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Part I Introductory Concepts in Structural Health Monitoring |
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3 | (38) |
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1.1 Overview on Structural Health Monitoring |
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3 | (11) |
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1.1.1 Why Do We Need Structural Health Monitoring? |
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3 | (2) |
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1.1.2 Basic Elements of SHM Systems |
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5 | (4) |
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1.1.3 Levels of Structural Health Monitoring |
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9 | (1) |
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1.1.4 State-of-Art and Technological Needs |
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10 | (4) |
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1.2 Dynamics-Based Structural Health Monitoring |
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14 | (7) |
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15 | (1) |
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1.2.2 Classification of Inspection Techniques Based on Frequency Range of Analysis |
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16 | (1) |
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1.2.3 Vibration-Based Techniques |
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17 | (2) |
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1.2.4 Guided Waves Inspection |
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19 | (1) |
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1.2.5 Ultrasonics and Nonlinear Ultrasound |
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20 | (1) |
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1.3 Sensing and Actuation Strategies |
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21 | (10) |
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1.3.1 Piezoelectric Actuators and Sensors |
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21 | (4) |
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1.3.2 Fiber Optics Sensors |
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25 | (4) |
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29 | (2) |
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1.4 Modeling and Simulation Techniques for SHM |
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31 | (6) |
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1.4.1 The Importance of Modeling in Structural Health Monitoring |
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31 | (1) |
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1.4.2 Finite Difference Techniques |
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32 | (1) |
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1.4.3 Finite Element Method |
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33 | (1) |
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1.4.4 Boundary Element Method |
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34 | (1) |
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1.4.5 Spectral Finite Element Method |
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34 | (2) |
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1.4.6 Perturbation Techniques |
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36 | (1) |
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1.5 Organization of the Book |
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37 | (1) |
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38 | (3) |
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2 Fundamentals Concepts in Elasticity, Mechanics and Wave Propagation |
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41 | (56) |
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41 | (1) |
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2.2 Basic Concepts in Elasticity |
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41 | (13) |
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2.2.1 Description of Motion |
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41 | (3) |
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44 | (2) |
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2.2.3 Strain-Displacement Relations |
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46 | (2) |
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48 | (2) |
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2.2.5 Constitutive Relations |
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50 | (2) |
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52 | (2) |
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2.3 Governing Equations of Motion and the Solution Methods |
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54 | (6) |
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2.3.1 Solution Procedures in Linear Theory of Elasticity |
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56 | (3) |
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2.3.2 Plane Problems in Elasticity |
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59 | (1) |
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2.4 Introduction to Theory of Composites |
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60 | (9) |
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2.4.1 Theory of Laminated Composites |
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60 | (6) |
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2.4.2 Stress-Strain Relation for a Lamina with Arbitrary Orientation of Fibers |
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66 | (3) |
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2.5 Introduction to Wave Propagation in Structures |
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69 | (5) |
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70 | (4) |
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2.6 Characteristics of Waves in Anisotropic Media |
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74 | (1) |
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2.7 Governing Equations for Beams and Plates |
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75 | (6) |
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2.7.1 Governing Equation for an Elementary Beam |
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76 | (1) |
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2.7.2 Governing Differential Equation for a Higher Order Beam |
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77 | (2) |
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2.7.3 Governing Equations for a Composite Plate |
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79 | (2) |
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2.8 Spectrum and Dispersion Relations |
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81 | (13) |
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2.8.1 Efficient Computation of the Wavenumber and Wave Amplitude |
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81 | (3) |
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2.8.2 Spectrum and Dispersion Relation for an Elementary Beam |
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84 | (2) |
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2.8.3 Spectrum and Dispersion Relation for a Higher Order Beam |
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86 | (3) |
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2.8.4 Spectrum and Dispersion Relation for an Anisotropic Plate |
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89 | (5) |
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94 | (3) |
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3 Signal Processing Techniques |
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97 | (60) |
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97 | (13) |
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97 | (2) |
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99 | (2) |
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3.1.3 Discrete Fourier Transform |
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101 | (2) |
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103 | (6) |
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3.1.5 Wavelet-Based Numerical Solutions of Wave Equations |
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109 | (1) |
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3.1.6 Comparative Advantages and Disadvantages of Different Transforms |
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109 | (1) |
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3.2 Signal Processing Issues |
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110 | (18) |
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3.2.1 Wraparound Problems |
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110 | (6) |
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3.2.2 Signal Processing of Sampled Waveforms |
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116 | (1) |
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3.2.3 Artificial Dispersion in Wavelet Transform |
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117 | (9) |
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3.2.4 Excitation Signals and Wave Dispersion |
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126 | (2) |
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3.3 Frequency/Wavenumber Analysis |
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128 | (25) |
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3.3.1 Analysis of a One-Dimensional Propagating Wave |
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130 | (4) |
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3.3.2 Analysis of 2D Wave Propagation |
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134 | (4) |
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3.3.3 Numerical Examples: Wave Propagation in a Damaged Rod |
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138 | (5) |
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3.3.4 Numerical Examples: Wave Propagation in a Homogeneous Medium |
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143 | (1) |
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3.3.5 Frequency/Wavenumber Filtering for Mode Separation |
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144 | (9) |
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153 | (4) |
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Part II Computational Simulation Techniques for Structural Health Monitoring |
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4 Application of the Finite Element Method in SHM |
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157 | (20) |
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4.1 Overview and Basic Principles |
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157 | (2) |
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4.2 Modeling Issues in FEM |
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159 | (5) |
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4.3 Damage Modeling Using FEM |
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164 | (4) |
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4.3.1 Stiffness Reduction Method |
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164 | (1) |
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4.3.2 Duplicate Node Method |
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165 | (1) |
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4.3.3 Kinematics Based Method |
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166 | (2) |
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168 | (4) |
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4.4.1 Static and Free Vibration Analysis of a Damaged Cantilever Beam Using DNM |
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168 | (2) |
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4.4.2 Response Analysis of a Cantilever Composite Beam with Different Damage Types |
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170 | (2) |
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4.5 Finite Element Modeling Suggestions |
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172 | (1) |
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4.6 Modeling Pitfalls in FEM for SHM and Their Remedies |
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173 | (1) |
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174 | (3) |
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5 Spectral Finite Element Method |
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177 | (42) |
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5.1 The Need for Spectral FEM in SHM |
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177 | (5) |
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5.1.1 General Formulation Procedure: Fourier Transform Based SFEM |
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178 | (2) |
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5.1.2 General Formulation Procedure: Wavelet Transform Based SFEM |
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180 | (2) |
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5.2 Spectral Elements for Rods and Beams |
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182 | (8) |
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5.2.1 Non-dispersive Isotropic Rod: FFT Based Spectral Element Formulation |
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182 | (2) |
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5.2.2 Non-dispersive Isotropic Rod: Wavelet Transform Based Spectral Element Formulation |
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184 | (1) |
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5.2.3 Dispersive Isotropic Timoshenko Beams-FFT Based Spectral Element Formulation |
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184 | (2) |
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5.2.4 Composite Beams-FFT Based Spectral Element Formulation |
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186 | (2) |
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5.2.5 Higher Order Composite Beam-FFT Based Spectral Element Formulation |
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188 | (2) |
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5.3 Spectral Elements for 2D Composite Layers-FFT Based Spectral Element Formulation |
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190 | (9) |
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5.3.1 Finite Layer Element (FLE) |
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195 | (1) |
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5.3.2 Infinite Layer (Throw-Off) Element (ILE) |
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196 | (1) |
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5.3.3 Expressions for Stresses and Strains |
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197 | (1) |
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5.3.4 Prescription of Force Boundary Conditions |
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197 | (1) |
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5.3.5 Determination of Lamb Wave Modes |
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198 | (1) |
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5.4 Anisotropic Plate-FFT Based Spectral Element Formulation |
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199 | (3) |
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5.4.1 Finite Plate Element |
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200 | (1) |
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5.4.2 Semi-infinite or Throw-Off Plate Element |
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201 | (1) |
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202 | (14) |
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5.5.1 Wave Transmission and Scattering Through an Angle-Joint |
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202 | (3) |
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5.5.2 Wave Propagation in 2D Portal Frame |
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205 | (2) |
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5.5.3 Propagation of Surface and Interfacial Waves in a Composite Layer |
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207 | (4) |
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5.5.4 Propagation of Lamb Wave |
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211 | (3) |
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5.5.5 Wave Propagation in a Composite Plate with Ply-Drop |
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214 | (2) |
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216 | (1) |
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216 | (3) |
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6 Simplified Spectral Models for Damaged Waveguides |
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219 | (54) |
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6.1 Need for Spectral Element Damage Models in Structural Health Monitoring |
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219 | (1) |
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6.2 Review of Simplified Models for Structural Defects |
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220 | (1) |
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6.3 Modeling of Single Delamination or Horizontal Cracks |
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221 | (9) |
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6.3.1 Wave Scattering in a Delaminated Beam Using Wavelet Spectral Elements |
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226 | (3) |
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6.3.2 Effect of Wave Scattering Due to Delamination at Ply-drops |
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229 | (1) |
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6.4 Modeling of Fiber Breakage and Vertical Cracks |
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230 | (11) |
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6.4.1 Interface Equilibrium of Forces |
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232 | (1) |
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6.4.2 Assembly of the Element Internal Waveguides |
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233 | (1) |
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6.4.3 Modeling Dynamic Contact Between Crack Surfaces |
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234 | (2) |
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6.4.4 Modeling of Surface Breaking Cracks |
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236 | (1) |
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6.4.5 Distributed Constraints at the Interfaces Between Sub-Laminates and Hanging Laminates |
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237 | (2) |
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6.4.6 Wave Scattering Due to Transverse Cracks |
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239 | (1) |
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6.4.7 Sensitivity of the Fiber Breakage Location and Configuration |
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240 | (1) |
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6.5 Modeling of Structures with Multiple Horizontal Cracks or Delaminations |
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241 | (7) |
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6.5.1 Wave Scattering from Delamination: Comparison with 2D FEM |
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246 | (1) |
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6.5.2 Computational Efficiency of FSFEM Compared to FEM |
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247 | (1) |
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6.6 Modeling of Corrosion Pits |
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248 | (5) |
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6.6.1 Wave Propagation Response Due to Corrosion Pits |
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250 | (3) |
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6.7 Modeling of Material Degradations |
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253 | (10) |
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6.7.1 Experimental Degraded Model (EDM) |
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254 | (5) |
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6.7.2 Average Degraded Model |
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259 | (3) |
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6.7.3 Wave Scattering in a Degraded Composite Beam Using ADM |
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262 | (1) |
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6.8 Modeling of Vertical Cracks in 2D Waveguides |
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263 | (6) |
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6.8.1 Flexibility Along the Crack |
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266 | (1) |
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6.8.2 Scattering Due to a Transverse Crack |
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267 | (2) |
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269 | (1) |
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270 | (3) |
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7 Perturbation Methods for Damaged Structures |
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273 | (40) |
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7.1 Perturbation Methods for Notched Structures |
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273 | (1) |
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7.2 Modal Analysis of Damaged Plates |
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274 | (15) |
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7.2.1 Governing Equations |
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274 | (3) |
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7.2.2 Perturbation Solution |
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277 | (1) |
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7.2.3 Fourier Series Solution of ε1 Equations |
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278 | (3) |
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7.2.4 Strain Energy Ratio for Damage Localization |
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281 | (2) |
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7.2.5 Effect of Notch Damage on the Plate Modal Properties |
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283 | (2) |
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7.2.6 Notch Damage Localization Through the Strain Energy Ratio |
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285 | (2) |
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7.2.7 Effect of Line Damage on the Plate Modal Properties |
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287 | (2) |
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7.3 Analysis of Wave Propagation in Notched Beams Through Spectral FE Solution |
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289 | (1) |
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290 | (12) |
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7.4.1 Spectral Finite Element Discretization |
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300 | (2) |
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7.5 Wave Propagation in Notched Beams: Numerical Examples |
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302 | (9) |
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7.5.1 Technique Validation: FSFEM Versus FE Predictions |
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302 | (2) |
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7.5.2 FSFEM and Modal Superposition Results |
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304 | (1) |
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7.5.3 Time Domain Results |
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305 | (5) |
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7.5.4 Frequency Domain Results |
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310 | (1) |
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311 | (2) |
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8 Bridging Scale Analysis of Wave Propagation in Heterogeneous Structures with Imperfections |
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313 | (36) |
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313 | (2) |
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8.2 Theoretical Background |
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315 | (6) |
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8.2.1 Coarse and Fine Scale Discretization and Bridging Matrices |
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315 | (1) |
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8.2.2 Multiscale Lagrangian |
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316 | (1) |
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8.2.3 Reduction of the Degrees of Freedom |
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317 | (1) |
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8.2.4 Time Domain Formulation |
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318 | (1) |
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8.2.5 Frequency Domain Formulation |
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319 | (2) |
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8.3 Results for Time-Domain Bridging |
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321 | (18) |
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8.3.1 Application to a One-Dimensional Rod |
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321 | (4) |
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8.3.2 Homogenized Bi-material Rod with Imperfections |
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325 | (6) |
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8.3.3 Energy-Based Time Integration Scheme |
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331 | (1) |
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8.3.4 Propagation of In-plane Waves in a 2D Elastic Domain |
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332 | (7) |
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8.4 Results for Frequency-Domain Bridging |
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339 | (8) |
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8.4.1 Time Domain Spectral Element Discretization |
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339 | (1) |
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340 | (1) |
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8.4.3 Damaged Timoshenko Beam |
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340 | (4) |
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8.4.4 Two Dimensional Waveguides |
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344 | (3) |
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347 | (1) |
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348 | (1) |
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9 Modeling of Actuators and Sensors for SHM |
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349 | (58) |
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349 | (1) |
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9.2 Modeling of Lamb Wave Generation |
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350 | (14) |
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9.2.1 Governing Equations |
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351 | (2) |
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9.2.2 Harmonic Far Field Response |
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353 | (2) |
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9.2.3 Actuator Directivity |
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355 | (1) |
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9.2.4 Example: Circular Actuator |
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355 | (3) |
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9.2.5 Experimental Validation |
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358 | (1) |
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9.2.6 Finite Element Evaluation of the Interface Stresses |
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359 | (3) |
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9.2.7 Example: Circular Patch |
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362 | (2) |
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9.2.8 Rectangular Isotropic Piezo Patch |
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364 | (1) |
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9.3 Beamforming Through One-Dimensional Phased Arrays: A Quick Overview |
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364 | (8) |
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9.3.1 Response Due to a Single Component |
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366 | (1) |
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367 | (1) |
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9.3.3 Beam Steering Strategies |
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368 | (4) |
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9.4 Two Dimensional Arrays for Frequency Based Beam Steering |
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372 | (19) |
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9.4.1 Application to SV Waves in a Membrane |
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374 | (9) |
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9.4.2 Application to Guided Waves in Thin Plates |
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383 | (8) |
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9.5 Modeling of Lamb Wave Sensors |
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391 | (12) |
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9.5.1 Plate Configuration and Piezoelectric Constitutive Relations |
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392 | (2) |
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9.5.2 Voltage Generated by Piezo Sensors of Arbitrary Shape |
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394 | (3) |
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9.5.3 Examples of Directivities for Simple Geometries |
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397 | (2) |
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9.5.4 Frequency Steerable Acoustic Transducer Periodic Array |
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399 | (4) |
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403 | (4) |
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Part III Computational Methodologies for Damage Detection and Quantification |
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10 Computational Techniques for Damage Detection, Classification and Quantification |
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407 | (56) |
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407 | (1) |
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10.2 A General Introduction to Vibration-Based Techniques |
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408 | (3) |
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10.2.1 Early Techniques Based on Natural Frequency Shifts |
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408 | (2) |
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10.2.2 Mode Shape Analysis |
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410 | (1) |
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10.2.3 Mode Shape Curvature Changes |
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410 | (1) |
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10.3 Damage Measure Based on Energy Functional Distributions |
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411 | (18) |
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10.3.1 Formulation for Beams and Plates |
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412 | (2) |
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10.3.2 Spline Interpolation of Operational Deflection Shapes |
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414 | (2) |
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10.3.3 Numerical Results on Beams |
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416 | (2) |
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10.3.4 Numerical Results on Plates |
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418 | (3) |
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10.3.5 Experimental Results on Beams |
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421 | (5) |
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10.3.6 Experimental Results on Plates |
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426 | (3) |
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10.4 Wave Propagation Techniques: Time Domain Damage Measure |
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429 | (7) |
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10.4.1 Theoretical Background |
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430 | (3) |
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10.4.2 Numerical Examples: Wave Propagation in a Homogeneous Medium |
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433 | (2) |
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10.4.3 Experimental Results: Aluminum Plate |
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435 | (1) |
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10.5 Phase Gradient and Conversion Coefficients Evaluation for Damage Localization and Quantification |
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436 | (14) |
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10.5.1 Simplified Description of a Multi-Modal Wave |
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437 | (1) |
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10.5.2 Phase Gradient for Damage Localization |
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437 | (2) |
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10.5.3 Reflection, Transmission and Conversion Coefficients for Damage Quantification |
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439 | (1) |
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10.5.4 Application to Simulated Data |
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440 | (6) |
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10.5.5 Application to Experimental Data |
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446 | (4) |
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10.6 Damage Force Indicator Technique |
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450 | (9) |
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10.6.1 Identification of Single Delamination Through Damage Force Indicator |
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452 | (1) |
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10.6.2 Identification of Multiple Delamination Through Damage Force Indicator |
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453 | (1) |
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10.6.3 Sensitivity of Damage Force Indicator Due to Variation in Delamination Size |
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454 | (3) |
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10.6.4 Sensitivity of Damage Force Indicator Due to Variation in Delamination Depth |
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457 | (2) |
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459 | (1) |
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459 | (4) |
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11 Use of Soft Computing Tools for Damage Detection |
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463 | (32) |
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463 | (15) |
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11.1.1 A Brief Introduction to Genetic Algorithms |
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463 | (3) |
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11.1.2 Genetic Algorithm Process for Damage Detection and Definitions |
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466 | (2) |
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11.1.3 Objective Functions in GA for Delamination Identification |
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468 | (4) |
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11.1.4 Case Studies with a Cantilever Beam |
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472 | (4) |
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11.1.5 Identification of Delamination Location, Size and Depth |
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476 | (2) |
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11.2 Artificial Neural Networks |
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478 | (12) |
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11.2.1 Simple Model of Neuron |
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478 | (2) |
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11.2.2 Types of Activation Function |
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480 | (1) |
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11.2.3 Multilayer Feedforward Networks |
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481 | (1) |
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11.2.4 Neural Network Integrated with SFEM |
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482 | (5) |
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11.2.5 Numerical Results and Discussion |
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487 | (3) |
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490 | (3) |
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493 | (2) |
Index |
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495 | |