Nonlinear vibrations of rotating solid containing a cavity partially filled with an ideal fluid

The nonlinear problem of the vibrations of a solid resting on an elastic anisotropic base is solved with allowance for the slushing of an ideal fluid with a free surface by reducing the problem to a system of 4N + 2 ordinary nonlinear differential equations with the same number of unknowns. N is the number of the first harmonics whose influence on the vibration process is taken into consideration in the analysis. Nonlinear terms of order higher than two are neglected in the solution.