 | Gopalakrishnan S. Wavelet methods for dynamical problems: with application to metallic, composite, and nanocomposite structures / S.Gopalakrishnan, M.Mitra. - Boca Raton: CRC Press/Taylor & Francis Group, 2010. - xxii, 276 p.: ill. - Ref.: p.265-276. - ISBN 978-1-4398-0461-2
|
List of Figures ................................................ xi
List of Tables ................................................ xix
Preface ....................................................... xxi
1 Introduction ................................................. 1
1.1 Solution of structural dynamics problem ................. 2
1.2 Solution of wave propagation problem .................... 4
1.3 Objective and outline of the book ....................... 6
2 Integral Transform Methods ................................... 9
2.1 Laplace transform ....................................... 9
2.2 Fourier transform ...................................... 10
2.2.1 Continuous Fourier transform .................... 11
2.2.2 Discrete Fourier transform ...................... 13
2.2.3 Short term Fourier transform .................... 16
2.3 Wavelet transform ...................................... 17
2.3.1 Multi-resolution analysis with wavelets ......... 18
2.3.2 Daubechies compactly supported wavelets ......... 20
2.3.3 Discrete wavelet transform ...................... 23
3 Structural Dynamics: Introduction and Wavelet Transform ..... 37
3.1 Free vibration of single degree of freedom systems ..... 38
3.2 Forced vibration of SDOF system ........................ 41
3.3 Harmonic loading ....................................... 43
3.3.1 Periodic excitation ............................. 45
3.4 Response to arbitrary loading .......................... 46
3.4.1 Impulse response ................................ 47
3.4.2 Convolution integral method ..................... 48
3.4.3 Direct time integration methods ................. 49
3.5 Response of SDOF through wavelet transform ............. 50
3.5.1 Non-periodic boundary condition ................. 53
3.6 Free vibration of multi-degree of freedom system ....... 57
3.7 Modal analysis for forced vibration response of MDOF ... 59
3.8 Response of MDOF system using wavelet transform ........ 61
4 Wave Propagation: Spectral Analysis ......................... 63
4.1 Spectrum and dispersion relations ...................... 63
4.2 Computations of wavenumbers and wave amplitudes ........ 68
4.2.1 SVD-based technique ............................. 69
4.2.2 PEP-based technique ............................. 70
4.3 Spectral finite element (SFE) method ................... 71
4.4 FSFE formulation of Timoshenko beam .................... 73
4.5 FSFE formulation of isotropic plate under in-plane
loading ................................................ 76
5 Wavelet Spectral Finite Element: Time Domain Analysis ....... 81
5.1 Reduction of wave equations for a rod .................. 81
5.2 Decoupling using eigenvalue analysis ................... 83
5.3 Wavelet spectral finite element formulation for a
rod .................................................... 84
5.4 Time domain response of elementary rod under impulse
load ................................................... 87
5.4.1 Comparison with finite element solution ......... 87
5.4.2 Advantage over Fourier transform-based
spectral finite element ......................... 89
5.5 Reduction of wave equations for Euler-Bernoulli beam ... 91
5.6 WSFE formulation for Euler-Bernoulli beam .............. 92
5.7 Time domain response of Euler-Bernoulli beam under
impulse load ........................................... 95
5.8 Wave propagation in frame structure .................... 98
5.9 Governing differential wave equations for higher
order composite beam .................................. 101
5.10 WSFE formulation for composite beam ................... 104
5.11 Time domain response of higher order composite beam ... 108
5.11.1 Response to impulse load ....................... 109
5.11.2 Response to modulated pulse load ............... 112
6 Wavelet Spectral Finite Element: Frequency Domain
Analysis ................................................... 117
6.1 Frequency domain analysis: periodic boundary
condition ............................................. 117
6.2 Computation of wavenumbers and wave speeds ............ 120
6.2.1 Elementary rod ................................. 123
6.2.2 Euler-Bernoulli and Timoshenko beam ............ 123
6.2.3 Higher order composite beam .................... 127
6.3 Constraint on time sampling rate ...................... 129
7 Wavelet Spectral Finite Element: Two-Dimensional
Structures ................................................. 141
7.1 Governing differential wave equations for isotropic
plate ................................................. 141
7.2 Reduction of wave equations through temporal
approximation ......................................... 144
7.3 Reduction of wave equations through spatial
approximation ......................................... 146
7.3.1 Un-restraint boundary condition ................ 147
7.3.2 Restraint boundary condition ................... 148
7.4 Wavelet spectral finite element for plate ............. 150
7.5 Wave propagation in isotropic plates .................. 152
7.5.1 Frequency domain analysis ...................... 155
7.5.2 Time domain response of plate to impulse
load ........................................... 156
7.5.3 Wave propagation in ply-dropped plate .......... 161
7.5.4 Wave propagation in folded plate structure ..... 161
7.6 Governing differential wave equations for
axisymmetric cylinder ................................. 162
7.7 Bessel function solution for axisymmetric cylinder .... 164
7.8 Wave propagation in isotropic axisymmetric
cylinders ............................................. 165
7.8.1 Wavenumber computation ......................... 166
7.8.2 Time domain analysis ........................... 166
8 Vibration and Wave Propagation in Carbon Nanotubes ......... 183
8.1 Carbon nanotubes: introduction ........................ 183
8.2 Axisymmetric shell model of single-walled carbon
nanotubes ............................................. 185
8.2.1 Frequency domain analysis ...................... 185
8.3 Thin shell model of multi-walled carbon nanotubes ..... 192
8.3.1 Governing differential equations ............... 193
8.3.2 Spectral finite element formulation ............ 195
8.4 Frequency domain analysis ............................. 196
8.5 Time domain analysis .................................. 200
9 Vibration and Wave Propagation in Nano-Composites .......... 207
9.1 Introduction: nano-composites ......................... 207
9.2 Beam model of MWNT embedded nano-composite ............ 209
9.3 Spectral finite element formulation for MWNT
embedded nanocomposite beam ........................... 215
9.4 Frequency domain analysis ............................. 217
9.5 Time domain analysis .................................. 225
9.5.1 Response to broad-band impulse load ............ 225
9.5.2 Response to narrow-banded pulse ................ 229
9.6 Shell model of SWNT-polymer nano-composite ............ 229
9.6.1 Modeling of pull out and partial interfacial
shear stress transfer .......................... 231
9.7 Time domain analysis .................................. 233
9.7.1 Pull-out of SWNT ............................... 233
9.7.2 Partial interfacial shear stress transfer ...... 235
10 Inverse Problems ........................................... 241
10.1 Force reconstruction .................................. 241
10.2 Numerical examples of impulse force reconstruction .... 243
10.3 Damage modeling and detection ......................... 247
10.4 Modeling of de-lamination in composite beam ........... 248
10.5 Damage detection and de-noising using wavelet
analysis .............................................. 251
10.1 Wavelet Methods for Dynamical Problems
10.6 Wave propagation in delaminated composite beam and
damage detection ...................................... 252
References .................................................... 265
Index ......................................................... 273
|
|
