Chladni figures of a circular plate floating in the bounded and unbounded water basins with the cantilevered central support

Abstract

In the case of circular symmetry, we conduct numerical and analytical studies of Chladni modes of an elastic plate floating on the liquid surface and cantilevered at the center to a vertical support. Using the theory of long waves in shallow water and the approximation of the Euler beam vibrations for the bounded and unbounded water basins, we obtain the dependence of the natural and quasinatural frequencies of Chladni figures on the geometric parameters of the plate and the vibration region in presence of the bottom unevenness.