12 5 Structure Systems5.1 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 Systems6.1 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
14 7 Coupled Systems7.1 Deterministic Subsystems and their Degrees of Freedom7.2 Coupling Deterministic Systems7.2.1 Fluid Subsystems7.2.2 Fluid Structure Coupling7.2.3 Deterministic Systems Coupled to the Free Field7.3 Coupling Random Systems7.3.1 Power Input to System (m) from the nth Reverberant Field7.3.2 Power Leaving the (m)th Subsystem7.3.3 Some Remarks on SEA Modelling7.4 Hybrid FEM/SEA Method7.4.1 Combining SEA and FEM Subsystems7.4.2 Work Flow of Hybrid Simulation7.5 Hybrid Modelling in Modal CoordinatesBibliography
15 8 Coupling Loss Factors8.1 Transmission Coefficients and Coupling Loss Factors8.1.1 τ-η Relationship from Diffuse Field Assumptions8.1.2 Angular Averaging8.2 Radiation Stiffness and Coupling Loss Factors8.2.1 Point Radiation Stiffness8.2.2 Point Junctions8.2.3 Area Radiation Stiffness8.2.4 Area Junctions8.2.5 Line Radiation Stiffness8.2.6 Line Junctions8.2.7 SummaryBibliography
16 9 Deterministic Applications9.1 Acoustic One-Dimensional Elements9.1.1 Transfer Matrix and Finite Element Convention9.1.2 Acoustic One-Dimensional Networks9.1.3 The Acoustic Pipe9.1.4 Volumes and Closed Pipes9.1.5 Limp Layer9.1.6 Membranes9.1.7 Perforated Sheets9.1.8 Branch Lumped Elements9.1.9 Boundary Conditions9.1.10 Performance Indicators9.2 Coupled One-Dimensional Systems9.2.1 Change in Cross Section9.2.2 Impedance Tube9.2.3 Helmholtz Resonator9.2.4 QuarterWave Resonator9.2.5 Muffler System9.2.6 T-Joint9.2.7 Conclusions of 1D-Systems9.3 Infinite Layers9.3.1 Plate Layer9.3.2 Lumped Elements Layers9.3.3 Fluid Layer9.3.4 Equivalent Fluid Fiber Material9.3.5 Performance Indicators9.3.6 Conclusions on Layer Formulation9.4 Acoustic Absorber9.4.1 Single Fiber Layer9.4.2 Multiple Layer Absorbers9.4.3 Absorber with Perforate9.4.4 Single Degree of Freedom Liner9.5 AcousticWall Constructions9.5.1 Double Walls9.5.2 Limp Double Walls with Fiber9.5.3 Two Plates with Fiber9.5.4 Conclusion on Double WallsBibliography
17 10 Application of Random systems10.1 Frequency Bands for SEA Simulation10.2 Fluid Systems10.2.1 Twin Chamber10.3 Algorithms of SEA10.4 Coupled Plate Systems10.4.1 Two Coupled Plates10.5 Fluid-Structure Coupled Systems10.5.1 Twin Chamber10.5.2 Noise Control Treatments10.5.3 Transmission Loss of Trimmed Plate10.5.4 Free Field Radiation into Half Space10.5.5 Isolating Box10.5.6 Rules of Noise ControlBibliography
18 11 Hybrid Systems11.1 Hybrid SEA Matrix11.2 Twin Chamber11.2.1 Step 1 – Setting up System Configurations11.2.2 Step 2 – Setting up System Matrices and Coupling Loss Factors11.2.3 Step 3 – External Loads11.2.4 Step 4 – Solving System Matrices11.2.5 Step 5 – Adding the Results11.3 Trim in Hybrid Theory11.3.1 The Trim Stiffness Matrix11.3.2 Hybrid Modal Formulation of Trim and Plate11.3.3 Modal Space11.3.4 Plate Example with TrimBibliography
19 12 Industrial Cases12.1 Simulation Strategy12.1.1 Motivation12.1.2 Choice of Simulation Method12.2 Aircraft12.2.1 Excitation12.2.2 Simulation Strategy12.2.3 Fuselage Sidewall12.2.4 SEA Model of a Fuselage Section12.3 Automotive12.3.1 Simulation Strategy12.3.2 Excitation12.3.3 Rear Carbody12.3.4 Full Scale SEA Models12.4 Trains12.4.1 Structural Design12.4.2 Interior Design12.4.3 Excitation and Transmission Paths12.4.4 Simulation Strategy12.4.5 Applications to Rail Structures – Double Walls12.4.6 Carbody Sections – High Speed Applications12.5 SummaryBibliography
20 13 Conclusions and Outlook13.1 Conclusions13.2 What Comes Next?13.3 Experimental Methods13.3.1 Transfer Path Analysis13.3.2 Experimental Modal Analysis13.3.3 Correlation Between Test and Simulation13.3.4 Experimental or Virtual SEA13.4 Further Reading on Simulation13.4.1 Advances in SEA and Hybrid FEM/SEA Methods13.5 Energy Flow Method and Influence Coefficient13.5.1 More Realistic Systems13.5.2 Anisotropic Material13.5.3 Porous Elastic Material13.5.4 Composite Material13.5.5 Sandwich13.5.6 Shell Theory13.5.7 Wave Finite Element Method (WFE)13.5.8 The High Frequency Limit13.6 Vibroacoustics Simulation SoftwareBibliography
21 A Basic MathematicsA.1 Fourier AnalysisA.1.1 Fourier SeriesA.1.2 Fourier TransformationA.1.3 Dirac Delta FunctionA.1.4 Signal PowerA.1.5 Fourier Transform of Real Harmonic SignalsA.1.6 Useful Properties of the Fourier TransformA.1.7 Fourier Transformation in SpaceA.2 Discrete Signal AnalysisA.2.1 Fourier Transform of Discrete SignalsA.2.2 The Discrete Fourier TransformA.2.3 WindowingA.3 Coordinate Transformation of Discrete Equation of MotionBibliography
22 B Specific SolutionsB.1 Second Moments of AreaB.2 Wave TransmissionB.2.1 The Blocked Forces InterpretationB.2.2 BendingWavesB.2.3 LongitudinalWavesB.2.4 ShearWavesB.2.5 In-planeWavesB.3 Conversion Formulas of Transfer MatrixB.3.1 Derivation of Stiffness Matrix from Transfer MatrixBibliography
23 C Symbols
24 Index
List of Illustrations
1 Chapter 2Figure 2.1 Histogram for the height...Figure 2.2 Histogram of triglycerides in...Figure 2.3 Bar chart of blood...Figure 2.4 Comparison of three “...Figure 2.5 Illustration of the statistical table.Figure 2.6 Bar chart of the...Figure 2.7 Percentage bar chart of...Figure 2.8 Pie chart of the...Figure 2.9 Stem-and-leaf plot...Figure 2.10 Boxplot of the iodine...Figure 2.11 Scatterplot of the correlation...Figure 2.12 Line graph of the...Figure 2.13 Semi-logarithmic line graph...Figure 2.14 Histograms of BMI and...
2 Chapter 3Figure 3.1 Venn diagram showing the...Figure 3.2 Venn diagrams showing the...Figure 3.3 Venn diagram showing the...Figure 3.4 Venn diagram showing event...Figure 3.5 Venn diagrams showing the...Figure 3.6 Venn diagram showing mutually...
3 Chapter