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An analytical and numerical study of the wobbling dynamics of friction disks is presented. Of particular interest is the excitation mechanism taking into account two contrarian effects both originating in dry friction: the circulatory terms describing the energy input due to the sliding contacts and the friction induced damping which stabilizes the system. Balance of these terms determines the instability domain in the parameter space. It is shown that there is a slip threshold so that, if the slip is under this limit, the system remains stable. If the slip is larger than this limit, then the criterion of stability is determined by the relation between the friction coefficient and the internal damping. The limit cycle appearing in the unstable domain is also investigated. It is shown that the limit cycle can be described as a kind of a regular reverse precession of the wobbling disc. Its amplitude is limited by the geometric nonlinearity and partial contact loss. Analytic results are compared with numeric simulations.
Multi-phase management is crucial for performance and durability of electrochemical cells such as batteries and fuel cells. In this paper we present a generic framework for describing the two-dimensional spatiotemporal evolution of gaseous, liquid and solid phases, as well as their interdependence with interfacial (electro-)chemistry and microstructure in a continuum description. The modeling domain consists of up to seven layers (current collectors, channels, electrodes, separator/membrane), each of which can consist of an arbitrary number of bulk phases (gas, liquid, solid) and connecting interfaces (two-phase or multi-phase boundaries). Bulk and interfacial chemistry is described using global or elementary kinetic reactions. Multi-phase management is coupled to chemistry and to mass and charge transport within bulk phases. The functionality and flexibility of this framework is demonstrated using four application areas in the context of post-lithium-ion batteries and fuel cells, that is, lithium-sulfur (Li-S) cells, lithium-oxygen (Li-O) cells, solid oxide fuel cells (SOFC) and polymer electrolyte membrane fuel cells (PEFC). The results are compared to models available in literature and properties of the generic framework are discussed.