Mathematical Models in Applied Mechanics

Tayler A. B. Mathematical models in applied mechanics(Oxford applied mathematics and computing science series; v.1)(OUP,1986)(ISBN 0198535414)(600dpi)(290p) iii ......Page 4
Copyright iv ......Page 5
Preface V ......Page 6
Contents vii ......Page 8
1.1 Introduction 1 ......Page 10
1.2 Normalization of the problem 2 ......Page 11
1.3 Perturbation procedures 5 ......Page 14
Problem A Furnace reaction analysis 6 ......Page 15
1.4 Analytical methods for ordinary differential equations 9 ......Page 18
1.5 Classical analogies 21 ......Page 30
Exercises 31 ......Page 40
2.1 Transverse waves on a stretched string 37 ......Page 46
Problem B Pantograph dynamics I, periodic motion 40 ......Page 49
2.2 Second-order hyperbolic equations and weak solutions 45 ......Page 54
Problem C Pantograph dynamics II 50 ......Page 59
2.3 Linear hyperbolic systems in two independent variables 53 ......Page 62
Problem D A regenerative heat exchanger 55 ......Page 64
2.4 Multiple reflections and use of transforms 59 ......Page 68
Problem E Short circuit in a transformer 61 ......Page 70
2.5 Wave motion with two or more space variables 65 ......Page 74
Problem F Submarine detection 68 ......Page 77
2.6 Waveguides and dispersion 74 ......Page 83
Problem G Coal seam exploration 78 ......Page 87
2.7 Quasi-linear systems 81 ......Page 90
Problem H Row of granular material in a hopper 83 ......Page 92
Exercises 89 ......Page 98
3.1 Potential theory 95 ......Page 104
Problem I Current flow between two plates joined by spigots 97 ......Page 106
3.2 Variational methods and variational inequalities 102 ......Page 111
Problem J Electrochemical painting 105 ......Page 114
3.3 Free-boundary problems 107 ......Page 116
Problem K Percolation in a sand dune 113 ......Page 122
3.4 Application of complex variable methods 116 ......Page 125
Problem L Wave reflection from a visco-elastic raft 122 ......Page 131
3.5 Quasi-static continuum models 128 ......Page 137
Problem M The hot rolling of steel 133 ......Page 142
Exercises 140 ......Page 149
4.1 The diffusion equation 145 ......Page 154
Problem N Smoke dispersion from a high chimney 150 ......Page 159
4.2 Stefan problems 154 ......Page 163
Problem O Welding of two steel plates 159 ......Page 168
4.3 Weak solutions 164 ......Page 173
Problem P Dendritic growth 171 ......Page 180
4.4 Diffusion and convection 175 ......Page 184
Problem Q The shape of laser melt-pools 181 ......Page 190
4.5 Non-linear diffusion 186 ......Page 195
Problem R The spreading of an oil film 193 ......Page 202
Exercises 197 ......Page 206
5.1 Non-linear ordinary differential equations 203 ......Page 212
Problem S Resonance in a gearbox 212 ......Page 221
5.2 Thin layers and lubrication theory 219 ......Page 228
Problem T The impregnation of paper by a resin 225 ......Page 234
5.3 Boundary layers 233 ......Page 242
Problem U Injection moulding 244 ......Page 253
5.4 Far-field solutions 249 ......Page 258
Problem V Seismic detection 257 ......Page 266
Exercises 263 ......Page 272
Bibliography 269 ......Page 278
Index 273 ......Page 282
cover......Page 1