Elastic Waves in Anisotropic Laminates

Przednia okładka
CRC Press, 13 lis 2001 - 472
Ultrasonic non-destructive evaluation (NDE) plays an increasingly important role in determining properties and detecting defects in composite materials, and the analysis of wave behavior is crucial to effectively using NDE techniques. The complexity of elastic wave propagation in anisotropic media has led to a reliance on numerical methods of analysis-methods that are often quite time-consuming and whose results yield even further difficulties in extracting explicit phenomena and characteristics.

Innovative and insightful, Elastic Waves in Anisotropic Laminates establishes a set of high-performance, analytical-numerical methods for elastic wave analysis of anisotropic layered structures. The treatment furnishes a comprehensive introduction, sound theoretical development, and applications to smart materials, plates, and shells. The techniques, detailed in both the time and frequency domains, include methods that combine the finite element method (FEM) with the Fourier transform approach and the strip element method (SEM). These -methods can also be used for expediently finding the Green's function for anisotropic laminates useful for inverse problems related to wave propagation, and methods for inverse analyses, including conjugate gradient methods, and genetic algorithms are also introduced.

The text is complemented by many examples generated using software codes based on the techniques developed. Filled with charts and illustrations, Elastic Waves in Anisotropic Laminates is accessible even to readers from non-engineering backgrounds and offers a unique opportunity to discover methods that can lead to an understanding of the dynamic characteristics and wave motion behaviors of advanced composite materials.
 

Spis treści

Fundamentals of Waves in Elastic Solids
1
12 Formulation of Longitudinal Wave in a Bar
4
112 StrainDisplacement Relation
5
13 Free Wave Motion in Infinite Bars
6
14 Free Wave Motion in a Finite Bar
10
15 Forced Wave Motion in an Infinite Bar
11
16 Forced Wave Motion in a Finite Bar
15
17 Transient Waves in an Infinite Bar
17
108 Displacement and Electrostatic Potential Response
217
109 Computation Procedure
218
1010 Dispersion Curves
220
1011 Excitation of TimeStep Shear Force in y Direction
227
1012 Excitation of a Line Electrode
228
1013 Excitation of Interdigital Electrodes
230
1014 Remarks
232
Strip Element Method for Stress Waves in Anisotropic Solids
235

18 Remarks
19
Waves in Plates of functionally Graded Material
21
22 Element of Linear Property Variation
22
23 Boundary and Continuity Conditions
24
24 Transient Response
26
25 Evaluation of Confluent Hypergeometric Function
28
251 Integral of Gamma Function
29
252 Integral of Confluent Hypergeometric Function
30
253 Interval Division and Error Control
32
26 Examples
34
262 Wave Fields in FGM Plates
35
27 Remarks
40
Free Wave Motion in Anisotropic Laminates
43
32 Basic Equations
44
322 Equation of Motion
45
325 Boundary Conditions
46
332 Lamb Waves in Laminates
48
34 Strain Energy Distribution
53
35 Examples
54
352 Strain Energy Distribution
59
36 Remarks
63
Forced Wave Motion in Composite Laminates
65
42 Basic Equations
66
421 StrainDisplacement Relation
67
422 StressStrain Relation
68
423 Equation of Motion
69
43 Boundary and Interface Conditions
70
45 A Technique for the Inverse Fourier Integration
74
46 Response in Time Domain
78
47 Poles and Complex Paths
79
48 Examples
81
49 Remarks
84
Characteristics of Waves in Composite Laminates
87
52 Dispersion Equation
88
53 Group Velocities
93
54 Phase Velocity Surface
96
55 Phase Slowness Surface
97
57 Group Velocity Surface
100
59 Group Wave Surface
101
510 Examples
102
5102 Results for GraphiteEpoxy Laminates
103
5103 Results for a Hybrid Composite Laminate
105
511 Remarks
106
Free Wave Motion in Anisotropic Laminated Bars Finite Strip Element Method
109
62 System Equation
110
63 Examples
116
64 Remarks
123
Free Wave Motion in Composite Laminated Bars SemiExact Method
125
73 Examples of Harmonic Waves in Bars
131
731 Results for a Clamped Bar
132
732 Results for a Free Bar
134
733 Anisotropic Laminated Bar
135
74 Edge Waves in SemiInfinite Laminates
136
741 Verification of Results for Edge Waves
138
742 Effect of Poissons Ratio on Edge Waves
139
743 Higher Modes of Edge Waves
142
75 Remarks
144
Transient Waves in Composite Laminates
147
82 HNM Formulation
149
83 Equation in Wavenumber Domain
152
84 Displacement in Wavenumber Domain
153
85 Response in SpaceTime Domain
155
853 Computational Procedure
156
862 Results for an Isotropic Plate
158
863 Results for a Hybrid Laminate
159
87 Response to Point TimeStep Load
161
871 Results for an Isotropic Plate
162
872 Results for a Hybrid Laminate
163
88 Techniques for Inverse Fourier Integral
165
882 Technique
166
883 Application
171
89 Response to Transient Load of Arbitrary Time Function
172
810 Remarks
175
Waves in Functionally Graded Plates
177
92 Dynamic System Equation
178
93 Dispersion Relation
179
94 Group Velocity
181
95 Response Analysis
182
97 Computational Procedure
183
98 Dispersion Curves
184
99 Transient Response to Line TimeStep Loads
189
992 Results for a Shear Load in the x Direction
193
993 Results for a Shear Load in the y Direction
194
994 Results for a Line TimePulse Load
196
910 Remarks
198
Waves in Anisotropic functionally Graded Piezoelectric Plates
201
102 Basic Equations
202
103 Approximated Governing Equations
205
104 Equations in Transform Domain
211
105 Characteristics of Waves in FGPM Plates
213
106 Transient Response Analysis
215
107 Interdigital Electrodes Excitation
216
1121 StrainDisplacement Relation
236
1122 StressStrain Relation
237
1123 Equation of Motion
238
1124 Strip Element Method Equation
239
113 SEM for Static Problems Flamants Problem
243
114 SEM for Dynamic Problems
244
1141 Harmonic Waves in 2D Space
247
1142 Harmonic Waves in HalfSpace Lambs Problem
249
115 Remarks
252
Wave Scattering by Cracks in Composite Laminates
255
122 Governing Differential Equations
257
123 Particular Solution
258
124 General Solution
262
125 Application of the SEM to Cracked Laminates
264
126 Solution in the Time Domain
265
127 Examples of Scattered Wave Fields
266
1271 Response in Frequency Domain
267
1272 Response in Time Domain
271
128 Characterization of Horizontal Cracks
273
1282 Technique for Crack Detection
277
1284 Detection of a Crack in an Anisotropic Laminate
284
129 Characterization of a Vertical SurfaceBreaking Crack
286
1292 Technique for Crack Detection
288
1293 Frequency Dependency
290
1295 Determination of Crack Length
291
1210 Characterization of Middle Interior Vertical Cracks
294
12102 Technique for Crack Detection
296
12103 Dependency of Load Frequency
297
12105 Determination of Crack Length
298
1211 Characterization of Arbitrary Interior Vertical Cracks
300
12112 Wave Scattering by Arbitrary Interior Vertical Cracks
301
12113 Dependency of Loading Position
305
12114 Determination of Crack Length
307
12115 Determination of the Crack Depth
309
1212 Remarks
312
Wave Scattering by Flaws in Composite Laminates
313
132 Application of the SEM to Plates Containing Flaws
314
133 Examples for Wave Scattering in Laminates
316
134 SH Waves in Sandwich Plates
321
135 Strip Element Equation for SH Waves
323
136 Particular Solution
325
137 Complementary Solution
326
139 SH Waves Scattered by Flaws
327
1310 Remarks
332
Bending Waves in Anisotropic Laminated Plates
333
142 Governing Equation
334
143 Strip Element Equation
336
144 Assembly of Element Equations
349
145 Static Problems for Orthotropic Laminated Plates
350
1452 Complementary Solution
351
1453 Particular Solution
352
1454 Imposition of Boundary Conditions
355
1455 Examples for Static Problems
358
146 Wave Motion in Anisotropic Laminated Plates
362
1462 Complementary Solution
363
1463 Particular Solution
364
1464 The General Solution
367
1465 Solution in the Time Domain
368
1466 Results for Anisotropic Laminated Plates
369
1467 Effect of Rotatory Inertia
377
146 Concluding Remarks
386
Characteristics of Waves in Composite Cylinders
387
152 Basic Equations
388
153 Dispersion Relations
390
154 Examples
393
155 Remarks
398
Wave Scattering by Cracks in Composite Cylinders
399
162 Basic Equations
400
163 Axisymmetric Strip Element
402
164 Examples
405
165 Remarks
406
Inverse Identification of Impact Loads Using Elastic Waves
409
172 TwoDimensional Line Load
411
1721 Greens Function
412
1722 TimeStep Response Function
413
173 TwoDimensional Extended Line Load
414
1731 Identification of Loading Time Function
415
1732 Identification of Loading Distribution Function
416
1733 Identification of Both Time History and Distribution Functions
417
175 Examples
419
1752 Identification for Extended Line Loads
420
1753 Concentrated ThreeDimensional Loads
422
Inverse Determination of Material Constants of Composite Laminates
429
182 Inverse Operation
431
183 UniformMicro Genetic Algorithms
432
184 Examples
433
1842 Effects of Noise
435
185 Remarks
438
References
439
Index
449
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