Reciprocity approach for determination of surface wave motion and its application in scattering of surface waves by cavities

다국어 초록 (Multilingual Abstract)

Closed-form solutions of surface wave motions generated by a time-harmonic load applied in the interior of a half-space are determined in a simple manner by the use of reciprocity in elastodynamics. The method requires expressions for the displacements and the stresses of free surface waves, preferably in analytical form, but numerically obtained forms can also be used. A virtual wave that satisfies appropriate conditions on the boundaries and is a solution of the elastodynamic equations is used as state in the reciprocity theorem. By choosing a suitable virtual wave, state , which is the actual solution can be solved directly from the reciprocity relations. The solutions of surface wave motions are also obtained by the use of integral transform techniques. It is then shown that the amplitudes of the scattered waves obtained by the reciprocity approach and the integral transform approach are mathematically identical.
Based on the obtained solutions of surface wave motions, a mathematical model for scattering of surface waves by a cavity at the surface of a half-space is investigated. The purpose of this study is therefore to introduce a novel theoretical approach for detection and characterization of cavities. The amplitudes of the scattered field are verified by the numerical results from the boundary element method (BEM). The analytical and BEM result are graphically displayed and show excellent agreement when the depth and the width of the cavity are small compared to the wavelength. Both results are then compared with the experiment data.
As an improvement, a model for multiple scattering of surface waves by cavities on the surface of a half-space is studied. For multiple scattering by cavities, the self-consistent method is employed to derive an implicit set of equations which approximates the scattered field. Numerical calculations based on the boundary element method are found in order to compare with the analytical results. Comparisons between the analytical and BEM results provide good agreement.

목차 (Table of Contents)

• Abstract I
• Acknowledgement III
• Contents V
• List of figures IX
• Chapter 1: Introduction. 1
• 1.1 Motivation for quantitative nondestructive evaluation (QNDE) and structural health monitoring (SHM) 1
• 1.2 Mathematical modeling for scattering of surface waves by cavities 5
• 1.3 Statement of problem 7
• 1.4 Literature survey 8
• 1.4.1 Studies on surface waves 8
• 1.4.2 Surface waves generated by a line load or a point load 10
• 1.4.3 Application of the reciprocity theorem 11
• 1.4.4 Scattering of surface waves by defects 13
• 1.5 Contribution of dissertation 15
• 1.6 Summary 16
• Chapter 2: Computation of surface waves by the reciprocity theorem 18
• 2.1 Introduction 18
• 2.2 Surface waves in an elastic half-space 20
• 2.3 Surface waves generated by a line load 24
• 2.4 Surface waves generated by a point load 29
• 2.5 Force-displacement reciprocity relation 36
• 2.6 Solutions of surface waves in the time domain 37
• Chapter 3: Verification of surface wave solutions obtained by the reciprocity approach 39
• 3.1 Introduction 39
• 3.2 Integral transform approach to surface wave motions generated by a time-harmonic line load 41
• 3.2.1 Surface waves due to a horizontal line load 43
• 3.2.2 Surface waves due to a vertical line load 46
• 3.2.3 Verification of the reciprocity approach for a line load 47
• 3.3 Integral transform approach to surface wave motions generated by a time-harmonic point load 50
• 3.3.1 Surface waves due to a vertical point load 50
• 3.3.2 Surface waves due to a horizontal point load 52
• 3.3.3 Verification of the reciprocity approach for a point load 52
• 3.4 Surface wave motions generated by a time-harmonic load applied inside a half-space 55
• 3.4.1 Surface waves due to an internal line load 56
• 3.4.2 Surface waves due to an internal point load 57
• Chapter 4: Scattering of surface waves by a single cavity 58
• 4.1 Introduction 58
• 4.2 Superposition technique 60
• 4.3 Scattering of surface waves by a two-dimensional cavity 62
• 4.3.1 Application to scattering by a cavity of arbitrary shape 62
• 4.3.2 Example of scattering by a cylindrical cavity 68
• 4.4 Scattering of surface waves by a three-dimensional cavity 71
• 4.4.1 Scattering by a spherical cavity using concentrated load 71
• 4.4.2 Scattering by a spherical cavity using distributed load over the cavity 78
• Chapter 5: Comparison with numerical and experimental results 82
• 5.1 Introduction 82
• 5.2 Boundary element method 83
• 5.2.1 Boundary element method for two-dimensional elastodynamic problems 85
• 5.2.2 Boundary element method for three-dimensional elastodynamic problems 88
• 5.3 Surface waves generated by uniform pressure on a cylindrical cavity 88
• 5.4 Comparison of scattering of surface waves by a cylindrical cavity 97
• 5.5 Comparison of scattering of surface waves by a spherical cavity 110
• 5.6 Experiment confirmation 112
• Chapter 6: Multiple scattering of surface waves by cavities 117
• 6.1 Introduction 117
• 6.2 Self-consistent methods 119
• 6.3 Multiple scattering by two-dimensional cavities 120
• 6.4 Numerical comparison 126
• Chapter 7: Study on probability of detection 134
• 7.1 Defect signal and noise signal in time domain 135
• 7.2 Probability of detection 136
• Chapter 8: Conclusions 142
• 8.1 Concluding remarks . 142
• 8.2 Potential extensions and applications 144
• Abstract in Korean 146
• References 148