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$3Eterov e)ce(te/rou sofo\v to/ te pa/lai to/ te nu=n. Ou ... - EleA@UniSA$

36 This velocity is called group velocity. On the other hand, the cosine term containing the average wavenumber k and frequency ω will be a high- frequency term, propagating at the average velocity c p . The low-frequency term acts as a modulation on the high-frequency carrier as shown in Fig.1.11. The individual harmonics travel with different phase velocities c p , but the superimposed packet travels with the group velocity c g . The velocity of the high-frequency carrier may actually be greater than, equal to, or less than the velocity c g . The actual relation will depend on the dispersion characteristics of the elastic system. Graphically the various cases can be represented considering Eq.1.37, which states that the group velocity is equal to the local slope of the frequency spectrum curve, as shown in Fig.1.12. Recalling that the slope of a chord to a point is the phase velocity, if that slope is higher than the local slope c < c , otherwise if the slope of the chord to a of the curve ( θ p > θ g ) , then g p point is lower than the local slope of the curve ( θ ) Fig. 1.11 - Group velocity example c > c . θ p < g , then g p
INTRODUCTION 37 Fig. 1.12 - Group velocity variation with phase velocity 1.7.1. WAVE IN PLATES - LAMB WAVES Now a more practical aspect of the wave propagation is presented. First, it is necessary to distinguish between bulk waves and guided waves. They are both governed by the same set of partial differential wave equations (reported in [33, 34]), but they differ in the boundary conditions. Bulk waves travel in the bulk of the material, hence away from the boundaries, for this reason mathematically there are no boundary conditions that need to be satisfied by the proposed solution. In contrast, the solution to a guided wave problem must satisfy the governing equation as well as some physical boundary conditions. The introduction of boundary conditions makes the guided waves problem difficult to solve analytically. However, some special cases of guided waves problems have been solved and these solutions take the names of the investigator. The Rayleigh waves are free waves on the surface of a semi-infinite solid. Stonely waves are free waves that occur at an interface between two media. Lamb waves are waves of plain strain that occur in a free plate. Another difference between bulk waves and guided waves is that bulk waves have just two mode of propagation that are the longitudinal mode and the transverse mode, whereas the guided waves have an infinite number of modes. Longitudinal waves, also called volumetric wave, imply no rotations of medium particles, whereas transverse waves, also called rotational waves, do not imply volume change in material. These waves propagate in infinite media at two different speeds, which are
Page 1: Unione Europea Università degli St
Page 5 and 6: RINGRAZIAMENTI E’ per me doveroso
Page 7: Vorrei, infine, disporre del vocabo
Page 11 and 12: CONTENTS Abstract of dissertation .
Page 13 and 14: LIST OF FIGURES AND TABLES Fig. 1.1
Page 15 and 16: Fig. 3.32 - : RMS of the field of r
Page 17 and 18: ABSTRACT OF DISSERTATION 7 ABSTRACT
Page 19 and 20: ABSTRACT OF DISSERTATION 9 are: The
Page 21 and 22: INTRODUCTION 11 Ideally, routinely
Page 23 and 24: INTRODUCTION 13 Feature extraction
Page 25 and 26: INTRODUCTION 15 1.3. GLOBAL VERSUS
Page 27 and 28: INTRODUCTION 17 damage. These inves
Page 29 and 30: INTRODUCTION 19 between shifts at v
Page 31 and 32: INTRODUCTION 21 Space Shuttle Orbit
Page 33 and 34: INTRODUCTION 23 1.6. GUIDED WAVES-B
Page 35 and 36: INTRODUCTION 25 Fig. 1.3 - Differen
Page 37 and 38: INTRODUCTION 27 Considering the arg
Page 39 and 40: INTRODUCTION 29 Fig. 1.6 - Differen
Page 41 and 42: INTRODUCTION 31 2 ω c 2 k = 2 ω
Page 43 and 44: INTRODUCTION 33 Fig. 1.8 - Frequenc
Page 45: INTRODUCTION 35 where 1 1 p1 c k =
Page 49 and 50: INTRODUCTION 39 Fig. 1.13 - Directi
Page 51 and 52: INTRODUCTION 41 for very simple cas
Page 53 and 54: INNOVATIVE SHM TECHNIQUES BASED ON
Page 63 and 64: EXPERIMENTAL ANALYSIS 53 3. EXPERIM
Page 65 and 66: EXPERIMENTAL ANALYSIS 55 Fig. 3.3 -
Page 67 and 68: EXPERIMENTAL ANALYSIS 57 same point
Page 73 and 74: EXPERIMENTAL ANALYSIS 63 of the ene
Page 75 and 76: EXPERIMENTAL ANALYSIS 65 Fig. 3.13
Page 79 and 80: EXPERIMENTAL ANALYSIS 69 Analysis g
Page 81 and 82: EXPERIMENTAL ANALYSIS 71 Analysis g
Page 83 and 84: EXPERIMENTAL ANALYSIS 73 and in spa
Page 85 and 86: EXPERIMENTAL ANALYSIS 75 and are tr
Page 87 and 88: EXPERIMENTAL ANALYSIS 77 obtained w
Page 91 and 92: EXPERIMENTAL ANALYSIS 81 (a) t = 68
Page 93 and 94: EXPERIMENTAL ANALYSIS 83 (a) t = 68
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EXPERIMENTAL ANALYSIS 87 (a) t = 44
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EXPERIMENTAL ANALYSIS 91 Fig. 3.38
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EXPERIMENTAL ANALYSIS 97 The data p
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EXPERIMENTAL ANALYSIS 101 To increa
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EXPERIMENTAL ANALYSIS 103 Both of t
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EXPERIMENTAL ANALYSIS 107 Complete
Page 119 and 120:
FINITE ELEMENT MODELING OF WAVE PRO
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CONCLUSIONS AND FUTURE WORK 131 5.
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CONCLUSIONS AND FUTURE WORK 133 cas
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REFERENCES 135 [6] Rose, J. L. “A
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REFERENCES 137 [20] Ko, J. M., Wong
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REFERENCES 139 [35] J. D. Achenbach
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