Generalization of the Faraday problem for the mechanical system «reservoir – liquid» in the presence of a vertical periodic two-frequency disturbance
DOI:
https://doi.org/10.15407/fmmit2025.40.122Keywords:
рухомий резервуар, рідина з вільною поверхнею, задача Фарадея, параметричні коливання, параметричний резонанс, області стійкості.Abstract
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 that, unlike the classical case, the presence of the second frequency leads to a narrowing of the parametric resonance region with an increase in the amplitude of the second harmonic of the external vertical disturbance of the reservoir.
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