Zur Elastostatik des gebetteten Kreisringbalkens

Beim schlanken kreisförmig geschlossenen schubstarren Balken auf nachgiebiger, vorgespannter Bettung zeigt sich die bekannte Konzentration der Verschiebung in der Umgebung der radial eingeleiteten Einzelkraft. Hier wird zusätzlich die lastinvariante Länge des Kreisbalkens berücksichtigt und das physikalisch nahe liegende Phänomen, dass die Bettung auch eine tangentiale Steifigkeit haben kann. Dann ergeben sich ein deutlich verändertes Verschiebungsfeld und ein steiferes System

Effects of Dissipation Energy on Vibrational and Sound Energy Flow

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Mathematisches Modell zur Simulation von Schwingungen an Horizontalachs-Windkraftanlagen

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Discrete Routh Reduction

This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical $J_2$ correction, as well as the double spherical pendulum. The $J_2$ problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a nontrivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the noncanonical nature of the symplectic structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added, fixed typo