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

在过去的几十年里，粘性液体与固体相互作用的运动研究已经成为应用研究的主要焦点之一。本项目的目标是解决固体-液体相互作用的两个基本方面，旨在实现以下目标。第一个专门研究具有完全充满粘性液体的内部空腔的刚体的运动。第二种是关于粘性液体中刚体的振动诱导运动。一个特别重要的例子是，当振动是由体内的时间周期性位移的质量引起的时，粘性液体与固体(无论是刚性的还是可变形的)的相互作用构成了一个复杂而有趣的理论和应用研究课题。事实上，它不仅具有基本的理论意义，而且也代表了许多不同规模的工程、生物和医学研究的重点。与本项目直接相关的重要应用一方面包括飞行动力学、空间技术和地球物理问题，另一方面包括机器人工程和微型和纳米技术设备的设计。

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.