Guided waves in structures for SHM the time - domain spectral element method

• Main Authors: Ostachowicz, Wieslaw, Kudela, Pawel, Krawczuk, Marek, Zak, Arkadiusz
• Format: eBook Book
• Language: English
• Published: Chichester, West Sussex WILEY 2012; John Wiley & Sons; John Wiley & Sons, Incorporated; Wiley-Blackwell; John Wiley & Sons Ltd
• Edition: 2
• Subjects: Analysis; Composite materials; Composite materials > Analysis; Elastic analysis (Engineering); Elastic wave propagation; Elastic wave propagation > Mathematical models; Finite element method; Mathematical models; Mechanics; Science

Understanding and analysing the complex phenomena related to elastic wave propagation has been the subject of intense research for many years and has enabled application in numerous fields of technology, including structural health monitoring (SHM). In the course of the rapid advancement of diagnost...

Table of Contents:

• Guided waves in structures for SHM: the time - domain spectral element method -- Contents -- Preface -- 1. Introduction to the Theory of Elastic Waves -- 2. Spectral Finite Element Method -- 3. Three-Dimensional Laser Vibrometry -- 4. One-Dimensional Structural Elements -- 5. Two-Dimensional Structural Elements -- 6. Three-Dimensional Structural Elements -- 7. Detection, Localisation and Identification of Damage by Elastic Wave Propagation -- Appendix: EWavePro Software -- Index.
• 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
• Intro -- 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