Efficient Theoretical and Numerical Methods for Solving Free Vibrations and Transient Responses of a Circular Plate Coupled with Fluid Subjected to Impact Loadings
This paper presents an easy-to-use theoretical method and an efficient numerical method for solving free vibrations and transient responses of a circular plate coupled with fluid subjected to impact loadings and provides insights into various coupling cases with these developed methods. The Kirchhoff plate theory, Mindlin-Reissner plate theory, and the linear velocity potential function are used. The wet mode of the coupled system is described as the superposition of dry modes of the plate, which has been considered in few studies. The natural frequencies and corresponding mode shapes are solved using the orthogonality of dry modes. The transient responses of the plate are then solved using the superposition of the wet modes and the orthogonality of dry modes. To validate the theoretical results, an efficient and flexible finite element method is proposed and verified by comparing with commercial software. The four-node mixed interpolation of the tensorial component quadrilateral plate finite element (MITC4) and the eight-node acoustic pressure element are used to model the plate and the fluid, respectively. The theoretical and numerical methods provide reliable and accurate results. Parametric studies are performed to investigate the influence of geometric sizes, plate material properties, and fluid properties on the natural frequencies of the coupled system. A coupling parameter of fluid-structure interaction is proposed. The non-dimensional added virtual mass incremental (NAVMI) factor decreases as the coupling parameter increases. Besides, the influence of fluid on wet modes of the plate decreases with order.
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