Guided Waves in Structures for SHM : The Time - domain Spectral Element Method

Preface ix1 Introduction to the Theory of Elastic Waves 11.1 Elastic Waves 11.1.1 Longitudinal Waves (Compressional/Pressure/Primary/P Waves) 21.1.2 Shear Waves (Transverse/Secondary/S Waves) 21.1.3 Rayleigh Waves 31.1.4 Love Waves 41.1.5 Lamb Waves 41.2 Basic Definitions 51.3 Bulk Waves in Three-Dimensional Media 101.3.1 Isotropic Media 101.3.2 Christoffel Equations for Anisotropic Media 121.3.3 Potential Method 141.4 Plane Waves 151.4.1 Surface Waves 161.4.2 Derivation of Lamb Wave Equations 171.4.3 Numerical Solution of Rayleigh-Lamb Frequency Equations 261.4.4 Distribution of Displacements and Stresses for Various Frequencies of Lamb Waves 291.4.5 Shear Horizontal Waves 321.5 Wave Propagation in One-Dimensional Bodies of Circular Cross-Section 351.5.1 Equations of Motion 351.5.2 Longitudinal Waves 361.5.3 Solution of Pochhammer Frequency Equation 391.5.4 Torsional Waves 421.5.5 Flexural Waves 43References 452 Spectral Finite Element Method 472.1 Shape Functions in the Spectral Finite Element Method 532.1.1 Lobatto Polynomials 542.1.2 Chebyshev Polynomials 562.1.3 Laguerre Polynomials 602.2 Approximating Displacement, Strain and Stress Fields 622.3 Equations of Motion of a Body Discretised Using Spectral Finite Elements 672.4 Computing Characteristic Matrices of Spectral Finite Elements 722.4.1 Lobatto Quadrature 752.4.2 Gauss Quadrature 762.4.3 Gauss-Laguerre Quadrature 782.5 Solving Equations of Motion of a Body Discretised Using Spectral Finite Elements 812.5.1 Forcing with an Harmonic Signal 822.5.2 Forcing with a Periodic Signal 832.5.3 Forcing with a Nonperiodic Signal 84References 923 Three-Dimensional Laser Vibrometry 933.1 Review of Elastic Wave Generation Methods 943.1.1 Force Impulse Methods 943.1.2 Ultrasonic Methods 943.1.3 Methods Based on the Electromagnetic Effect 973.1.4 Methods Based on the Piezoelectric Effect 983.1.5 Methods Based on the Magnetostrictive Effect 1023.1.6 Photothermal Methods 1033.2 Review of Elastic Wave Registration Methods 1043.2.1 Optical Methods 1063.3 Laser Vibrometry 1093.4 Analysis of Methods of Elastic Wave Generation and Registration 1143.5 Exemplary Results of Research on Elastic Wave Propagation Using 3D Laser Scanning Vibrometry 116References 1214 One-Dimensional Structural Elements 1254.1 Theories of Rods 1254.2 Displacement Fields of Structural Rod Elements 1274.3 Theories of Beams 1334.4 Displacement Fields of Structural Beam Elements 1354.5 Dispersion Curves 1414.6 Certain Numerical Considerations 1434.6.1 Natural Frequencies 1444.6.2 Wave Propagation 1474.7 Examples of Numerical Calculations 1554.7.1 Propagation of Longitudinal Elastic Waves in a Cracked Rod 1564.7.2 Propagation of Flexural Elastic Waves in a Rod 1584.7.3 Propagation of Coupled Longitudinal and Flexural Elastic Waves in a Rod 162References 1645 Two-Dimensional Structural Elements 1675.1 Theories of Membranes, Plates and Shells 1675.2 Displacement Fields of Structural Membrane Elements 1695.3 Displacement Fields of Structural Plate Elements 1755.4 Displacement Fields of Structural Shell Elements 1815.5 Certain Numerical Considerations 1845.6 Examples of Numerical Calculations 1895.6.1 Propagation of Elastic Waves in an Angle Bar 1895.6.2 Propagation of Elastic Waves in a Half-Pipe Aluminium Shell 1925.6.3 Propagation of Elastic Waves in an Aluminium Plate 195References 1986 Three-Dimensional Structural Elements 2016.1 Solid Spectral Elements 2026.2 Displacement Fields of Solid Structural Elements 2026.2.1 Six-Mode Theory 2026.2.2 Nine-Mode Theory 2036.3 Certain Numerical Considerations 2046.4 Modelling Electromechanical Coupling 2086.4.1 Assumptions 2136.4.2 Linear Constitutive Equations 2136.4.3 Basic Equations of Motion 2146.4.4 Static Condensation 2156.4.5 Inducing Waves 2166.4.6 Recording Waves 2166.4.7 Electrical Boundary Conditions 2166.5 Examples of Numerical Calculations 2206.5.1 Propagation of Elastic Waves in a Half-Pipe Aluminium Shell 2206.5.2 Propagation of Elastic Waves in an Isotropic Plate - Experimental Verification 2226.6 Modelling the Bonding Layer 227References 2307 Detection, Localisation and Identification of Damageby ElasticWave Propagation 2337.1 Elastic Waves in Structural Health Monitoring 2357.2 Methods of Damage Detection, Localisation and Identification 2477.2.1 Energy Addition Method 2537.2.2 Phased Array Method 2557.2.3 Methods Employing Continuous Registration of Elastic Waves within the Analysed Area 2637.2.4 Damage Identification Algorithms 2667.3 Examples of Damage Localisation Methods 2697.3.1 Localisation Algorithms Employing Sensor Networks 2697.3.2 Algorithms Based on Full Field Measurements of Elastic Wave Propagation 275References 288Appendix: EWavePro Software 295A.1 Introduction 295A.2 Theoretical Background and Scope of Applicability (Computation Module) 296A.3 Functional Structure and Software Environment (Pre- and Post-Processors) 298A.4 Elastic Wave Propagation in aWing Skin of an Unmanned Plane (UAV) 312A.5 Elastic Wave Propagation in a Composite Panel 320References 333Index 335