smart technologies for safety engineering

Contents ix
8.2.2 The Classical Displacement Formulation 273
8.2.3 The Mixed Displacement–Pressure Formulation 275
8.3 Porous and Poroelastic Material Data and Coefficients 277
8.3.1 Porous Materials with a Rigid Frame 277
8.3.2 Poroelastic Materials 278
8.4 Weak Forms of Poroelasticity, Elasticity, Piezoelectricity and Acoustics 279
8.4.1 Weak Form of the Mixed Formulation of Poroelasticity 279
8.4.2 Weak Form for an Elastic Solid 280
8.4.3 Weak Form of Piezoelectricity 282
8.4.4 Weak Form for an Acoustic Medium 285
8.5 Boundary Conditions for Poroelastic Medium 286
8.5.1 The Boundary Integral 286
8.5.2 Imposed Displacement Field 286
8.5.3 Imposed Pressure Field 287
8.6 Interface Coupling Conditions for Poroelastic and Other Media 288
8.6.1 Poroelastic–Poroelastic Coupling 288
8.6.2 Poroelastic–Elastic Coupling 288
8.6.3 Poroelastic–Acoustic Coupling 289
8.6.4 Acoustic–Elastic Coupling 290
8.7 Galerkin Finite Element Model of a Coupled System of Piezoelectric,
Elastic, Poroelastic and Acoustic Media 290
8.7.1 A Coupled Multiphysics System 290
8.7.2 Weak Form of the Coupled System 293
8.7.3 Galerkin Finite Element Approximation 294
8.7.4 Submatrices and Couplings in the Algebraic System 298
8.8 Modeling of Poroelastic Layers with Mass Implants Improving
Acoustic Absorption 300
8.8.1 Motivation 300
8.8.2 Two Approaches in Modeling Small Solid Implants 300
8.8.3 Acoustic Absorption of the Poroelastic Layer 301
8.8.4 Results of Analyses 301
8.8.5 Concluding Remarks 304
8.9 Designs of Active Elastoporoelastic Panels 304
8.9.1 Introduction 304
8.9.2 Active Sandwich Panel 305
8.9.3 Active Single-Plate Panel 306
8.10 Modeling and Analysis of an Active Single-Plate Panel 308
8.10.1 Kinds and Purposes of Numerical Tests 308
8.10.2 Plate Tests 309
8.10.3 Multilayer Analysis 311
8.10.4 Analysis of Passive Behavior of the Panel 313
8.10.5 Test of Active Behavior of the Panel 315
8.10.6 Concluding Remarks 318
References 319
Acknowledgements 323
Index 327