r4.07.03 Mass matrix calculation added on a modal basis

Summary:

This document presents an aspect of fluid/structure coupling: when a vibrating structure is surrounded by a fluid that is assumed to be flowless, incompressible and non-viscous, it experiences pressure forces whose resultant is proportional to the acceleration of the structure in the fluid: the coefficient of proportionality is homogeneous to a mass: it is called added mass. Here we specify the means of constructing an added mass matrix for one (or more) structures with several degrees of freedom on the modal basis of the structure (s) established beforehand in the absence of fluid. This matrix of added mass is obtained under the hypothesis of small movements for both the structure and the fluid.

• 1. Ratings
• 2. Introduction
• 3. Reminders of the equations of the problem
  • 3.1. Equations in the fluid
  • 3.2. Equations in structures
  • 3.3. Coupled problem equations - highlighting the added mass matrix
  • 3.4. Some definitions
  • 3.5. Properties of the added mass matrix
• 4. Digital implementation
  • 4.1. Solving the Laplace equation by volume finite elements
  • 4.2. Calculation of the coefficients of the added mass matrix on a modal basis
• 5. Implemented in Code_Aster
  • 5.1. Thermal analogy
  • 5.2. Practical implementation
• 6. Bibliography
• 7. Description of document versions