Abstract
In the previous Chap. 5 we have seen how the spatial discretization of a flexible multibody system leads to a differential-algebraic equation in time. The partitioning into two types of state variables, namely, those for the gross motion, on the one hand, and those for the elastic deformations, on the other, quite often involves widely different time scales. This chapter is devoted to such stiff mechanical systems. In numerical analysis, the adjective “stiff” typically characterizes an ordinary differential equation whose eigenvalues have strongly negative real parts. However, numerical stiffness may also arise in case of second order differential equations with large eigenvalues on or close to the imaginary axis. If such high frequencies are viewed as a parasitic effect which perturbs a slowly varying smooth solution, implicit time integration methods with adequate numerical dissipation are an option and usually superior to explicit methods. For a mechanical system, this form of numerical stiffness is directly associated with large stiffness forces, and thus the notion of a stiff mechanical system has a twofold meaning.
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Simeon, B. (2013). Stiff Mechanical System. In: Computational Flexible Multibody Dynamics. Differential-Algebraic Equations Forum. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35158-7_6
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DOI: https://doi.org/10.1007/978-3-642-35158-7_6
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