Mathematical Models in Applied Mechanics

✍ Scribed by A. B. Tayler

• Publisher: Oxford University Press
• Year: 1986
• Tongue: English
• Leaves: 290
• Series: Oxford Applied Mathematics and Computing Science 1
• Category: Library

✦ Synopsis

The book is not intended as a research monograph on industrial problems nor as a standard text on differential equations, which, however, are its main mathematical theme. Rather, it is an attempt to demonstrate the power of mathematics and the diversity of its application, in the hope of stimulating readers with some background knowledge of Applied Analysis and Mechanics into constructing their own models of new situations. It is designed to be a coherent text so that each problem described develops the theme, and each extension of the theme leads on to a new problem.

✦ Table of Contents

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