Problem of the Parametric Oscillations of a Noncylindrical Tank Partially Filled with a Fluid

The nonlinear dynamics of a mechanical system consisting of a cylindrical tank partially filled with a fluid for the generalized Faraday problem is studied. Unlike the classical Faraday problem, the tank can undergo transverse horizontal motion, which is an additional degree of freedom for the system. Also, the tank can undergo vertical harmonic oscillations either in a prescribed manner (as in the classical Faraday problem) or under a vertical force. The parametric oscillations of the free liquid surface in a noncylindrical tank are considered. It is shown that with the additional degree of freedom, the dynamic processes in the system combine a parametric resonance and forced oscillations. In this case, the system can oscillate nonlinearly due to both kinematic perturbations and dynamic excitation (force). The effect of the inclination of the tank walls on the parametric oscillations is established © 2016, Springer Science+Business Media New York.