Integrated Analytical, Experimental, and Numerical Study of the Effect of Hydro-static Loading on the Vibrational Response of Clamped Circular Plates

Abstract

This paper presents a comprehensive investigation, comprised of analytical, experimental and numerical approaches, into the interaction between a water cavity of varying fluid cavity height and the vibration of a thin circular plate subjected to its hydro-static pressure. We extend the application of the strong modal coupling method to derive a solution for this unexplored physical problem by utilising classic plate theory, Fourier-Bessel series formulation and the uncoupled solution of a thin clamped circular plate with uniform radial tension. Using a set of geometric and physical properties for the system, the resonance frequencies, response functions and non-dimensionalised added virtual mass incremental (NAVMI) factors are calculated and investigated as a function of hydro-static pressure and fluid cavity height, providing novel fundamental insights into the physical system. We construct an experimental rig to embody the conditions of the analytical investigation for the purpose of validation and to uncover experimental insights into the physical problem. Finite element analysis (FEA), employing modal analysis and transient dynamic analysis, is used to further validate and extend the analytical insights while more accurately mirroring the experimental conditions. The response functions, resonance frequencies and NAVMI factors and their dependence on the cavity pressure were experimentally measured and numerically simulated, with direct comparisons made with the analytical model. A high degree of accuracy for the analytical model is validated, along with its ability to describe the underlying physical phenomena. The validated analytical model is then leveraged to perform fundamental explorations into the modal compositions of the coupled system modes as a function of cavity height and hydro-pressure, the deformation of the coupled system mode shapes and a parametric sensitivity analysis on the effects of plate radii and plate thickness on the coupled system resonance frequencies and NAVMI factors. In totality, this study provides detailed modelling and prediction of the frequency response, resonance frequencies, added mass factors, modal contributions, and deformation of the coupled mode shapes, offering comprehensive insights with wide applicability.