a free surface of water.