Preface |
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Acknowledgments |
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1 Basic Concepts and Acoustic Fundamentals |
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1 | (60) |
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1 | (1) |
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2 | (1) |
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3 | (11) |
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1.3.1 Acoustic Field Variables |
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3 | (1) |
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1.3.2 Mean Square Quantities |
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4 | (1) |
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5 | (1) |
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1.3.4 Addition of Incoherent Sounds (Logarithmic Addition) |
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6 | (1) |
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1.3.5 Subtraction of Sound Pressure Levels |
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6 | (1) |
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7 | (1) |
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7 | (2) |
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9 | (1) |
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1.3.9 Basic Frequency Analysis |
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10 | (4) |
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1.4 Acoustic Wave Equation |
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14 | (16) |
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1.4.1 Conservation of Mass |
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14 | (1) |
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15 | (1) |
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16 | (1) |
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1.4.4 Wave Equation (Linearised) |
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17 | (1) |
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1.4.5 Acoustic Potential Function |
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18 | (2) |
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1.4.6 Inhomogeneous Wave Equation |
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20 | (1) |
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1.4.7 Wave Equation for One-Dimensional Mean Flow |
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20 | (1) |
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1.4.8 Wave Equation in Cartesian, Cylindrical and Spherical Coordinates |
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21 | (1) |
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1.4.8.1 Cartesian Coordinates |
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21 | (1) |
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1.4.8.2 Cylindrical Coordinates |
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22 | (1) |
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1.4.8.3 Spherical Coordinates |
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22 | (1) |
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1.4.9 Plane and Spherical Waves |
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23 | (1) |
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1.4.10 Plane Wave Propagation |
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23 | (4) |
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1.4.11 Spherical Wave Propagation |
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27 | (1) |
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28 | (1) |
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1.4.13 Plane Standing Waves |
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29 | (1) |
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1.4.14 Spherical Standing Waves |
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30 | (1) |
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1.5 Application of the Wave Equation to Analysis of Acoustic Enclosures |
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30 | (5) |
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1.5.1 Rectangular Enclosures |
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31 | (3) |
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34 | (1) |
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1.5.3 Boundary between Low-Frequency and High-Frequency Behaviour |
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35 | (1) |
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1.6 Sound Propagation in Porous Media |
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35 | (26) |
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35 | (4) |
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1.6.2 Parameters for Characterising Sound Propagation in Porous Media |
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39 | (2) |
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1.6.3 Sound Reduction Due to Propagation through a Porous Material |
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41 | (1) |
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1.6.4 Measurement of Absorption Coefficients of Porous Materials |
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41 | (1) |
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1.6.4.1 Moving Microphone Method |
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41 | (8) |
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1.6.4.2 2-Microphone Method |
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49 | (3) |
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1.6.4.3 4-Microphone Method |
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52 | (5) |
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1.6.5 Calculation of Absorption Coefficients of Porous Materials |
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57 | (1) |
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1.6.5.1 Porous Materials with a Backing Cavity |
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57 | (1) |
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1.6.5.2 Multiple Layers of Porous Liner Backed by an Impedance |
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58 | (1) |
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1.6.5.3 Porous Liner Covered with a Limp Impervious Layer |
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58 | (1) |
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1.6.5.4 Porous Liner Covered with a Perforated Sheet |
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58 | (1) |
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1.6.5.5 Porous Liner Covered with a Limp Impervious Layer and a Perforated Sheet |
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59 | (2) |
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2 Structural Mechanics Fundamentals |
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61 | (68) |
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61 | (1) |
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2.2 Vibration of Discrete Systems |
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61 | (13) |
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2.2.1 Summary of Newtonian Mechanics |
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61 | (2) |
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2.2.1.1 Systems of Particles |
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63 | (1) |
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2.2.2 Summary of Analytical Mechanics |
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63 | (1) |
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2.2.2.1 Generalised Coordinates |
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63 | (1) |
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2.2.2.2 Principle of Virtual Work |
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64 | (2) |
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2.2.2.3 D'Alembert's Principle |
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66 | (1) |
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2.2.2.4 Hamilton's Principle |
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66 | (3) |
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2.2.2.5 Lagrange's Equations of Motion |
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69 | (4) |
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2.2.2.6 Influence Coefficients |
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73 | (1) |
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2.3 Vibration of Continuous Systems |
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74 | (55) |
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2.3.1 Nomenclature and Sign Conventions |
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74 | (2) |
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76 | (1) |
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77 | (1) |
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2.3.3.1 Longitudinal Waves |
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77 | (3) |
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2.3.3.2 Torsional Waves (Transverse Shear Waves) |
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80 | (1) |
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81 | (10) |
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2.3.3.4 Summary of Beam Resonance Frequency Formulae |
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91 | (5) |
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2.3.4 Waves in Thin Plates |
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96 | (1) |
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2.3.4.1 Longitudinal Waves |
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96 | (1) |
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2.3.4.2 Transverse Shear Waves |
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96 | (3) |
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99 | (12) |
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2.3.5 Waves in Thin Circular Cylinders |
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111 | (6) |
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2.3.5.1 Boundary Conditions |
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117 | (5) |
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2.3.5.2 Cylinder Equations of Motion: Alternative Derivation |
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122 | (1) |
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2.3.5.3 Solution of the Equations of Motion |
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123 | (4) |
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2.3.5.4 Effect of Longitudinal and Circumferential Stiffeners |
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127 | (1) |
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2.3.5.5 Other Complicating Effects |
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128 | (1) |
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3 Sound Radiation and Propagation Fundamentals |
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129 | (24) |
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129 | (1) |
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129 | (2) |
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3.3 Acoustic Green's Functions |
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131 | (11) |
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131 | (2) |
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133 | (1) |
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3.3.3 Three-Dimensional Bounded Fluid |
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134 | (3) |
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3.3.4 Two-Dimensional Duct of Infinite Length |
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137 | (3) |
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3.3.4.1 Experimental Determination of the Sound Pressure for Waves Propagating in One Direction |
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140 | (2) |
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3.4 Green's Function for a Vibrating Surface |
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142 | (2) |
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3.5 General Application of Green's Functions |
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144 | (2) |
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3.5.1 Excitation of a Structure by Point Forces |
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144 | (1) |
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3.5.2 Excitation of a Structure by a Distributed Force |
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144 | (1) |
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3.5.3 Excitation of an Acoustic Medium by Point Acoustic Sources |
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145 | (1) |
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3.5.4 Excitation of an Acoustic Medium by a Vibrating Structure |
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145 | (1) |
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3.6 Structural Sound Radiation and Wavenumber Transforms |
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146 | (7) |
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4 Acoustic and Structural Impedance and Intensity |
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153 | (70) |
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153 | (1) |
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153 | (19) |
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4.2.1 Specific Acoustic Impedance, Zs |
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153 | (1) |
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4.2.2 Acoustic Impedance, ZA |
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154 | (1) |
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4.2.3 Mechanical Impedance, Zm |
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154 | (1) |
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4.2.4 Radiation Impedance and Radiation Efficiency |
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154 | (7) |
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4.2.4.1 Structural Input Impedance |
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161 | (2) |
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4.2.5 Force Impedance of an Infinite Beam (bending Waves) |
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163 | (2) |
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4.2.6 Summary of Impedance Formulae for Beams and Plates |
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165 | (1) |
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4.2.7 Point Force Impedance of Finite Systems |
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166 | (4) |
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4.2.8 Point Force Impedance of Cylinders |
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170 | (1) |
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4.2.8.1 Infinite cylinder |
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170 | (1) |
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4.2.8.2 Finite Cylinder --- Shear Diaphragm Ends |
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170 | (1) |
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4.2.9 Wave Impedance of Finite Structures |
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171 | (1) |
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172 | (12) |
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4.3.1 Plane Wave and Far Field Intensity |
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174 | (1) |
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4.3.2 Spherical Wave Intensity |
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175 | (1) |
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176 | (1) |
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4.3.4 Measurement of Sound Intensity |
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176 | (1) |
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4.3.4.1 Sound Intensity Measurement by the p --- u Method |
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177 | (1) |
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4.3.4.2 Accuracy of the p -- u Method |
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178 | (1) |
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4.3.4.3 Sound Intensity Measurement by the p --- p Method |
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178 | (3) |
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4.3.4.4 Accuracy of the p --- p Method |
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181 | (2) |
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4.3.5 Frequency Decomposition of the Intensity |
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183 | (1) |
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4.3.5.1 Direct Frequency Decomposition |
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183 | (1) |
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4.3.5.2 Indirect Frequency Decomposition |
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183 | (1) |
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4.4 Structural Intensity and Structural Power Transmission |
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184 | (39) |
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4.4.1 Intensity and Power Transmission Measurement in Beams |
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189 | (1) |
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4.4.1.1 Longitudinal Waves |
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189 | (4) |
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193 | (1) |
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193 | (5) |
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4.4.1.4 Total Power Transmission |
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198 | (1) |
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4.4.1.5 Measurement of Beam Accelerations |
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199 | (3) |
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4.4.1.6 Effect of Transverse Sensitivity of Accelerometers |
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202 | (1) |
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4.4.2 Structural Power Transmission Measurement in Plates |
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203 | (1) |
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4.4.2.1 Longitudinal Waves |
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203 | (1) |
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4.4.2.2 Transverse Shear Waves |
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204 | (1) |
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204 | (2) |
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4.4.3 Intensity Measurement in Circular Cylinders |
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206 | (1) |
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4.4.4 Sources of Error in the Measurement of Structural Intensity |
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206 | (2) |
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4.4.5 Power into Structures via a Machine Support Point or a Shaker |
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208 | (2) |
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4.4.6 Power Transmission into Structures via Vibration Isolators |
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210 | (1) |
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4.4.6.1 Single-Degree-of-Freedom Systems |
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211 | (5) |
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4.4.6.2 Surging in Coil Springs |
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216 | (1) |
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4.4.6.3 Four-Isolator Systems |
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216 | (2) |
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4.4.6.4 Two-Stage Vibration Isolation |
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218 | (1) |
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4.4.6.5 Measurement of Power Flow through a Vibration Isolator |
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219 | (4) |
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223 | (46) |
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223 | (1) |
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5.2 Modal Analysis: Analytical |
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224 | (13) |
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5.2.1 Single-Degree-of-Freedom System with Viscous Damping |
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224 | (2) |
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5.2.2 Single-Degree-of-Freedom System with Hysteretic Damping |
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226 | (1) |
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5.2.3 Multi-Degree-of-Freedom Systems |
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226 | (3) |
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5.2.3.1 Forced Response of Undamped Systems |
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229 | (2) |
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5.2.3.2 Damped MDOF Systems: Proportional Damping |
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231 | (2) |
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5.2.3.3 Damped MDOF Systems: General Viscous Damping |
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233 | (3) |
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5.2.3.4 Damped MDOF Systems: General Hysteretic Damping |
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236 | (1) |
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237 | (1) |
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5.3 Modal Analysis: Numerical |
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237 | (4) |
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5.3.1 Modal Coupling Analysis |
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238 | (3) |
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5.4 Modal Analysis: Experimental |
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241 | (22) |
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5.4.1 Structural Modal Analysis |
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243 | (1) |
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243 | (1) |
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5.4.1.2 Excitation by Step Relaxation |
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244 | (1) |
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5.4.1.3 Excitation by Electrodynamic Shaker |
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244 | (1) |
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5.4.1.4 Excitation by Impact Hammer |
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245 | (2) |
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5.4.1.5 Structural Response Transducers |
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247 | (1) |
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5.4.2 Acoustic Modal Analysis |
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248 | (1) |
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5.4.3 Measuring the Transfer Function (or Frequency Response) |
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248 | (5) |
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5.4.4 Modal Parameter Identification |
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253 | (1) |
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253 | (1) |
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5.4.4.2 SDOF Curve Fit of FRF Data -- Peak Amplitude Method |
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254 | (1) |
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5.4.4.3 SDOF Curve Fit of FRF Data -- Circle Fit Method, Structural Damping |
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254 | (3) |
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5.4.4.4 SDOF Curve Fitting of FRF Data -- Circle Fit Method, Viscous Damping |
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257 | (1) |
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5.4.4.5 Circle Fit Analysis Procedure |
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258 | (1) |
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5.4.4.6 Reconstructing Frequency Response Curves |
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259 | (2) |
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5.4.4.7 Multi-Degree-of-Freedom Curve Fitting FRF Data |
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261 | (1) |
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5.4.4.8 Computational Mode Elimination |
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261 | (1) |
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5.4.4.9 Global Fitting of FRF Data |
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261 | (1) |
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262 | (1) |
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5.4.4.11 Structural or Acoustic Response Prediction |
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263 | (1) |
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5.5 Modal Amplitude Determination from System Response Measurements |
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263 | (6) |
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6 Statistical Energy Analysis |
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269 | (24) |
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269 | (1) |
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6.2 Model Construction and Problem Formulation |
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270 | (4) |
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6.2.1 Vibroacoustic System Analysis |
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271 | (2) |
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6.2.2 Subsystem Response as a Result of Subsystem Energy |
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273 | (1) |
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274 | (2) |
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276 | (4) |
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276 | (1) |
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276 | (2) |
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278 | (1) |
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279 | (1) |
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279 | (1) |
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280 | (1) |
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6.6 Damping Loss Factor (DLF) |
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280 | (5) |
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6.6.1 Measurement of Damping Loss Factors |
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282 | (1) |
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6.6.1.1 Modal Bandwidth Method |
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282 | (1) |
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6.6.1.2 Reverberant Decay Method |
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283 | (1) |
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6.6.1.3 Frequency Response Curve Fitting Method |
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283 | (1) |
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6.6.1.4 Power Balance Method |
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284 | (1) |
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284 | (1) |
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6.7 Coupling Loss Factors |
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285 | (5) |
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6.7.1 Coupling Loss Factors for Point Connections |
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286 | (1) |
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6.7.2 Coupling Loss Factors for Line Connections |
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286 | (1) |
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6.7.2.1 Multiple Thin Plates Connected at Their Edges |
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287 | (1) |
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6.7.2.2 Two Panels Separated along a Line by a Beam |
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288 | (1) |
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6.7.3 Coupling Loss Factors for Area Connections |
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288 | (1) |
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6.7.3.1 Coupling Loss Factor for Radiation from a Panel |
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289 | (1) |
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6.7.4 Measurement of Coupling Loss Factors |
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289 | (1) |
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6.8 Steps in Solving an SEA problem |
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290 | (3) |
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293 | (32) |
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293 | (1) |
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293 | (3) |
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7.2.1 Octave and 1/3-Octave Filter Rise Times and Settling Times |
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295 | (1) |
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7.3 Advanced Frequency Analysis |
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296 | (29) |
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7.3.1 Auto Power Spectrum and Power Spectral Density |
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299 | (4) |
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303 | (1) |
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303 | (1) |
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304 | (2) |
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7.3.4.1 Amplitude Scaling to Compensate for Window Effects |
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306 | (1) |
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7.3.4.2 Window Function Coefficients |
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307 | (3) |
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7.3.4.3 Power Correction and RMS Calculation |
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310 | (1) |
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7.3.5 Sampling Frequency and Aliasing |
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311 | (1) |
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311 | (1) |
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312 | (1) |
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7.3.8 Uncertainty Principle |
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313 | (1) |
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7.3.9 Time Synchronous Averaging and Synchronous Sampling |
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313 | (1) |
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313 | (2) |
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315 | (1) |
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316 | (1) |
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7.3.13 Coherent Output Power |
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317 | (1) |
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7.3.14 Frequency Response (or Transfer) Function |
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317 | (1) |
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318 | (2) |
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7.3.16 Auto-Correlation and Cross-Correlation Functions |
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320 | (2) |
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7.3.17 Maximum Length Sequence (MLS) |
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322 | (3) |
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A Review of Complex Numbers and Relevant Linear Matrix Algebra |
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325 | (8) |
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325 | (1) |
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325 | (1) |
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A.3 Addition, Subtraction and Multiplication by a Scalar |
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326 | (1) |
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A.4 Multiplication of Matrices |
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327 | (1) |
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327 | (1) |
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328 | (1) |
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329 | (1) |
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A.8 Positive and Non-Negative Definite Matrices |
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329 | (1) |
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A.9 Eigenvalues and Eigenvectors |
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329 | (1) |
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329 | (1) |
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330 | (1) |
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A.12 Singular Value Decomposition |
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331 | (1) |
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331 | (2) |
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B Properties of Materials |
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333 | (6) |
References |
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339 | (8) |
Index |
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347 | |