Stationary response of liquid free surface under wide-band random parametric excitation

The stationary response of a liquid free surface in a partially filled cylindrical container, to a wide band random parametric excitation, is investigated. Two analytical approaches are employed. The first is the Gaussian closure scheme to truncate the infinite hierarchy moment equations obtained through the Fokker-Planck equation, and the second is the Stratonovich stochastic averaging approach. The validity of the two solutions is examined by comparing the two analytically predicted probability densities with the one obtained through experiments. The comparison reveals poor agreement with the Gaussian probability density. In contrast, the probability density derived by the averaging method agrees very well with the experimental density.