Generalization of the Faraday problem for the mechanical system «reservoir – liquid» in the presence of a vertical periodic (inharmonic) disturbance

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, in contrast to the classical case,
there is no parametric resonance in the resonance regions with odd numbers.For regions with even
numbers, on the contrary, it is characterized by an increase in the width of the region of instability, the
amplitude of oscillations of the free surface of the liquid and the influence of higher forms of
oscillations.