Vibroacoustic Simulation An Introduction to Statistical Energy Analysis and Hybrid Methods

Learn to master the full range of vibroacoustic simulation using both SEA and hybrid FEM/SEA methods

Vibroacoustic simulation is the discipline of modelling and predicting the acoustic waves and vibration of particular objects, systems, or structures. This is done through finite element methods (FEM) or statistical energy analysis (SEA) to cover the full frequency range. In the mid-frequency range, both methods must be combined into a hybrid FEM/SEA approach. By doing so, engineers can model full frequency vibroacoustic simulations in complex technical systems used in aircraft, trains, cars, ships, and satellites. Indeed, hybrid approaches are increasingly used in the automotive, aerospace, and rail industries.

Previously covered primarily in scientific journals, Vibroacoustic Simulation provides a practical approach that helps readers master the full frequency range of vibroacoustic simulation. Through a systematic approach, the book illustrates why both FEM and SEA are necessary in acoustic engineering and how both can be used in combination through hybrid methodologies. Striking a crucial balance between complex theories and practical applications, the text provides real-world examples of vibroacoustic simulation, such as fuselage simulation, interior-noise prediction for electric and combustion vehicles, train profiles, and more, to help elucidate the concepts described within.

Vibroacoustic Simulation also features:

• A balance of complex theories with the nuts and bolts of real-world applications
• Detailed worked examples of junction equations
• Case studies from companies like Audi and Airbus that illustrate how the methods discussed have been applied in real-world projects
• A companion website that provides corresponding Python codes for all examples, allowing readers to work through the examples on their own

Vibroacoustic Simulation is a useful reference for acoustic and mechanical engineers working in the automotive, aerospace, defense, or rail industries, as well as researchers and graduate students studying acoustics.

Alexander Peiffer, PhD, is Head of Team Whole Vehicle Acoustics of Electric Platforms and Active Systems at Audi AG. He has over 20 years’ experience in technical acoustics and industrial research, focusing on statistical energy analysis methods and finite element simulation. He previously held positions as Head of Vibroacoustics and Dynamics and Head of Noise and Vibration Control at Airbus Group Innovations and serves as a guest lecturer for industrial acoustics courses at Technical University-Munich.

Preface xv

Acknowledgments xix

Acronyms xxi

1 Linear Systems, Random Process and Signals 1

1.1 The Damped Harmonic Oscillator 1

1.2 Forced Harmonic Oscillator 5

1.3 Two Degrees of Freedom Systems (2DOF) 15

1.4 Multiple Degrees of Freedom Systems MDOF 20

1.5 Random Process 27

1.6 Systems 34

1.7 Multiple-input--multiple-output Systems 37

2 Waves in Fluids 43

2.1 Introduction 43

2.2 Wave Equation for Fluids 43

2.3 Solutions of the Wave Equation 48

2.4 Fundamental Acoustic Sources 53

2.5 Reflection of Plane Waves 59

2.6 Reflection and Transmission of Plane Waves 60

2.7 Inhomogeneous Wave Equation 62

2.8 Units, Measures, and levels 72

3 Wave Propagation in Structures 75

3.1 Introduction 75

3.2 Basic Equations and Definitions 76

3.3 Wave Equation 83

3.4 Waves in Infinite Solids 87

3.5 Beams 88

3.6 Membranes 99

3.7 Plates 101

3.8 Propagation of Energy in Dispersive Waves 115

3.9 Findings 116

4 Fluid Systems 119

4.1 One-dimensional Systems 119

4.2 Three-dimensional Systems 128

4.3 Numerical Solutions 139

4.4 Reciprocity 142

5 Structure Systems 145

5.1 Introduction 145

5.2 One-dimensional Systems 146

5.3 Two-dimensional Systems 151

5.4 Reciprocity 155

5.5 Numerical Solutions 156

6 Random Description of Systems 159

6.1 Diffuse Wave Field 160

6.2 Ensemble Averaging of Deterministic Systems 169

6.3 One-Dimensional Systems 169

6.4 Two-Dimensional Systems 178

6.5 Three-Dimensional Systems -- Cavities 182

6.6 Surface Load of Diffuse Acoustic Fields 188

6.7 Mode Wave Duality 189

6.8 SEA System Description 192

7 Coupled Systems 201

7.1 Deterministic Subsystems and their Degrees of Freedom 202

7.2 Coupling Deterministic Systems 202

7.3 Coupling Random Systems 206

7.4 Hybrid FEM/SEA Method 213

7.5 Hybrid Modelling in Modal Coordinates 220

8 Coupling Loss Factors 223

8.1 Transmission Coefficients and Coupling Loss Factors 224

8.2 Radiation Stiffness and Coupling Loss Factors 227

9 Deterministic Applications 271

9.1 Acoustic One-Dimensional Elements 271

9.2 Coupled One-Dimensional Systems 286

9.3 Infinite Layers 296

9.4 Acoustic Absorber 302

9.5 Acoustic Wall Constructions 308

10 Application of Random systems 319

10.1 Frequency Bands for SEA Simulation 319

10.2 Fluid Systems 320

10.3 Algorithms of SEA 323

10.4 Coupled Plate Systems 324

10.5 Fluid-Structure Coupled Systems 327

11 Hybrid Systems 343

11.1 Hybrid SEA Matrix 343

11.2 Twin Chamber 343

11.3 Trim in Hybrid Theory 350

12 Industrial Cases 359

12.1 Simulation Strategy 359

12.2 Aircraft 361

12.3 Automotive 372

12.4 Trains 380

12.5 Summary 394

13 Conclusions and Outlook 399

13.1 Conclusions 399

13.2 What Comes Next? 399

13.3 Experimental Methods 399

13.4 Further Reading on Simulation 404

13.5 Energy Flow Method and Influence Coefficient 404

13.6 Vibroacoustics Simulation Software 406

A Basic Mathematics 411

A.1 Fourier Analysis 411

A.2 Discrete Signal Analysis 418

A.3 Coordinate Transformation of Discrete Equation of Motion 423

Bibliography 424

B Specific Solutions 425

B.1 Second Moments of Area 425

B.2 Wave Transmission 426

B.3 Conversion Formulas of Transfer Matrix 436

Bibliography 437

C Symbols 439

Index 445

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