Generalizations of the Faraday problem in mechanical system "reservoir–liquid with a free surface"

: pp. 45-60
Received: June 30, 2014
Taras Shevchenko Kyiv National University
Institute of Mathematics NAS of Ukraine

Two generalizations of the classical Faraday problem on development of parametric resonance in mechanical system "reservoir – liquid with  free surface", namely, the effect of supplementary degree of freedom, i.e., possibility of horizontal motion of reservoir due to transversal motion of free surface of liquid, and effect of supplementary degree of freedom, i.e., possibility of angular oscillations of reservoir, which is suspended as pendulum, due to transversal oscillations of a free surface of liquid. Investigation is done on the basis of efficient nonlinear multimodal model, which considers combined motion of reservoir and free surface of the liquid. It was shown that, in contrast to the classical Faraday problem, dynamical processes in the system are developed as aggregate of parametric and forced mechanisms of oscillations. For the considered generalizations of the Faraday problem transition of oscillations of free surface of the liquid into nonlinear range of excitations is possible for any frequency of external vertical excitation of reservoir.

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Math. Model. Comput. Vol. 1, No. 1, pp. 45-60 (2014)