Non-linear parametric liquid sloshing under wide band random excitation

Abstract

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. These are the Gaussian closure scheme to truncate the infinite hierarchy moment equations, and the Stratonovich stochastic averaging method. The validity of the two solutions is examined by comparing the two predicted probability densities with the one measured experimentally. The comparison reveals poor agreement with the Gaussian closure results in contrast to those obtained by the stochastic averaging method, which gives a good description for the random surface motion. In general, the results compare well for surface amplitudes greater than the most probable amplitude, but below the most probable amplitude there is a remarkable deviation. This deviation is found to increase as the excitation level decreases. It is concluded that the uncertainty of the experimental measurements and the inaccuracy of the experimental fitting curves are the main source of the resulting difference.