Guided Waves in Structures for SHM -- Contents -- Preface -- 1 Introduction to the Theory of Elastic Waves -- 1.1 Elastic Waves -- 1.1.1 Longitudinal Waves (Compressional/Pressure/Primary/P Waves) -- 1.1.2 Shear Waves (Transverse/Secondary/S Waves) -- 1.1.3 Rayleigh Waves -- 1.1.4 Love Waves -- 1.1.5 Lamb Waves -- 1.2 Basic Definitions -- 1.3 Bulk Waves in Three-Dimensional Media -- 1.3.1 Isotropic Media -- 1.3.2 Christoffel Equations for Anisotropic Media -- 1.3.3 Potential Method -- 1.4 Plane Waves -- 1.4.1 Surface Waves -- 1.4.2 Derivation of Lamb Wave Equations -- 1.4.3 Numerical Solution of Rayleigh-Lamb Frequency Equations -- 1.4.4 Distribution of Displacements and Stresses for Various Frequencies of Lamb Waves -- 1.4.5 Shear Horizontal Waves -- 1.5 Wave Propagation in One-Dimensional Bodies of Circular Cross-Section -- 1.5.1 Equations of Motion -- 1.5.2 Longitudinal Waves -- 1.5.3 Solution of Pochhammer Frequency Equation -- 1.5.4 Torsional Waves -- 1.5.5 Flexural Waves -- References -- 2 Spectral Finite Element Method -- 2.1 Shape Functions in the Spectral Finite Element Method -- 2.1.1 Lobatto Polynomials -- 2.1.2 Chebyshev Polynomials -- 2.1.3 Laguerre Polynomials -- 2.2 Approximating Displacement, Strain and Stress Fields -- 2.3 Equations of Motion of a Body Discretised Using Spectral Finite Elements -- 2.4 Computing Characteristic Matrices of Spectral Finite Elements -- 2.4.1 Lobatto Quadrature -- 2.4.2 Gauss Quadrature -- 2.4.3 Gauss-Laguerre Quadrature -- 2.5 Solving Equations of Motion of a Body Discretised Using Spectral Finite Elements -- 2.5.1 Forcing with an Harmonic Signal -- 2.5.2 Forcing with a Periodic Signal -- 2.5.3 Forcing with a Nonperiodic Signal -- References -- 3 Three-Dimensional Laser Vibrometry -- 3.1 Review of Elastic Wave Generation Methods -- 3.1.1 Force Impulse Methods -- 3.1.2 Ultrasonic Methods.

3.1.3 Methods Based on the Electromagnetic Effect -- 3.1.4 Methods Based on the Piezoelectric Effect -- 3.1.5 Methods Based on the Magnetostrictive Effect -- 3.1.6 Photothermal Methods -- 3.2 Review of Elastic Wave Registration Methods -- 3.2.1 Optical Methods -- 3.3 Laser Vibrometry -- 3.4 Analysis of Methods of Elastic Wave Generation and Registration -- 3.5 Exemplary Results of Research on Elastic Wave Propagation Using 3D Laser Scanning Vibrometry -- References -- 4 One-Dimensional Structural Elements -- 4.1 Theories of Rods -- 4.2 Displacement Fields of Structural Rod Elements -- 4.3 Theories of Beams -- 4.4 Displacement Fields of Structural Beam Elements -- 4.5 Dispersion Curves -- 4.6 Certain Numerical Considerations -- 4.6.1 Natural Frequencies -- 4.6.2 Wave Propagation -- 4.7 Examples of Numerical Calculations -- 4.7.1 Propagation of Longitudinal Elastic Waves in a Cracked Rod -- 4.7.2 Propagation of Flexural Elastic Waves in a Rod -- 4.7.3 Propagation of Coupled Longitudinal and Flexural Elastic Waves in a Rod -- References -- 5 Two-Dimensional Structural Elements -- 5.1 Theories of Membranes, Plates and Shells -- 5.2 Displacement Fields of Structural Membrane Elements -- 5.3 Displacement Fields of Structural Plate Elements -- 5.4 Displacement Fields of Structural Shell Elements -- 5.5 Certain Numerical Considerations -- 5.6 Examples of Numerical Calculations -- 5.6.1 Propagation of Elastic Waves in an Angle Bar -- 5.6.2 Propagation of Elastic Waves in a Half-Pipe Aluminium Shell -- 5.6.3 Propagation of Elastic Waves in an Aluminium Plate -- References -- 6 Three-Dimensional Structural Elements -- 6.1 Solid Spectral Elements -- 6.2 Displacement Fields of Solid Structural Elements -- 6.2.1 Six-Mode Theory -- 6.2.2 Nine-Mode Theory -- 6.3 Certain Numerical Considerations -- 6.4 Modelling Electromechanical Coupling -- 6.4.1 Assumptions.

6.4.2 Linear Constitutive Equations -- 6.4.3 Basic Equations of Motion -- 6.4.4 Static Condensation -- 6.4.5 Inducing Waves -- 6.4.6 Recording Waves -- 6.4.7 Electrical Boundary Conditions -- 6.5 Examples of Numerical Calculations -- 6.5.1 Propagation of Elastic Waves in a Half-Pipe Aluminium Shell -- 6.5.2 Propagation of Elastic Waves in an Isotropic Plate - Experimental Verification -- 6.6 Modelling the Bonding Layer -- References -- 7 Detection, Localisation and Identification of Damage by ElasticWave Propagation -- 7.1 Elastic Waves in Structural Health Monitoring -- 7.2 Methods of Damage Detection, Localisation and Identification -- 7.2.1 Energy Addition Method -- 7.2.2 Phased Array Method -- 7.2.3 Methods Employing Continuous Registration of Elastic Waves within the Analysed Area -- 7.2.4 Damage Identification Algorithms -- 7.3 Examples of Damage Localisation Methods -- 7.3.1 Localisation Algorithms Employing Sensor Networks -- 7.3.2 Algorithms Based on Full Field Measurements of Elastic Wave Propagation -- References -- Appendix: EWavePro Software -- A.1 Introduction -- A.2 Theoretical Background and Scope of Applicability (Computation Module) -- A.3 Functional Structure and Software Environment (Pre- and Post-Processors) -- A.4 Elastic Wave Propagation in a Wing Skin of an Unmanned Plane (UAV) -- A.5 Elastic Wave Propagation in a Composite Panel -- References -- Index.