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1 Electromagnetic Acoustic Transducer |
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1 | (42) |
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1 | (1) |
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1.2 Research Status of EMAT |
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2 | (8) |
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2 | (4) |
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1.2.2 Energy Conversion Mechanism and Analytical Method of EMAT |
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6 | (4) |
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1.3 Optimal Design of EMAT and Its New Configuration |
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10 | (33) |
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1.3.1 Optimal Design of Meander Coil |
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10 | (13) |
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1.3.2 Multibelt Coil Axisymmetric Guided Wave EMAT |
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23 | (12) |
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1.3.3 SH Guided Wave EMAT Used in Non-ferromagnetic Material |
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35 | (3) |
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1.3.4 Calculation of the Impedance Matching Capacitance of EMAT [ 5] |
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38 | (4) |
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42 | (1) |
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2 Analytical Method of EMAT Based on Lorentz Force Mechanism |
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43 | (60) |
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2.1 Multifield Coupling Equation of EMAT Based on Lorentz Force Mechanism |
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43 | (6) |
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2.1.1 Magnetic Field Equation of a Permanent Magnet |
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44 | (1) |
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2.1.2 Dynamic Magnetic Field Equation of the Pulsed Eddy Current [ 1] |
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45 | (2) |
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2.1.3 Motion Equation of Particle in the Specimen |
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47 | (1) |
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2.1.4 Receiving Equation of Ultrasonic Signal |
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48 | (1) |
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2.2 The Weak Form of the Coupling Field Equations |
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49 | (6) |
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2.2.1 The Weak Form of Coupled Equations Under Two-Dimensional Cartesian Coordinates |
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49 | (3) |
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2.2.2 The Weak Form of Coupled Equations in the Axisymmetric Coordinate System |
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52 | (3) |
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2.3 Finite Element Simulation of EMAT by COMSOL Multiphysics [ 2] |
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55 | (12) |
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2.3.1 Simulation Procedure of EMAT by COMSOL Multiphysics |
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55 | (2) |
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2.3.2 Example of the Numerical Simulation and Experimental Verification |
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57 | (10) |
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2.4 Analytical Modeling and Calculation of EMAT with Spiral Coil [ 3] |
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67 | (14) |
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2.4.1 Configurations of the EMAT with Spiral Coils |
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67 | (1) |
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2.4.2 Frequency-Domain Solution |
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68 | (8) |
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2.4.3 The Time-Domain Solutions |
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76 | (1) |
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2.4.4 Results Comparison and Discussion |
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77 | (4) |
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2.5 Analytical Modeling and Calculation of the Meander Coil EMAT [ 4] |
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81 | (16) |
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2.5.1 Meander Coil EMAT Configuration and Calculation Model |
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82 | (1) |
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2.5.2 The Frequency-Domain Calculation of the Coil's Impedance and Magnetic Field |
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83 | (9) |
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2.5.3 The Calculation of the Time-Domain Pulsed Magnetic Field |
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92 | (1) |
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2.5.4 Example and Comparison of Results |
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93 | (4) |
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2.6 The Analytical Method of EMAT Under Impulse Voltage Excitation [ 5] |
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97 | (6) |
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2.6.1 Calculating the Pulsed Current Using the Analytical Equation |
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97 | (1) |
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2.6.2 Calculating the Pulsed Current Using the Field-Circuit Coupling Finite Element Method |
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98 | (3) |
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2.6.3 The Coil's Current Calculation Examples Realized Using the Circuit-Field Coupled Finite Element Method |
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101 | (1) |
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102 | (1) |
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3 Analytical Method of EMAT Based on Magnetostrictive Mechanism |
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103 | (50) |
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3.1 Magnetic and Magnetostrictive Property of Ferromagnetic Materials |
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104 | (4) |
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3.1.1 Magnetic Characteristics and Magnetic Permeability of Ferromagnetic Materials |
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104 | (1) |
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3.1.2 Magnetostrictive Property of the Ferromagnetic Material |
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105 | (3) |
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3.2 Finite Element Method of EMAT Based on the Magnetostrictive Mechanism [ 1] |
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108 | (24) |
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3.2.1 Basic Physical Equations |
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108 | (3) |
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3.2.2 Calculations of Magnetostrictive Force and Magnetostrictive Current Density in the Two-Dimensional Cartesian Coordinate System |
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111 | (3) |
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3.2.3 Calculation of the Magnetostrictive Force and Magnetostrictive Current Density in the Axisymmetric Coordinates |
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114 | (2) |
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3.2.4 Determination of the Piezomagnetic Coefficient |
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116 | (6) |
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3.2.5 Numerical Simulation of EMAT Based on Magnetostrictive Mechanism |
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122 | (10) |
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3.3 Analytical Modeling and Calculation of SH Guided Waves by EMAT [ 2] |
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132 | (5) |
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3.4 Analytical Modeling and Calculation of an Axial Guided Wave in a Pipe by EMAT |
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137 | (16) |
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3.4.1 The Magnetic Vector Potential of the δ Coil |
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138 | (3) |
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3.4.2 Magnetic Vector Potential of the Coil with the Rectangular Cross Section |
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141 | (2) |
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3.4.3 The Impedance, Eddy Current, and Magnetic Induction Intensity of the Coil |
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143 | (1) |
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3.4.4 One-Layer Conductor |
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144 | (4) |
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3.4.5 Magnetic Elasticity of the Axial Guided Wave EMAT in Pipe |
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148 | (1) |
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3.4.6 Calculation of the Pulsed Magnetic Field of the T-Mode Guided Wave |
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149 | (2) |
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151 | (2) |
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4 The Propagation Characteristics of Ultrasonic Guided Waves in Plate and Pipe |
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153 | (30) |
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4.1 Dispersion and Wave Structures of the Lamb Waves in the Plate |
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153 | (6) |
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4.1.1 The Dispersion Characteristics of the Lamb Waves in the Plate |
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154 | (1) |
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4.1.2 The Wave Structures of the Lamb Waves in the Plate |
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155 | (4) |
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4.2 The Characteristics of Dispersion and Wave Structures of SH Guided Waves in the Plate |
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159 | (2) |
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4.2.1 Dispersion of SH Guided Waves in the Plate |
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159 | (1) |
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4.2.2 Wave Structure of SH Guided Waves in the Plate |
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159 | (2) |
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4.3 Dispersion and Wave Structure of Circumferential Lamb Waves in Pipe [ 1] |
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161 | (10) |
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4.3.1 Dispersion Equations and Their Solution of Circumferential Lamb Waves in Pipe |
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161 | (7) |
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4.3.2 Wave Structure of Circumferential Lamb Waves in the Pipe |
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168 | (3) |
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4.4 Dispersion and Wave Structure of Circumferential SH Guided Waves in the Pipe [ 2] |
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171 | (9) |
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4.4.1 The Dispersive Equations and Solutions of the Circumferential SH Guided Waves in the Pipe |
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171 | (6) |
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4.4.2 Wave Structure of Circumferential SH Guided Waves in the Pipe |
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177 | (3) |
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4.5 Comparison of the Propagation Characteristics Between Guided Waves in the Plate and Circumferential Guided Waves in the Pipe |
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180 | (3) |
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181 | (2) |
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5 Simulation of Interactions Between Guided Waves and the Defects by Boundary Element Method |
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183 | (54) |
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5.1 Hybrid BEM Model of the External Defects in a Plate |
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184 | (1) |
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5.2 Elastodynamic Integration Equation and Its Fundamental Solution |
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184 | (2) |
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5.3 Boundary Integration Equation and Its Discretized Numerical Solution |
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186 | (7) |
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5.3.1 The Solution of the Elements in Matrix G |
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189 | (3) |
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5.3.2 The Solution of the Elements in Matrix H |
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192 | (1) |
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5.4 Construction of the Boundary Condition Based on Mode Expansion |
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193 | (9) |
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5.5 Structure of the BEM Program |
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202 | (3) |
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5.6 Factors of Computational Accuracy |
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205 | (6) |
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5.6.1 Sweeping of the Model Length |
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205 | (4) |
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5.6.2 Sweeping of the Boundary Elements Size |
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209 | (2) |
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5.7 Calculation of the Reflections at the End of the Plate |
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211 | (3) |
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5.8 Simulation of the External Defect in the Plate [ 1] |
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214 | (5) |
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5.8.1 Sweeping of the Crack Depth on the External Surface of the Plate |
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214 | (3) |
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5.8.2 Sweeping of the Crack Width on the External Surface of the Plate |
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217 | (1) |
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5.8.3 Sweeping of the Frequency Thickness Product in the Plate with External Defect |
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218 | (1) |
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5.9 Model and Numerical Simulation of Internal Defect in the Plate |
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219 | (9) |
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5.9.1 Internal Crack's Height in the Plate |
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222 | (1) |
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5.9.2 Internal Crack's Width in the Plate |
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223 | (2) |
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5.9.3 Frequency Thickness Product of Internal Crack in the Plate |
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225 | (2) |
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5.9.4 Internal Crack's Movement Along the Vertical Direction |
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227 | (1) |
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5.10 Quantitative Crack Detection by Electromagnetic Ultrasonic Guided Waves |
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228 | (9) |
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235 | (2) |
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6 Finite Element Simulation of Ultrasonic Guided Waves |
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237 | (34) |
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6.1 The Explicit Integration Finite Element Method |
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237 | (1) |
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6.2 Finite Element Simulation of the Lamb Wave in the Plate [ 1] |
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238 | (10) |
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6.2.1 Establishment of the Lamb Wave Equation in the Elastic Plate |
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238 | (2) |
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6.2.2 Finite Element Simulation of the Lamb Wave in the Plate |
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240 | (4) |
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6.2.3 Example of Lamb Wave Simulation in the Plate |
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244 | (4) |
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6.3 Finite Element Simulation of the Circumferential Lamb Wave in Pipe [ 2] |
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248 | (14) |
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6.3.1 Establishment of the Dispersion Equation of Circumferential Lamb Waves |
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248 | (4) |
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6.3.2 Finite Element Simulation of the Circumferential Lamb Wave in the Pipe |
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252 | (1) |
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6.3.3 Simulation of the Circumferential Lamb Wave in the Pipe |
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253 | (9) |
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6.4 Finite Element Simulation of the L-Type Guided Wave Along the Axial Direction of the Pipeline |
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262 | (5) |
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6.5 Finite Element Simulation of the T-type Guided Wave Along the Axial Direction in the Pipeline |
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267 | (4) |
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270 | (1) |
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7 Applications of the Electromagnetic Ultrasonic Guided Wave Technique |
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271 | |
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7.1 Thickness Measurement by Electromagnetic Ultrasonics |
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271 | (8) |
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7.1.1 Principle of the Thickness Measurement by Electromagnetic Ultrasonics |
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271 | (1) |
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7.1.2 Setup of the Electromagnetic Ultrasonic Thickness Measurement [ 1] |
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272 | (1) |
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7.1.3 Hardware of the Electromagnetic Ultrasonic Thickness Measurement [ 2] |
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273 | (2) |
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7.1.4 Analysis and Processing of the Echo Signal in the Electromagnetic Ultrasonic Thickness Measurement [ 3] |
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275 | (4) |
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7.2 Electromagnetic Ultrasonic Guided Wave Test Along the Axial Direction of the Pipeline |
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279 | (17) |
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7.2.1 Electromagnetic Ultrasonic Transducers |
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279 | (3) |
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7.2.2 Electromagnetic Ultrasonic Excitation Source and the Filter Amplifier [ 4] |
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282 | (2) |
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7.2.3 Experiment of the Electromagnetic Ultrasonic Guided Wave Test and the Factors |
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284 | (12) |
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7.3 Electromagnetic Ultrasonic Guided Wave Detection for Cracks in the Natural Gas Pipeline [ 5--7] |
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296 | |
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7.3.1 The Main Structure of the Detector |
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296 | (4) |
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7.3.2 Relative Detection Experiment |
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300 | (1) |
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300 | |
