Chladni figures of a circular plate floating in bounded and unbounded water bodies with securing support at the center

In the framework of circular symmetry, we carry out numerical and analytical research into the Chladni modes an elastic plate that floats on the surface of a fluid and is cantilever fitted at the center to a vertical support. Using the theory of long waves in shallow water and the approximation of the vibrations of an Euler beam for bounded and unbounded water bodies, we obtain the expressions for the dependency of the natural and quasi-natural frequencies of the Chladni figures on the geometric parameters of the plate and the vibration domain with the bottom irregularity taken into account.