Fundamentals of Fluid-Solid Interactions-Analytical and

xii Contents
3.3. Basin of attractions and control of chaos 142
3.3.1 Lyapunov methods 142
3.3.2 Robust control; sliding mode; adaptive control; FIV model 147
Chapter 4. Flow-Induced Vibrations 163
4.1. Attenuator and flutter suppression 163
4.1.1 Helmholtz resonator; attenuator design 164
4.1.2 Reynolds equations; spatial and temporal discretizations;
suppression results 169
4.2. Stability issues of axial flow models 183
4.2.1 Internal flow; concentric flow 183
4.2.2 Buckling and flutter; parametric instability and Bolotin method 194
4.2.3 Collapsible tube; tube law; transverse and axial oscillations 214
4.3. Dynamics of thin structures 229
4.3.1 Stationary and moving panel; MITC elements 230
4.3.2 Bending and torsion; aeroelasticity models 244
Chapter 5. Boundary Integral Approaches 267
5.1. Underlying physics and formulations 267
5.1.1 Potential flow 267
5.1.2 Acoustic medium 273
5.1.3 Stokes flow 274
5.2. Green’s functions and boundary integrals 275
5.2.1 Reciprocal relations 275
5.2.2 Boundary element approaches 277
5.3. FSI systems with potential flows 279
5.3.1 Interaction with rigid body; added mass; lift surface 279
5.3.2 Radiation and scattering 299
5.3.3 Rigid body surface waves interactions 305
Chapter 6. Computational Linear Models 313
6.1. Potential and displacement-based formulations 313
6.1.1 φ-u and p-φ-u formulations 314
6.1.2 u/p and u-p-Λ formulations 321
6.1.3 Solvability and stability; FSI interfaces; zero modes 328
6.2. Solution procedures and convergence issues 344
6.2.1 Mode superposition; direct integration methods 347
6.2.2 Acoustoelastic/slosh FSI systems 356
6.2.3 Inf-Sup conditions of mixed formulations 386