Fluid-Structure Interaction

Jean-François SIGRIST, DCNS Research, France.

• Foreword ixImages Credits xiPreface xiii1 Fluid–Structure Interaction 11.1 A Wide Variety of Problems 21.2 Analytical Modelling of Fluid–Structure Interactions 31.2.1 Potential Flow. Inertial Coupling 41.2.2 Viscous Flow. Viscous Damping 71.2.3 Compressible Flow. Radiation Damping 101.3 Numerical Simulation of Fluid–Structure Interactions 131.4 Finite Element and Boundary Element Methods 202 Structure Finite Elements 252.1 Vibrations of an Elastic Structure 262.1.1 Modelling Assumptions 262.1.2 Equations of Motion 332.2 Finite Element Method: Practical Implementation 352.2.1 Weighted Integral Formulation 352.2.2 Finite Elements 372.2.3 Elementary Matrices 382.2.4 Mass and Stiffness Matrices 402.2.5 Calculating and Assembling Matrices 452.2.6 Modal Analysis 502.3 Example: Bending Modes 522.3.1 Bending Motion of a Straight Elastic Beam 522.3.2 Bernoulli Beam Elements: 1D Element 542.3.3 Bending Modes 572.4 Example: Coupled Bending/Membrane Modes 612.4.1 Bending and Membrane Motion of a Circular Elastic Ring 612.4.2 Fourier Component Representation: 0D Element 622.4.3 Bending/Membrane Modes 643 Fluid Finite Elements 753.1 Fluid Flow Equations 763.2 Compressibility Waves 843.2.1 Wave Equation 843.2.2 Boundary Conditions 883.3 Finite Element Method 963.3.1 Pressure-Based Formulation 963.3.2 Displacement-Based Formulations 1003.3.3 Finite Element Matrices 1033.4 Boundary Element Method 1053.4.1 Green Function and Green’s Integral Theorem 1053.4.2 Interior and Exterior Problems 1063.4.3 Direct and Indirect Boundary Element Method 1083.4.4 Boundary Element Matrices 1113.5 Example: Sloshing Modes 1133.5.1 Circular Reservoir with Fluid-Free Surface 1133.5.2 2D Axisymmetric Elements with Gravity 1153.5.3 Sloshing Modes 1173.6 Example: Acoustic Modes in an Open Reservoir 1193.6.1 Cylindrical Acoustic Opened Cavity 1193.6.2 2D Axisymmetric Elements with Compressibility 1203.6.3 Acoustic Modes 1213.7 Example: Acoustic Modes in a Closed Reservoir 1223.7.1 Rectangular Acoustic Closed Cavity 1223.7.2 2D Fluid Elements with Compressibility 1243.7.3 Acoustic Modes 1253.8 Example: Acoustic Radiation in Infinite Fluid 1253.8.1 Pulsating Ring in Infinite Acoustic Fluid 1253.8.2 1D Axisymmetric Element with Radiation Condition 1273.8.3 1D Boundary Elements 1283.8.4 Acoustic Radiation 1314 Inertial Coupling 1374.1 Mathematical Modelling 1384.2 Added Mass Matrix 1404.2.1 Coupling Matrix 1404.2.2 Added Mass Matrix 1424.2.3 Inertial Effect 1434.3 Modelling Inertial Coupling for Complex Systems: Example of Tube Bundle 1504.3.1 Analytical Models for Added Mass 1504.3.2 ‘Term-to-Term’ Computation of the Added Mass Matrix 1504.3.3 A Homogenisation Technique 1544.4 Examples: Inertial Effect in Bounded Domain 1644.4.1 Analytical Calculation of the Added Mass Matrix 1644.4.2 Numerical Computation of the Added Mass Matrix 1694.5 Example: Inertial Effect in Unbounded Domain 1754.5.1 Elastic Ring Immersed in a Fluid 1754.5.2 Finite Element Coupling with Infinite Element 1775 Fluid–Structure Coupling 1855.1 Modelling Assumption 1865.2 Interior Problems: Vibro-Acoustic and Hydro-Elastic Coupling 1865.2.1 Non-Symmetric Formulation 1865.2.2 Symmetric Formulation 1905.3 Exterior Problem: Vibro-Acoustic 1995.4 Example: Vibro-Acoustic Coupling and Hydro-Elastic Sloshing 2055.5 Example: Acoustic Damping 2125.5.1 Analytical Modelling 2125.5.2 Numerical Computation 2156 Structural Dynamics with Fluid–Structure Interaction 2256.1 Introduction 2266.2 Time-Domain Analysis 2286.2.1 Direct Methods 2286.2.2 Modal Methods 2376.3 Frequency-Domain Analysis 2486.3.1 Direct and Modal Methods 2486.3.2 Computation of the Projection Basis 2506.4 Example: Time-Domain Analysis 2546.4.1 Accelerated Cantilever Beam with Fluid Coupling 2546.4.2 System and Excitation Spectra 2586.4.3 Seismic Response: Direct and Modal Methods 2596.5 Example: Frequency-Domain Analysis 2646.5.1 Acoustic Radiation of a Damped Structure Immersed in a Fluid 2646.5.2 Frequency Response: Direct and Modal Methods 266Index 281

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