tesi R. Valiante.pdf - EleA@UniSA

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

28 Another solution to the wave equation is given by D’Alembert and it is reported in Eq.1.16. ( x, t) f ( x − c t) + g( x + c t) y 0 0 = (1.16) This equation satisfies Eq.1.8 for any arbitrary function f and g, as long as the initial and boundary conditions can eventually be satisfied. The functions f and g represent propagating disturbance. Whatever the initial shape of the disturbances, that shape is maintained during the propagation, so the waves propagate without distortion, as represented in Fig.1.5. The undistorted nature of wave propagation represents a fundamental characteristic of the one-dimensional wave equation. Fig. 1.5 - Undistorted propagation of wave envelope 1.7.2. STRING ON AN ELASTIC BASE – DISPERSION The wave equation Eq.1.8 considered up to this point is simple. Moreover, in the system described by this equation, the pulses propagate without distortions. Now, a more complicated situation, in which the string rests on an elastic foundation, is considered. This situation is represented in Fig.1.6.
INTRODUCTION 29 Fig. 1.6 - Differential element of a string on an elastic base The external load may be interpreted as due to the elastic foundation, as expressed by Eq.1.17 q( x, t) = −Ky( x, t) (1.17) where K is the elastic modulus of the foundation. The resulting governing equation, in the absence of other external forces, is given by Eq.1.18. 2 2 ∂ y K 1 ∂ y − y = 2 2 ∂x F c ∂t 2 0 c = F ρ 0 (1.18) This equation is no longer of simple wave equation form. Thus, a solution of the form ( x c t) f 0 ± may not satisfy it. Since the major characteristic of such a solution is undistorted wave pulse propagation, it is now logical to expect a distortion. This phenomenon is known as dispersion. Now, the necessary conditions for the propagation of harmonic waves are determined. Assuming the solution Eq.1.19 y i( kx−ωt ) ( x t) = Ae , (1.19) and substituting it in Eq.1.18, it gives the expression Eq.1.20, which is called characteristic equation or dispersion equation.
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: INTRODUCTION 27 Considering the arg
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 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 77 and 78: EXPERIMENTAL ANALYSIS 67 Fig. 3.16
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 89 and 90:
EXPERIMENTAL ANALYSIS 79 Fig. 3.26
Page 91 and 92:
EXPERIMENTAL ANALYSIS 81 (a) t = 68
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EXPERIMENTAL ANALYSIS 97 The data p
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EXPERIMENTAL ANALYSIS 101 To increa
Page 113 and 114:
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
Page 149:
REFERENCES 139 [35] J. D. Achenbach
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