Generalization of the Faraday problem for the mechanical system «reservoir – liquid» in the presence of a vertical periodic (sawtooth) disturbance
DOI:
https://doi.org/10.15407/fmmit2024.39.005Keywords:
movingreservoir, freesurfaceliquid, Faradayproblem, parametricoscillations, stablearea, sawtoothexcitationAbstract
The generalization of Faraday's classic problem about the parametric resonance of the free surface
during vertical oscillations of the tank according to the periodic law of the modulus of the cosine is
considered. Regions of stability and instability are designed, which are compared with similar results for
the classical Faraday problem. The behavior of the system is considered on the basis of a nonlinear
multimode model, which describes the combined movement of the tank and fluid under the influence of
external force excitation or kinematic disturbance. It is shown,the oscillations of the free surface liquid
in both cases of Faraday problem are qualitatively similar, and therefore any of the selected types of
disturbances can be used in research on parametric resonance to obtain a qualitative effecton the
oscillations of the free surface liquid.
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