Analysis of a Model for a Floating Platform Coupled with a Flexible Beam

TL;DR

This paper rigorously analyzes a complex coupled system involving a floating platform, a flexible beam, and a tip mass, using mathematical tools to establish well-posedness and energy conservation.

Contribution

It provides a novel mathematical framework for modeling and analyzing the coupled fluid-structure-elastic system with energy conservation.

Findings

Proved well-posedness of the coupled system

Derived exact energy balance and conservation laws

Formulated the system as an abstract Cauchy problem

Abstract

We provide a rigorous mathematical analysis of a coupled system consisting of a floating platform in a fluid of finite depth, clamped to a flexible Euler-Bernoulli beam. The superstructure supports a rigid tip mass at its free end, resulting in a complex multi-physics interaction between potential flow, rigid-body dynamics, and elasticity. We derive the governing equations by coupling the linearised water-wave equations with the dynamics of the floating foundation and the tip-mass payload. The resulting system is formulated as an abstract Cauchy problem in an appropriate Hilbert space. By employing C0-semigroup theory, we establish its well-posedness. Finally, we derive the exact physical energy balance and prove the energy conservation of the system.