Analytical and Numerical Study of Two Problems Arising in solid-Liquid Interaction

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Over the past decades, the study of the motion of a viscous liquid interacting with solid bodies has become one of the main focuses of applied research. Objective of this project is to address two fundamental aspects of solid-liquid interaction directed toward the accomplishment of the following objectives. The first one is devoted to the motion of a rigid body with internal cavities that are completely filled with a viscous liquid. The second one concerns the vibration-induced motion of a rigid body in a viscous liquid. A particularly significant case is when the vibration is induced by a time-periodically displaced mass inside the body.The interaction of a viscous liquid with a solid body (either rigid or deformable) constitutes a complex and intriguing topic of theoretical and applied research. In fact, not only is it of fundamental theoretical interest, but it also represents the focus of many engineering, biological and medical studies at different scales. Important applications that are immediately related to the present project include, on the one hand, dynamics of flight, space technology, and geophysical problems, and on the other hand, robotic engineering and design of micro- and nano-technological equipment.