Experimental and Numerical Study of Linear Vibrations of a Thin Plate in contact with a bounded Liquid

In this paper the dynamical response of a thin plate in contact with a liquid (water) on one side has been experimentally studied, considering different filling levels. The free liquid surface is free to slosh and the water is delimited by practically rigid walls, except for the thin plate. In particular, the specific case of rectangular tank with a vibrating thin plate wall is analyzed in the present study. In particular, the execution of the linear tests is the primary objective of this thesis: the five experimental tests have been realized with the aim to describe the dynamic response (natural frequency) of the thin plate, both when the tank is empty that when the tank is filled with different levels of liquid. For this purpose, the liquid-coupled natural frequencies of the plate are obtained carrying out Modal Analysis which allows to extract Modal Shapes of the thin plate. The Modal Shapes have been derived from the Frequency Response Functions (FRFs) measured by the use of a Mesh Grid Points which consent to calculate, for each point, the dynamical response of the plate as a result of an excitation transmitted to the system. In particular, the plate deflection due to hydrostatic pressure plays a significant role in changing the plate nonlinearity, and experimental tests carried out by the use of a scanning laser confirm a non-linear dependency between the hydrostatic pressure exerted by the liquid on the plate surface and its consequent deformation. In order to check and verify the experimental results, three-dimensional finite element analyses is also carried out for the plate-tank system using a commercial computer code, Comsol Multiphysics. In this specific study, numerical simulations have been particularly useful to verify and quantify the deviation between numerical natural frequencies obtained during the experimental tests and those achieved by the FEM analysis. In this regard, it is necessary to emphasize that the plate presents microscopic geometric imperfections, can not be eliminated and attributable, mainly, to the processes of machining and to thermal stress.