Abstract
This paper reviews the simplest mathematical theories that have been advanced to describe the effects of nonlinearity on fluid resonance in two paradigm situations, namely gas oscillating in a container and water sloshing in a tank. These configurations illustrate what can happen when nonlinearity competes with geometrical asymmetry, dispersion or various kinds of damping in limiting the resonant response. In all situations the qualitative form of the response depends crucially on whether or not the natural frequencies of the system are rationally related to each other.
Sommario. Questo lavoro passa in rassegna le più semplici teorie matematiche disponibili per la descrizione degli effetti delle nonlinearità sulla risonanza dei fluidi in due situazioni paradigmatiche, un gas oscillante in un recipiente e l'acqua oscillante in una vasca. Queste configurazioni illustrano le situazioni che possono verificarsi quando le nonlinearità competono con l'asimmetrica geometrica, la dispersione o diversi tipi di smorzamento, nel limitare la risposta risonante. In tutte le situazioni, gli aspetti qualitativi della risposta dipendono in modo cruciale dall'esistenza o meno di rapporti razionali fra le frequenze naturali del sistema.
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Ockendon, H., Ockendon, J. Nonlinearity in Fluid Resonances. Meccanica 36, 297–321 (2001). https://doi.org/10.1023/A:1013911407811
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DOI: https://doi.org/10.1023/A:1013911407811