tesi R. Valiante.pdf - EleA@UniSA

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

30 ⎛ ⎜ ⎜− k ⎝ 2 − K F 2 ω ⎞ + 2 ⎟ ⎟e c0 ⎠ ( kx−ωt ) i = 0 (1.20) This equation must fulfill Eq.1.21 in order to admit non-trivial solutions 2 ⎛ = c0 ⎜k ⎝ or, alternatively, Eq.1.22. K ⎞ + ⎟ F ⎠ 2 2 ω ω( k) 2 2 ω k = − 2 c 0 K F Here the phase velocity, p ω = (1.21) ( ω) c , is different from the 0 k = k (1.22) c of the taut string. Indeed, substituting ω = kc p in Eq.1.21 or Eq.1.22, the result of Eq.1.23 is obtained. ⎛ K ⎜1+ ⎝ Fk 2 2 = c0 2 ⎞ ⎟ ⎠ c p c ( k) c p p Alternatively, one can obtain the results in Eq.1.24. k 2 = K F 2 2 ( c c ) −1 p 0 = (1.23) ( c ) k = k (1.24) Another set of relations can be obtained by eliminating k from Eq.1.22 or ω from Eq.1.24, to give Eq.1.25 and Eq. 1.26 K Fc 2 p ω = ω( c 2 2 p ) ( c c ) −1 p 0 2 p ω = (1.25)
INTRODUCTION 31 2 ω c 2 k = 2 ω − 2 2 0 0 ( k c F ) ( ω) k = k (1.26) The results show that a harmonic wave of frequency ω can propagate only at a specific velocity, c p , as it is indicated by the relation ω = ω( c p ) . Considering a pulse shape at a given time t = t0 as a Fourier superposition of harmonic waves, as the time advance, each Fourier component of the original pulse will propagate with its own individual velocity. The various components will become increasingly out-of-phase relative to their original position, so that the original pulse shape will became increasingly distorted, as shown in Fig.1.7. In the taut string, where K=0, this phenomenon is not present. Another important result comes from the analysis of the roots of Eq.1.22, which are reported in Eq.1.27. Fig. 1.7 - Distorted propagation of a wave envelope 2 ω k = ± − 2 c 0 K F (1.27) 2 2 The roots are real if ω c > K F , thus the propagation is possible to the right 0 or left, depending on which sign is selected, as expressed by Eq.1.28. y −i( ± kx+ ωt ) = (1.28) Ae
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: INTRODUCTION 29 Fig. 1.6 - Differen
Page 43 and 44: INTRODUCTION 33 Fig. 1.8 - Frequenc
Page 45 and 46: INTRODUCTION 35 where 1 1 p1 c k =
Page 47 and 48: INTRODUCTION 37 Fig. 1.12 - Group v
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
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EXPERIMENTAL ANALYSIS 85 Fig. 3.32
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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
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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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