Generalizing the Faraday Problem of the Parametric Oscillations of a Cylindrical Tank Partially Filled with a Fluid

The nonlinear dynamics of a tank partially filled with a fluid for the generalized Faraday problem is studied. The classical Faraday problem is generalized in two ways: (i) the mechanical system is allowed to translate in a horizontal plane, which is an additional degree of freedom and (ii) the tank can undergo vertical harmonic oscillations either in a prescribed manner (as in the classical Faraday problem) or under the action of a vertical force. It is shown that in the presence of the additional degree of freedom, the dynamic processes in the system develop as a combination of parametric resonance and forced oscillations. In this case, the nonlinear vibrations of the system can be induced by either kinematic perturbations or dynamic excitation (force)