{"product_id":"engineering-vibroacoustic-analysis-methods-and-applications-9781119953449","title":"Engineering Vibroacoustic Analysis  Methods and Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe book describes analytical methods (based  primarily on classical modal synthesis), the Finite Element Method (FEM), Boundary Element Method (BEM), Statistical Energy Analysis (SEA), Energy Finite Element Analysis (EFEA), Hybrid Methods (FEM-SEA and Transfer Path Analysis), and Wave-Based Methods.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eWiley Series in Acoustics, Noise and Vibration xiv\u003c\/p\u003e \u003cp\u003eList of Contributors xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Overview 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Traditional Vibroacoustic Methods 2\u003c\/p\u003e \u003cp\u003e1.2.1 Finite Element Method 2\u003c\/p\u003e \u003cp\u003e1.2.2 Boundary Element Method 3\u003c\/p\u003e \u003cp\u003e1.2.3 Statistical Energy Analysis 3\u003c\/p\u003e \u003cp\u003e1.3 New Vibroacoustic Methods 4\u003c\/p\u003e \u003cp\u003e1.3.1 Hybrid FE\/SEA Method 4\u003c\/p\u003e \u003cp\u003e1.3.2 Hybrid FE\/TPA Method 4\u003c\/p\u003e \u003cp\u003e1.3.3 Energy FE Analysis 4\u003c\/p\u003e \u003cp\u003e1.3.4 Wave‐Based Structural Analysis 5\u003c\/p\u003e \u003cp\u003e1.3.5 Future Developments 5\u003c\/p\u003e \u003cp\u003e1.4 Choosing Numerical Methods 5\u003c\/p\u003e \u003cp\u003e1.4.1 Geometrical Discretization 5\u003c\/p\u003e \u003cp\u003e1.4.2 Solution Frequency Ranges 6\u003c\/p\u003e \u003cp\u003e1.4.3 Type of Application 7\u003c\/p\u003e \u003cp\u003e1.5 Chapter Organization 9\u003c\/p\u003e \u003cp\u003eReferences 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Structural Vibrations 10\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 10\u003c\/p\u003e \u003cp\u003e2.2 Waves in Structures 11\u003c\/p\u003e \u003cp\u003e2.2.1 Compressional and Shear Waves in Isotropic, Homogeneous Structures 11\u003c\/p\u003e \u003cp\u003e2.2.2 Bending (Flexural) Waves in Beams and Plates 13\u003c\/p\u003e \u003cp\u003e2.2.3 Bending Waves in Anisotropic Plates 17\u003c\/p\u003e \u003cp\u003e2.2.4 Bending Waves in Stiffened Panels 20\u003c\/p\u003e \u003cp\u003e2.2.5 Structural Wavenumbers 21\u003c\/p\u003e \u003cp\u003e2.3 Modes of Vibration 22\u003c\/p\u003e \u003cp\u003e2.3.1 Modes of Beams 22\u003c\/p\u003e \u003cp\u003e2.3.2 Modes of Plates 25\u003c\/p\u003e \u003cp\u003e2.3.3 Global and Local Modes of Stiffened Panels 28\u003c\/p\u003e \u003cp\u003e2.3.4 Modal Density 30\u003c\/p\u003e \u003cp\u003e2.4 Mobility and Impedance 30\u003c\/p\u003e \u003cp\u003e2.4.1 Damping 34\u003c\/p\u003e \u003cp\u003e2.5 Bending Waves in Infinite Structures 39\u003c\/p\u003e \u003cp\u003e2.6 Coupled Oscillators, Power Flow, and the Basics of Statistical Energy Analysis 42\u003c\/p\u003e \u003cp\u003e2.6.1 Equations of Motion 42\u003c\/p\u003e \u003cp\u003e2.6.2 Power Input, Flow, and Dissipation 44\u003c\/p\u003e \u003cp\u003e2.6.3 Oscillator-based Statistical Energy Analysis (SEA) 45\u003c\/p\u003e \u003cp\u003e2.7 Environmental and Installation Effects 48\u003c\/p\u003e \u003cp\u003e2.8 Summary 50\u003c\/p\u003e \u003cp\u003eReferences 50\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Interior and Exterior Sound 52\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 52\u003c\/p\u003e \u003cp\u003e3.2 Interior Sound 52\u003c\/p\u003e \u003cp\u003e3.2.1 Acoustic Wave Equation 52\u003c\/p\u003e \u003cp\u003e3.2.2 Boundary Conditions 54\u003c\/p\u003e \u003cp\u003e3.2.3 Natural Frequencies and Mode Shapes 55\u003c\/p\u003e \u003cp\u003e3.2.4 Forced Sound‐Pressure Response 59\u003c\/p\u003e \u003cp\u003e3.2.5 Steady‐State Sound‐Pressure Response 60\u003c\/p\u003e \u003cp\u003e3.2.6 Enclosure Driven at Resonance 64\u003c\/p\u003e \u003cp\u003e3.2.7 Random Sound‐Pressure Response 66\u003c\/p\u003e \u003cp\u003e3.2.8 Transient Sound‐Pressure Response 68\u003c\/p\u003e \u003cp\u003e3.3 Exterior Sound 70\u003c\/p\u003e \u003cp\u003e3.3.1 Sound Radiation Measures 72\u003c\/p\u003e \u003cp\u003e3.3.2 One‐Dimensional Sound Radiation 73\u003c\/p\u003e \u003cp\u003e3.3.3 Sound Radiation from Basic Sources and Radiators 75\u003c\/p\u003e \u003cp\u003e3.3.3.1 Pulsating Sphere and Monopole Source 75\u003c\/p\u003e \u003cp\u003e3.3.3.2 Oscillating Sphere and Dipole Source 77\u003c\/p\u003e \u003cp\u003e3.3.4 Helmholtz and Rayleigh Integral Equations 78\u003c\/p\u003e \u003cp\u003e3.3.5 Example Applications 81\u003c\/p\u003e \u003cp\u003e3.3.5.1 Planar Baffled Vibrating Plate 81\u003c\/p\u003e \u003cp\u003e3.3.5.2 Vibrating Crown Surface 84\u003c\/p\u003e \u003cp\u003e3.4 Summary 86\u003c\/p\u003e \u003cp\u003eReferences 86\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Sound‐Structure Interaction Fundamentals 88\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 88\u003c\/p\u003e \u003cp\u003e4.2 Circular Piston Vibrating against an Acoustic Fluid 89\u003c\/p\u003e \u003cp\u003e4.3 Fluid Loading of Structures 95\u003c\/p\u003e \u003cp\u003e4.4 Structural Waves Vibrating against an Acoustic Fluid 99\u003c\/p\u003e \u003cp\u003e4.5 Complementary Problem: Structural Vibrations Induced by Acoustic Pressure Waves 105\u003c\/p\u003e \u003cp\u003e4.6 Summary 113\u003c\/p\u003e \u003cp\u003eReferences 113\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Structural‐Acoustic Modal Analysis and Synthesis 114\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 114\u003c\/p\u003e \u003cp\u003e5.2 Coupled Structural‐Acoustic System 114\u003c\/p\u003e \u003cp\u003e5.2.1 Acoustic Cavity Modal Expansion 115\u003c\/p\u003e \u003cp\u003e5.2.2 Absorption Wall Impedance 117\u003c\/p\u003e \u003cp\u003e5.2.3 Structural Modal Expansion 118\u003c\/p\u003e \u003cp\u003e5.2.4 Coupled Structural‐Acoustic Modal Expansions 120\u003c\/p\u003e \u003cp\u003e5.3 Simplified Models 121\u003c\/p\u003e \u003cp\u003e5.3.1 Helmholtz Resonator Model 121\u003c\/p\u003e \u003cp\u003e5.3.2 Flexible Wall Model 122\u003c\/p\u003e \u003cp\u003e5.3.3 Coupled Structural and Acoustic Modes 123\u003c\/p\u003e \u003cp\u003e5.3.4 Dominant Structural Mode 125\u003c\/p\u003e \u003cp\u003e5.3.5 Dominant Cavity Mode 127\u003c\/p\u003e \u003cp\u003e5.4 Component Mode Synthesis 132\u003c\/p\u003e \u003cp\u003e5.4.1 Coupled Structural‐Acoustic Model 132\u003c\/p\u003e \u003cp\u003e5.4.2 Coupled Structures 134\u003c\/p\u003e \u003cp\u003e5.4.3 Coupled Cavities 138\u003c\/p\u003e \u003cp\u003e5.5 Summary 142\u003c\/p\u003e \u003cp\u003eReferences 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Structural‐Acoustic Finite‐Element Analysis for Interior Acoustics 144\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 144\u003c\/p\u003e \u003cp\u003e6.2 Acoustic Finite‐Element Analysis 144\u003c\/p\u003e \u003cp\u003e6.2.1 Acoustic Finite‐Element Formulation 144\u003c\/p\u003e \u003cp\u003e6.2.2 Flexible and Absorbent Walls 147\u003c\/p\u003e \u003cp\u003e6.2.3 Cavity Modal Analysis 148\u003c\/p\u003e \u003cp\u003e6.2.4 Flexible Wall Excitation 150\u003c\/p\u003e \u003cp\u003e6.2.5 Acoustic Impedance Modeling 151\u003c\/p\u003e \u003cp\u003e6.2.6 Porous Material Modeling 152\u003c\/p\u003e \u003cp\u003e6.3 Structural‐Acoustic Finite‐Element Analysis 155\u003c\/p\u003e \u003cp\u003e6.3.1 Structural Finite‐Element Formulation 155\u003c\/p\u003e \u003cp\u003e6.3.2 Structural System Synthesis 158\u003c\/p\u003e \u003cp\u003e6.4 Coupled Structural‐Acoustic Finite‐Element Formulation 159\u003c\/p\u003e \u003cp\u003e6.4.1 Coupled Modes and Resonance Frequencies 160\u003c\/p\u003e \u003cp\u003e6.4.2 Direct and Modal Frequency Response 161\u003c\/p\u003e \u003cp\u003e6.4.3 Random Response 164\u003c\/p\u003e \u003cp\u003e6.4.4 Participation Factors 166\u003c\/p\u003e \u003cp\u003e6.4.5 Transient Response 171\u003c\/p\u003e \u003cp\u003e6.4.5.1 Inverse Fourier Transform 171\u003c\/p\u003e \u003cp\u003e6.4.5.2 Direct Transient Response 172\u003c\/p\u003e \u003cp\u003e6.4.5.3 Modal Transient Response 172\u003c\/p\u003e \u003cp\u003e6.4.6 Structural‐ and Acoustic‐Response Variation 173\u003c\/p\u003e \u003cp\u003e6.5 Summary 177\u003c\/p\u003e \u003cp\u003eReferences 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Boundary‐Element Analysis 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Theory—Assumptions 179\u003c\/p\u003e \u003cp\u003e7.2 Theory—Overview of Theoretical Basis 180\u003c\/p\u003e \u003cp\u003e7.3 Boundary‐Element Computations 183\u003c\/p\u003e \u003cp\u003e7.4 The Rayleigh Integral 184\u003c\/p\u003e \u003cp\u003e7.5 The Kirchhoff–Helmholtz Equation 186\u003c\/p\u003e \u003cp\u003e7.6 Nonexistence\/Nonuniqueness Difficulties 191\u003c\/p\u003e \u003cp\u003e7.7 Impedance Boundary Conditions 199\u003c\/p\u003e \u003cp\u003e7.8 Interpolation 202\u003c\/p\u003e \u003cp\u003e7.9 Applicability over Frequency and Spatial Resolution 205\u003c\/p\u003e \u003cp\u003e7.10 Implementation – Software Required 208\u003c\/p\u003e \u003cp\u003e7.11 Computer Resources Required 210\u003c\/p\u003e \u003cp\u003e7.12 Inputs and How to Determine them 213\u003c\/p\u003e \u003cp\u003e7.13 Outputs 213\u003c\/p\u003e \u003cp\u003e7.14 Applications 214\u003c\/p\u003e \u003cp\u003e7.15 Verification and Validation 220\u003c\/p\u003e \u003cp\u003e7.16 Error Analysis 225\u003c\/p\u003e \u003cp\u003e7.17 Summary 225\u003c\/p\u003e \u003cp\u003eReferences 226\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Structural and Acoustic Noise Control Material Modeling 230\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 230\u003c\/p\u003e \u003cp\u003e8.2 Damping Materials 231\u003c\/p\u003e \u003cp\u003e8.2.1 Damping Mechanisms 231\u003c\/p\u003e \u003cp\u003e8.2.2 Viscoelastic Damping 232\u003c\/p\u003e \u003cp\u003e8.2.3 Representation of the Frequency‐Dependent Properties of Viscoelastic Materials 233\u003c\/p\u003e \u003cp\u003e8.2.4 Identification of the Dynamic Properties of VEM 234\u003c\/p\u003e \u003cp\u003e8.2.5 Damping Design 235\u003c\/p\u003e \u003cp\u003e8.2.6 Modeling Structures with added Viscoelastic Damping 238\u003c\/p\u003e \u003cp\u003e8.2.7 Poroelastic Materials 241\u003c\/p\u003e \u003cp\u003e8.2.8 Open‐Cell Porous Materials 241\u003c\/p\u003e \u003cp\u003e8.2.9 Acoustic Impedance 242\u003c\/p\u003e \u003cp\u003e8.2.10 Models of Sound Propagation in a Porous Material 244\u003c\/p\u003e \u003cp\u003e8.2.11 Fluids Equivalent to Porous Materials 244\u003c\/p\u003e \u003cp\u003e8.2.12 Models for the Effective Density and the Bulk Modulus 245\u003c\/p\u003e \u003cp\u003e8.2.13 Perforated Plates 247\u003c\/p\u003e \u003cp\u003e8.2.14 Porous Materials having an Elastic Frame 249\u003c\/p\u003e \u003cp\u003e8.2.15 Measurement of the Parameters Governing Sound Propagation in Porous Materials 249\u003c\/p\u003e \u003cp\u003e8.2.15.1 Porosity 249\u003c\/p\u003e \u003cp\u003e8.2.15.2 Flow Resistivity 250\u003c\/p\u003e \u003cp\u003e8.2.15.3 Tortuosity 250\u003c\/p\u003e \u003cp\u003e8.2.15.4 Characteristics Lengths 253\u003c\/p\u003e \u003cp\u003e8.2.15.5 Mechanical Properties 257\u003c\/p\u003e \u003cp\u003e8.3 Modeling Multilayer Noise Control Materials 257\u003c\/p\u003e \u003cp\u003e8.3.1 Use of the Transfer Matrix Method 258\u003c\/p\u003e \u003cp\u003e8.3.2 Modeling a Sound Package within SEA 263\u003c\/p\u003e \u003cp\u003e8.3.3 Modeling a Sound Package within FE 264\u003c\/p\u003e \u003cp\u003e8.4 Conclusion 265\u003c\/p\u003e \u003cp\u003eReferences 265\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Structural–Acoustic Optimization 268\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 268\u003c\/p\u003e \u003cp\u003e9.2 Brief Survey of Structural–Acoustic Optimization 269\u003c\/p\u003e \u003cp\u003e9.3 Structural–Acoustic Optimization Procedures and Literature 271\u003c\/p\u003e \u003cp\u003e9.3.1 Applications 271\u003c\/p\u003e \u003cp\u003e9.3.2 Choice of Parameters 272\u003c\/p\u003e \u003cp\u003e9.3.3 Constraints 273\u003c\/p\u003e \u003cp\u003e9.3.4 Objective Functions 274\u003c\/p\u003e \u003cp\u003e9.4 Process of Structural–Acoustic Optimization 277\u003c\/p\u003e \u003cp\u003e9.4.1 Structural–Acoustic Simulation 277\u003c\/p\u003e \u003cp\u003e9.4.2 Strategy of Optimization 279\u003c\/p\u003e \u003cp\u003e9.4.2.1 Formulation of Optimization Problem 279\u003c\/p\u003e \u003cp\u003e9.4.2.2 Multiobjective Optimization 280\u003c\/p\u003e \u003cp\u003e9.4.2.3 Approximation Concepts and Approximate Optimization 280\u003c\/p\u003e \u003cp\u003e9.4.2.4 Optimization Methods 282\u003c\/p\u003e \u003cp\u003e9.4.3 Sensitivity Analysis 284\u003c\/p\u003e \u003cp\u003e9.4.3.1 Global Finite Differences 284\u003c\/p\u003e \u003cp\u003e9.4.3.2 Semi‐Analytic Sensitivity Analysis 285\u003c\/p\u003e \u003cp\u003e9.4.3.3 Adjoint Operators 286\u003c\/p\u003e \u003cp\u003e9.4.4 Special Techniques 287\u003c\/p\u003e \u003cp\u003e9.4.4.1 General Aspects and Ideas 287\u003c\/p\u003e \u003cp\u003e9.4.4.2 Efficient Reanalysis 288\u003c\/p\u003e \u003cp\u003e9.4.4.3 Frequency Ranges 289\u003c\/p\u003e \u003cp\u003e9.5 Minimization of Radiated Sound Power from a Finite Beam 289\u003c\/p\u003e \u003cp\u003e9.5.1 General Remarks 289\u003c\/p\u003e \u003cp\u003e9.5.2 Simulation Models 289\u003c\/p\u003e \u003cp\u003e9.5.3 Noise Transfer Function of Original Configurations 291\u003c\/p\u003e \u003cp\u003e9.5.4 Objective Function 293\u003c\/p\u003e \u003cp\u003e9.5.5 Formulation of Optimization Problem 293\u003c\/p\u003e \u003cp\u003e9.5.6 Optimization Strategy 293\u003c\/p\u003e \u003cp\u003e9.5.7 Optimization Results 294\u003c\/p\u003e \u003cp\u003e9.5.8 Discussion of Results 297\u003c\/p\u003e \u003cp\u003e9.5.9 Optimization of Complex Models 298\u003c\/p\u003e \u003cp\u003e9.6 Conclusions 298\u003c\/p\u003e \u003cp\u003eReferences 299\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Random and Stochastic Structural–Acoustic Analysis 305\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 305\u003c\/p\u003e \u003cp\u003e10.2 Uncertainty Quantification in Vibroacoustic Problems 308\u003c\/p\u003e \u003cp\u003e10.2.1 Antioptimization Method 308\u003c\/p\u003e \u003cp\u003e10.2.2 Possibilistic Method 309\u003c\/p\u003e \u003cp\u003e10.2.3 Probabilistic Method 309\u003c\/p\u003e \u003cp\u003e10.3 Random Variables and Random Fields 310\u003c\/p\u003e \u003cp\u003e10.4 Discretization of Random Quantities 313\u003c\/p\u003e \u003cp\u003e10.4.1 Karhunen–Loève Expansion 313\u003c\/p\u003e \u003cp\u003e10.4.2 Polynomial Chaos Expansion 314\u003c\/p\u003e \u003cp\u003e10.5 Stochastic FEM Formulation of Structural Vibrations 317\u003c\/p\u003e \u003cp\u003e10.5.1 General SFEM Formulation of Vibration Problems 319\u003c\/p\u003e \u003cp\u003e10.5.2 Stochastic FEM Formulation of Vibroacoustic Problems 321\u003c\/p\u003e \u003cp\u003e10.6 Numerical Simulation Procedures 322\u003c\/p\u003e \u003cp\u003e10.6.1 Intrusive SFEM 322\u003c\/p\u003e \u003cp\u003e10.6.2 Non‐intrusive SFEM 323\u003c\/p\u003e \u003cp\u003e10.7 Numerical Examples 324\u003c\/p\u003e \u003cp\u003e10.7.1 Discrete 2‐DOF Undamped System 324\u003c\/p\u003e \u003cp\u003e10.7.2 Free Vibration of Orthotropic Plate with Uncertain Parameters 328\u003c\/p\u003e \u003cp\u003e10.7.3 Random Equivalent Radiated Power 333\u003c\/p\u003e \u003cp\u003e10.8 Summary and Concluding Remarks 335\u003c\/p\u003e \u003cp\u003eReferences 335\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Statistical Energy Analysis 339\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 339\u003c\/p\u003e \u003cp\u003e11.2 SEA Background 339\u003c\/p\u003e \u003cp\u003e11.2.1 Characteristic Wavelengths 340\u003c\/p\u003e \u003cp\u003e11.2.2 Modes and Complexity 341\u003c\/p\u003e \u003cp\u003e11.2.3 Uncertainty 342\u003c\/p\u003e \u003cp\u003e11.3 General Wave‐Based SEA Formulation 343\u003c\/p\u003e \u003cp\u003e11.3.1 Piston Coupled with a Single Room 344\u003c\/p\u003e \u003cp\u003e11.3.2 Direct Field 344\u003c\/p\u003e \u003cp\u003e11.3.3 Reverberant Field 345\u003c\/p\u003e \u003cp\u003e11.3.4 Uncertainty 346\u003c\/p\u003e \u003cp\u003e11.3.5 Piston Response 347\u003c\/p\u003e \u003cp\u003e11.3.6 A Diffuse Reverberant Field 348\u003c\/p\u003e \u003cp\u003e11.3.7 Reciprocity between Direct Field Impedance and Diffuse Reverberant Load 348\u003c\/p\u003e \u003cp\u003e11.3.8 Coupling Power Proportionality 349\u003c\/p\u003e \u003cp\u003e11.3.9 Reverberant Power Balance Equations 352\u003c\/p\u003e \u003cp\u003e11.3.10 Recovering Local Responses 354\u003c\/p\u003e \u003cp\u003e11.3.11 Numerical Example 354\u003c\/p\u003e \u003cp\u003e11.3.12 An Arbitrary Number of Coupled Subsystems 355\u003c\/p\u003e \u003cp\u003e11.3.13 Summary 356\u003c\/p\u003e \u003cp\u003e11.4 Energy Storage 356\u003c\/p\u003e \u003cp\u003e11.4.1 Energy Storage in 1D Waveguides 356\u003c\/p\u003e \u003cp\u003e11.4.1.1 A Thin Beam 359\u003c\/p\u003e \u003cp\u003e11.4.1.2 Higher‐Order Wavetypes 360\u003c\/p\u003e \u003cp\u003e11.4.2 Energy Storage in 2D Waveguides 361\u003c\/p\u003e \u003cp\u003e11.4.2.1 A Thin Plate 363\u003c\/p\u003e \u003cp\u003e11.4.2.2 A Singly Curved Shell 363\u003c\/p\u003e \u003cp\u003e11.4.2.3 Higher Order Wavetypes 364\u003c\/p\u003e \u003cp\u003e11.4.3 Energy Storage in 3D Waveguides 366\u003c\/p\u003e \u003cp\u003e11.4.3.1 Numerical Example 368\u003c\/p\u003e \u003cp\u003e11.4.4 Summary of Modal Density Formulas 369\u003c\/p\u003e \u003cp\u003e11.5 Energy Transmission 370\u003c\/p\u003e \u003cp\u003e11.5.1 Point Junctions 371\u003c\/p\u003e \u003cp\u003e11.5.2 Line Junctions 373\u003c\/p\u003e \u003cp\u003e11.5.3 Area Junctions 374\u003c\/p\u003e \u003cp\u003e11.6 Power Input and Dissipation 377\u003c\/p\u003e \u003cp\u003e11.7 Example Applications 378\u003c\/p\u003e \u003cp\u003e11.7.1 Using SEA to Diagnose Transmission Paths 378\u003c\/p\u003e \u003cp\u003e11.7.2 Industrial Applications 379\u003c\/p\u003e \u003cp\u003e11.8 Summary 382\u003c\/p\u003e \u003cp\u003eReferences 383\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Hybrid FE‐SEA 385\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 385\u003c\/p\u003e \u003cp\u003e12.2 Overview 385\u003c\/p\u003e \u003cp\u003e12.2.1 Low‐, Mid‐, and High‐Frequency Ranges 385\u003c\/p\u003e \u003cp\u003e12.2.2 The Mid‐Frequency Problem 386\u003c\/p\u003e \u003cp\u003e12.3 The Hybrid FE‐SEA Method 387\u003c\/p\u003e \u003cp\u003e12.3.1 System 387\u003c\/p\u003e \u003cp\u003e12.3.2 A Statistical Subsystem 387\u003c\/p\u003e \u003cp\u003e12.3.3 Direct and Reverberant Fields 388\u003c\/p\u003e \u003cp\u003e12.3.4 Ensemble Average Reverberant Loading 388\u003c\/p\u003e \u003cp\u003e12.3.5 Coupling a Deterministic and Statistical Subsystem 389\u003c\/p\u003e \u003cp\u003e12.4 Example 390\u003c\/p\u003e \u003cp\u003e12.4.1 System 390\u003c\/p\u003e \u003cp\u003e12.4.2 Deterministic Equations of Motion 390\u003c\/p\u003e \u003cp\u003e12.4.3 Direct Field Dynamic Stiffness of SEA Subsystems 392\u003c\/p\u003e \u003cp\u003e12.4.4 Ensemble Average Response 392\u003c\/p\u003e \u003cp\u003e12.4.5 Reverberant Power Balance 393\u003c\/p\u003e \u003cp\u003e12.4.6 Computing the Coupled Response 394\u003c\/p\u003e \u003cp\u003e12.5 Implementation and Algorithms 395\u003c\/p\u003e \u003cp\u003e12.5.1 Overview 395\u003c\/p\u003e \u003cp\u003e12.5.2 Point Connection 395\u003c\/p\u003e \u003cp\u003e12.5.3 Line Connection 396\u003c\/p\u003e \u003cp\u003e12.5.4 Area Connection 396\u003c\/p\u003e \u003cp\u003e12.6 Application Examples 397\u003c\/p\u003e \u003cp\u003e12.6.1 Simple Numerical Example 397\u003c\/p\u003e \u003cp\u003e12.6.2 Industrial Applications 398\u003c\/p\u003e \u003cp\u003e12.7 Summary 403\u003c\/p\u003e \u003cp\u003eReferences 403\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Hybrid Transfer Path Analysis 406\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 406\u003c\/p\u003e \u003cp\u003e13.2 Transfer Path Analysis 406\u003c\/p\u003e \u003cp\u003e13.3 Hybrid Transfer Path Analysis 408\u003c\/p\u003e \u003cp\u003e13.4 Vibro‐Acoustic Transfer Function 409\u003c\/p\u003e \u003cp\u003e13.4.1 Measured VATF 409\u003c\/p\u003e \u003cp\u003e13.4.2 Predicted VATF 411\u003c\/p\u003e \u003cp\u003e13.5 Operating Powertrain Loads 412\u003c\/p\u003e \u003cp\u003e13.5.1 Measured Stiffness Method 412\u003c\/p\u003e \u003cp\u003e13.5.2 Matrix Inversion Method 415\u003c\/p\u003e \u003cp\u003e13.5.3 Predicted Powertrain Loads 416\u003c\/p\u003e \u003cp\u003e13.6 HTPA Applications 417\u003c\/p\u003e \u003cp\u003e13.6.1 Predicted Operating Loads + Measured VATFs 417\u003c\/p\u003e \u003cp\u003e13.6.1.1 Predicted Powertrain Loads 418\u003c\/p\u003e \u003cp\u003e13.6.1.2 Measured VATFs 419\u003c\/p\u003e \u003cp\u003e13.6.1.3 Predicted Interior SPL 421\u003c\/p\u003e \u003cp\u003e13.6.2 Predicted VATFs + Measured Operating Loads 424\u003c\/p\u003e \u003cp\u003e13.6.2.1 Predicted VATFs 424\u003c\/p\u003e \u003cp\u003e13.6.2.2 Measured Operating Loads 426\u003c\/p\u003e \u003cp\u003e13.6.2.3 Predicted Interior SPL 426\u003c\/p\u003e \u003cp\u003e13.6.2.4 Structural Modification 427\u003c\/p\u003e \u003cp\u003e13.7 Vibrational Power Flow 429\u003c\/p\u003e \u003cp\u003e13.8 Summary 430\u003c\/p\u003e \u003cp\u003eReferences 431\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Energy Finite Element Analysis 433\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Overview of Energy Finite Element Analysis 433\u003c\/p\u003e \u003cp\u003e14.2 Developing the Governing Differential Equations in EFEA 435\u003c\/p\u003e \u003cp\u003e14.2.1 Derivation of the Governing Differential Equation for an Acoustic Space 436\u003c\/p\u003e \u003cp\u003e14.2.2 Derivation of the Governing Differential Equation for the Bending Response of a Plate 439\u003c\/p\u003e \u003cp\u003e14.3 Power Transfer Coefficients 441\u003c\/p\u003e \u003cp\u003e14.3.1 Power Transfer Coefficients between Two Plates 441\u003c\/p\u003e \u003cp\u003e14.3.2 Power Transfer Coefficients between a Plate and an Acoustic Space 444\u003c\/p\u003e \u003cp\u003e14.3.2.1 Power Transmission from Plate to Acoustic Space 445\u003c\/p\u003e \u003cp\u003e14.3.2.2 Power Transmission from Acoustic Space to Plate 447\u003c\/p\u003e \u003cp\u003e14.4 Formulation of Energy Finite Element System of Equations 447\u003c\/p\u003e \u003cp\u003e14.4.1 Finite Element Formulation of EFEA System of Equations 447\u003c\/p\u003e \u003cp\u003e14.4.2 EFEA Joint Matrix 448\u003c\/p\u003e \u003cp\u003e14.4.3 Input Power 450\u003c\/p\u003e \u003cp\u003e14.4.4 EFEA System of Equations for a Simple Plate‐Acoustic System 451\u003c\/p\u003e \u003cp\u003e14.5 Applications 455\u003c\/p\u003e \u003cp\u003e14.5.1 Automotive Application 455\u003c\/p\u003e \u003cp\u003e14.5.2 Aircraft Application 461\u003c\/p\u003e \u003cp\u003e14.5.3 Naval Application 464\u003c\/p\u003e \u003cp\u003eReferences 470\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Wave‐based Structural Modeling 472\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 General Approach 472\u003c\/p\u003e \u003cp\u003e15.1.1 Background 473\u003c\/p\u003e \u003cp\u003e15.1.2 Advantages\/Limitations 474\u003c\/p\u003e \u003cp\u003e15.2 Theoretical Formulation 475\u003c\/p\u003e \u003cp\u003e15.2.1 Elementary Rod Theory 475\u003c\/p\u003e \u003cp\u003e15.2.2 Straight Beams, Timoshenko Beam Theory 477\u003c\/p\u003e \u003cp\u003e15.2.3 Reflections at Boundaries 479\u003c\/p\u003e \u003cp\u003e15.2.4 Wave Propagation Solution 480\u003c\/p\u003e \u003cp\u003e15.2.5 Spectral Element Method 481\u003c\/p\u003e \u003cp\u003e15.3 Wave‐based Spectral Finite Element Formulation 483\u003c\/p\u003e \u003cp\u003e15.3.1 Dynamic Stiffness Matrix of a Substructure 483\u003c\/p\u003e \u003cp\u003e15.3.2 State Vector Formulation and the Eigenvalue Problem 484\u003c\/p\u003e \u003cp\u003e15.3.3 Relations between Dynamic Stiffness and Transfer Matrices 485\u003c\/p\u003e \u003cp\u003e15.3.4 Derivation of a Numerical Spectral Matrix for Beam Problems 487\u003c\/p\u003e \u003cp\u003e15.3.5 Numerical Spectral Matrix for General Periodic Structures 489\u003c\/p\u003e \u003cp\u003e15.4 Applications 491\u003c\/p\u003e \u003cp\u003e15.4.1 Beam Analysis via Analytical Approaches 491\u003c\/p\u003e \u003cp\u003e15.4.2 Beam Analysis via Numerical Approach (WSFEM) 491\u003c\/p\u003e \u003cp\u003e15.4.3 General Periodic Structure Analysis via Numerical Approach (WSFEM) 495\u003c\/p\u003e \u003cp\u003e15.4.4 Range of Applicability 499\u003c\/p\u003e \u003cp\u003e15.4.5 Implementation–Software Required 500\u003c\/p\u003e \u003cp\u003e15.4.6 Computer Resources Required 500\u003c\/p\u003e \u003cp\u003e15.4.7 Inputs and How to Determine Them 501\u003c\/p\u003e \u003cp\u003e15.4.8 Forces\/Enforced Displacements 501\u003c\/p\u003e \u003cp\u003e15.4.9 Boundary Conditions 501\u003c\/p\u003e \u003cp\u003e15.4.10 Material Properties 502\u003c\/p\u003e \u003cp\u003e15.4.11 Outputs 502\u003c\/p\u003e \u003cp\u003e15.4.12 Verification and Validation 502\u003c\/p\u003e \u003cp\u003e15.5 Conclusion\/Summary 503\u003c\/p\u003e \u003cp\u003eReferences 503\u003c\/p\u003e \u003cp\u003eIndex 506\u003c\/p\u003e","brand":"Wiley-Blackwell","offers":[{"title":"Default Title","offer_id":51769056919895,"sku":"9781119953449","price":94.95,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119953449.jpg?v=1758719484","url":"https:\/\/bookcurl.com\/products\/engineering-vibroacoustic-analysis-methods-and-applications-9781119953449","provider":"Book Curl","version":"1.0","type":"link"}