Partitioned vibration analysis of internal fluid‐structure interaction problems

Abstract

SUMMARY A partitioned, continuum‐based, internal fluid–structure interaction (FSI) formulation is developed for modeling combined sloshing, acoustic waves, and the presence of an initial pressurized state. The present formulation and its computer implementation use the method of localized Lagrange multipliers to treat both matching and non‐matching interfaces. It is shown that, with the context of continuum Lagrangian kinematics, the fluid sloshing and acoustic stiffness terms originate from an initial pressure term akin to that responsible for geometric stiffness effects in solid mechanics. The present formulation is applicable to both linearized vibration analysis and nonlinear FSI transient analysis provided that a convected kinematics is adopted for updating the mesh geometry in a finite element discretization. Numerical examples illustrate the capability of the present procedure for solving coupled vibration and nonlinear sloshing problems. Copyright © 2012 John Wiley & Sons, Ltd.

Modal Analysis of Liquid–Structure Interaction

“…and that its density in the reference state is homogeneous (∇ X ρ F 0 = 0), then the linearized form of the mass conservation equation (8) can be written…”

“…As a result, the liquid small motions are irrotational. This constraint can be taken into account through various procedures [2,8]. Using a scalar description for the fluid, alternative symmetric variational formulations have been derived [10,13].…”

Mechanical Interaction in Pressurized Pipe Systems: Experiments and Numerical Models

“…In this way, an explicit method can be employed [30]. After discretizing the governing fluid and structural fields, the equilibrium and compatibility conditions must be satisfied at the interface [31][32][33]. The fluid solution is computed using the Navier-Stokes solver on the overlapping domain.…”

A gap element for treating non-matching discrete interfaces

“…As discussed at length in [15], while the frame is akin to the intermediate surface [16], the frame is endowed with its independent displacement degrees of freedom and its associated equilibrium equations. This distinctive frame property has been shown to be applicable not only to interface and contact formulations possessing symmetric systems amenable to variational formulations, but also to a host of couple-field problems leading to partitioned analysis of fluid-structure interaction [31][32][33], parallel computations [34][35][36], boundary element-finite element coupling [37], MEMS problems [38], control-structure interaction [39] and damage detection [40], among others. The rest of the present paper is organized as follows.…”