Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Vicente Ocqueteau

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.

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

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.
Paper Structure (7 sections, 6 theorems, 58 equations)

This paper contains 7 sections, 6 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. Model Description
  3. Coupling the Fluid and the Platform
  4. Coupling the Floating Platform and the Flexible Beam
  5. Statement of the Main Results
  6. Operator Form of the Governing Equations
  7. Proof of the Main Results

Key Result

Proposition A

For every $f \in H^1(\mathcal{E})$, the system Dirichlet_op_pb admits a unique solution $D_\Omega f \in \dot{H}^1(\Omega) = \{ u \in L_{\rm loc}^1(\Omega) \mid \nabla u \in L^2(\Omega)^2 \}$. Moreover, the Dirichlet-to-Neumann map associated with Dirichlet_op_pb, defined by is well-defined, with $\Lambda_\Omega f \in L^2(\mathcal{E})$. Furthermore, $\Lambda_\Omega$ defines a self-adjoint, positiv

Theorems & Definitions (15)

  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 2.4
  • Proposition A: lannes2025posednessfjohnsfloating
  • Proposition B: ocqueteau2025initialvalueproblemdescribing
  • Remark 3.1
  • Theorem 3.2
  • Theorem 3.3
  • Proposition 4.1
  • ...and 5 more