Dynamics of Partially Filled Tank Undergoing Vertical Oscillations in Different Frequency Ranges

The stability diagram for the parametric resonance in the mechanical tank–free surface fluid system in the classical Faraday problem has been derived analytically. Unlike the previous studies, the stability diagram is based on the nonlinear equation of the fluid free surface oscillations, which is transformed into the Ince–Strutt form. Perturbation theory, specifically the method of small parameters, has been employed to derive the stability boundary equations. The findings have shown that the cubic nonlinearities in the equation of the fluid parametric oscillations significantly influence only the location of the first instability domain (parametric resonance). To accurately evaluate the effect of third-order nonlinearities on the boundaries of the second and third resonance domains, higher-order nonlinear terms need to be considered.