Alexander Peiffer - Vibroacoustic Simulation

Alexander Peiffer

This edition first published 2022

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Hardback ISBN: 9781119849841; ePub ISBN: 9781119849865; ePDF ISBN: 9781119849858; Obook ISBN: 9781119849872

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To my parents and Ivonnne my love who always supported me

1 Cover

2 Title page Vibroacoustic Simulation An Introduction to Statistical Energy Analysis and Hybrid Methods Alexander Peiffer

3 Copyright

4 Dedication

5 Preface

6 Acknowledgments

7 Acronyms

8 1 Linear Systems, Random Process and Signals 1.1 The Damped Harmonic Oscillator1.1.1 Homogeneous Solutions1.1.2 The Overdamped Oscillator (ζ < 1)1.1.3 The Underdamped Oscillator (ζ < 1)1.1.4 The Critically Damped Oscillator (ζ = 1)1.2 Forced Harmonic Oscillator1.2.1 Frequency Response1.2.2 Energy, Power and Impedance1.2.3 Impedance and Response Functions1.2.4 Damping1.2.5 Damping in Real Systems1.3 Two Degrees of Freedom Systems (2DOF)1.3.1 Natural Frequencies of the 2DOF System1.4 Multiple Degrees of Freedom Systems MDOF1.4.1 Assembling the Mass Matrix1.4.2 Assembling the Stiffness Matrix1.4.3 Power Input into MDOF Systems1.4.4 Normal Modes1.5 Random Process1.5.1 Probability Function1.5.2 Correlation Coefficient1.5.3 Correlation Functions for Random Time Signals1.5.4 Fourier Analysis of Random Signals1.5.5 Estimation of Power and Cross Spectra1.6 Systems1.6.1 SISO-System Response in Frequency Domain1.6.2 System Response in Time Domain1.6.3 Systems Excited by Random Signals1.7 Multiple-input.multiple-output Systems1.7.1 Multiple Random Inputs1.7.2 Response of MIMO Systems to Random LoadBibliography

9 2 Waves in Fluids 2.1 Introduction2.2 Wave Equation for Fluids2.2.1 Conservation of Mass2.2.2 Newton’s law – Conservation of Momentum2.2.3 Equation of State2.2.4 Linearized Equations2.2.5 AcousticWave Equation2.3 Solutions of theWave Equation2.3.1 HarmonicWaves2.3.2 Helmholtz equation2.3.3 Field Quantities: Sound Intensity, Energy Density and Sound Power2.3.4 Damping inWaves2.4 Fundamental Acoustic Sources2.4.1 Monopoles – Spherical Sources2.5 Reflection of PlaneWaves2.6 Reflection and Transmission of PlaneWaves2.7 InhomogeneousWave Equation2.7.1 Acoustic Green’s Functions2.7.2 Rayleigh integral2.7.3 Piston in a Wall2.7.4 Power Radiation2.8 Units, Measures, and levelsBibliography

10 3 Wave Propagation in Structures 3.1 Introduction3.2 Basic Equations and Definitions3.2.1 Mechanical Strain3.2.2 Mechanical Stress3.2.3 Material Laws3.3 Wave Equation3.3.1 The One-dimensionalWave Equation3.3.2 The Three-dimensionalWave Equation3.4 Waves in Infinite Solids3.4.1 LongitudinalWaves3.4.2 Shear waves3.5 Beams3.5.1 LongitudinalWaves3.5.2 Power, Energy, and Impedance3.5.3 BendingWaves3.5.4 Power, Energy, and Impedance3.6 Membranes3.7 Plates3.7.1 Strain––displacement Relations3.7.2 In-planeWave Equation3.7.3 LongitudinalWaves3.7.4 ShearWaves3.7.5 Combination of Longitudinal and ShearWaves3.7.6 BendingWave Equation3.8 Propagation of Energy in DispersiveWaves3.9 FindingsBibliography

11 4 Fluid Systems 4.1 One-dimensional Systems4.1.1 System Response4.1.2 Power Input4.1.3 Pressure Field4.1.4 Modes4.2 Three-dimensional Systems4.2.1 Modes4.2.2 Modal Frequency Response4.2.3 System Responses4.3 Numerical Solutions4.3.1 Acoustic Finite Element Methods4.3.2 Deterministic Acoustic Elements4.4 ReciprocityBibliography

12 5 Structure Systems 5.1 Introduction5.2 One-dimensional Systems5.2.1 LongitudinalWaves in Finite Beams5.2.2 Bending wave in Finite Beams5.3 Two-dimensional Systems5.3.1 BendingWaves in Flat Plates5.4 Reciprocity5.5 Numerical Solutions5.5.1 Normal Modes in Discrete FormBibliography

13 6 Random Description of Systems 6.1 DiffuseWave Field6.1.1 Wave-Energy Relationships6.1.2 Diffuse Field Parameter of One-Dimensional Systems6.1.3 Diffuse Field Parameter of Two-Dimensional Systems6.1.4 Diffuse Field Parameter of Three-Dimensional Systems6.1.5 Topology Conclusions6.1.6 Auto Correlation and Boundary Effects6.1.7 Sources in the Diffuse Acoustic Field – the Direct Field6.1.8 Some Comments on the Diffuse Field Approach6.2 Ensemble Averaging of Deterministic Systems6.3 One-Dimensional Systems6.3.1 Fluid Tubes6.4 Two-Dimensional Systems6.4.1 Plates6.4.2 Monte Carlo Simulation6.5 Three-Dimensional Systems–Cavities6.5.1 Energy and Intensity6.5.2 Power Input to the Reverberant Field6.5.3 Dissipation6.5.4 Power Balance6.5.5 Monte Carlo Simulation6.6 Surface Load of Diffuse Acoustic Fields6.7 ModeWave Duality6.7.1 Diffuse Field Energy6.7.2 Free Field Power Input6.8 SEA System Description6.8.1 Power Balance in Diffuse Fields6.8.2 Reciprocity Relationships6.8.3 Fluid Analogy6.8.4 Power Input6.8.5 Engineering Units6.8.6 MultipleWave FieldsBibliography