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Regarding aerodynamic bearings, mainly two basic types can be distinguished: air bearings with a rigid housing and air foil bearings with an elastic supporting structure. Here, a modified bearing concept – called air ring bearing – is investigated, which may be considered as a further development of rigid air bearings or as a combination of the two basic bearing types. The idea of air ring bearings is to insert a ring-shaped bearing bushing between the shaft and the foil structure. Alternatively, a visco-elastic supporting structure (e.g., an elastomer) can be applied to connect the bushing ring with the housing. In the first case, external dissipation is mainly generated by dry friction. In the latter case, viscous damping is used to provide external dissipation. Due to the external friction/damping generated by the ring mounting structure, rotor systems with air ring bearings can be operated above the linear threshold speed of instability so that stable self-excited vibrations with moderate amplitudes can be achieved in the complete speed range. Here, a detailed transient co-simulation model for rotor systems with air ring bearings is presented. The rotor is represented by a multibody model. The air films of the two bearings are represented by two nonlinear time-dependent finite element systems. The multibody model and the two finite element subsystems are solved simultaneously by means of an explicit sequential co-simulation technique. Due to the strong nonlinearities, the system shows interesting vibration and bifurcation effects, which are investigated in detail with the help of runup simulations.

We study the Helmholtz equation with periodic coefficients in a closed waveguide. A functional analytic approach is used to formulate and solve the radiation problem in a self‐contained exposition. In this context, we simplify the non‐degeneracy assumption on the frequency. Limiting absorption principles (LAPs) are studied, and the radiation condition corresponding to the chosen LAP is derived; we include an example to show different LAPs lead, in general, to different solutions of the radiation problem. Finally, we characterize the set of all bounded solutions to the homogeneous problem. [ABSTRACT FROM AUTHOR]

The wave equation with stochastic rapidly oscillating coefficients can be classically homogenized on bounded time intervals; solutions converge in the homogenization limit to solutions of a wave equation with constant coefficients. This is no longer true on large time scales: Even in the periodic case with periodicity ε, classical homogenization fails for times of the order ε − 2 . We consider the one-dimensional wave equation with random rapidly oscillating coefficients on scale ε and are interested in the critical time scale ε − β from where on classical homogenization fails. In the general setting, we derive upper and lower bounds for β in terms of the growth rate of correctors. In the specific setting of i.i.d. coefficients with matched impedance, we show that the critical time scale is ε − 1 . [ABSTRACT FROM AUTHOR]

We consider the wave equation in an unbounded domain and are interested in domain truncation methods. Our aim is to develop a numerical scheme that allows calculations for truncated waveguide geometries with periodic coefficient functions. The scheme is constructed with radiation boxes that are attached to the artificially introduced boundaries. A Dirichlet-to-Neumann operator |$N$| is calculated in these radiation boxes. Efficiency of the scheme is obtained by calculating |$N$| not with an iteration, but with a single run through the time interval. We observe speed-up factors of up to |$20$| in comparison to calculations without domain truncation. [ABSTRACT FROM AUTHOR]