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 |  موضوع: كتاب Numerical Analysis of Vibrations of Structures under Moving Inertial Load الإثنين 27 نوفمبر 2017, 10:27 pm | |
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أحضرت لكم كتاب
Numerical Analysis of Vibrations of Structures under Moving Inertial Load
Czeslaw I. Bajer and Bartlomiej Dyniewicz
ويتناول الموضوعات الأتية :
Contents
1 Introduction 1
1.1 Literature Review . 5
1.2 Solution Methods . 7
1.3 Approximate Methods . 9
1.4 Review of Analytical-Numerical Methods in Moving Load
Problems 12
1.4.1 d’Alembert Method . 13
1.4.2 Fourier Method . 14
1.4.3 Lagrange Formulation . 17
1.5 Examples 18
2 Analytical Solutions . 21
2.1 A Massless String under a Moving Inertial Load 22
2.1.1 Case of ? = 1 23
2.1.2 Case of ? = 1 25
2.2 Discontinuity of the Solution 26
2.3 Conclusions 29
3 Semi-analytical Methods . 31
3.1 String . 32
3.1.1 Fourier Analysis 32
3.1.2 The Lagrange Equation 37
3.2 Bernoulli–Euler Beam . 46
3.2.1 Fourier Solution 47
3.2.2 The Lagrange Equation of the Second Kind . 50
3.2.3 Conclusions 55
3.3 Timoshenko Beam . 55
3.3.1 Fourier Solution 56
3.3.2 The Lagrange Equation 56
3.3.3 Examples 59
3.3.4 Conclusions and Discussion 61VIII Contents
3.4 Bernoulli–Euler Beam vs. Timoshenko Beam 66
3.5 Plate 67
3.6 The Renaudot Approach vs. The Yakushev Approach . 70
3.6.1 The Renaudot Approach . 71
3.6.2 The Yakushev Approach . 72
4 Review of Numerical Methods of Solution . 77
4.1 Oscillator 79
4.1.1 String Vibrations under a Moving Oscillator . 79
4.1.2 Beam Vibrations under a Moving Oscillator . 83
4.2 Inertial Load 84
4.2.1 A Bernoulli–Euler Beam Subjected to an Inertial Load 85
4.2.2 A Timoshenko Beam Subjected to an Inertial Load . 89
5 Classical Numerical Methods of Time Integration 95
5.1 Integration of the First Order Differential Equations . 97
5.2 Single-Step Method SSpj . 102
5.3 Central Difference Method 105
5.3.1 Stability of the Method 107
5.3.2 Accuracy of the Method . 108
5.4 The Adams Methods . 109
5.4.1 Explicit Adams Formulas (Open) 110
5.4.2 Implicit Adams Formulas (Closed) 112
5.5 The Newmark Method . 114
5.6 The Bossak Method . 117
5.7 The Park Method 118
5.8 The Park–Housner Method . 118
5.8.1 Stability of the Park–Housner Method 119
5.9 The Trujillo Method . 121
6 Space–Time Finite Element Method . 123
6.1 Formulation of the Method—Displacement Approach 129
6.1.1 Space–Time Finite Elements in the Displacement
Description 135
6.2 Properties of the Integration Schemes . 138
6.2.1 Accuracy of Methods 140
6.3 Velocity Formulation of the Method 140
6.3.1 One Degree of Freedom System . 140
6.3.2 Discretization of the Differential Equation of String
Vibrations . 144
6.3.3 General Case of Elasticity 149
6.3.4 Other Functions of the Virtual Velocity . 151
6.4 Space–Time Element Method and Other Time Integration
Methods . 154Contents IX
6.4.1 Convergence . 154
6.4.2 Phase Error 157
6.4.3 Non-inertial Problems . 158
6.5 Space–Time Finite Element Method vs. Newmark Method . 160
6.6 Simplex Elements . 161
6.6.1 Property of Space Division . 162
6.6.2 Numerical Efficiency 167
6.7 Simplex Elements in the Displacement Description . 169
6.7.1 Triangular Element of a Bar Vibrating Axially 169
6.7.2 Space–Time Finite Element of the Beam of Moderate
Height 170
6.7.3 Tetrahedral Space–Time Element of a Plate . 172
6.8 Triangular Elements Expressed in Velocities . 176
7 Space–Time Finite Elements and a Moving Load . 181
7.1 Space–Time Finite Element of a String . 182
7.1.1 Discretization of the String Element Carrying a Moving
Mass 182
7.1.2 Numerical Results 184
7.1.3 Conclusions 188
7.2 Space–Time Elements for a Bernoulli–Euler Beam Carrying
a Moving Mass . 188
7.2.1 Numerical Results 190
7.3 Space–Time Element of Timoshenko Beam Carrying a Moving
Mass 198
7.3.1 Conclusions 203
7.4 Space–Time Finite Plate Element Carrying a Moving Mass 204
7.4.1 Thin Plate . 204
7.4.2 Thick Plate 213
7.4.3 Plate Placed on an Elastic Foundation 215
7.5 Problems with Zero Mass Density 218
8 The Newmark Method and a Moving Inertial Load . 223
8.1 The Newmark Method in Moving Mass Problems 223
8.2 The Newmark Method in the Vibrations of String . 226
8.3 The Newmark Method in Vibrations of the Bernoulli–Euler
Beam . 229
8.4 The Newmark Method in Vibrations of a Timoshenko Beam . 230
8.5 Numerical Results . 230
8.6 Accelerating Mass—Numerical Approach . 233
8.6.1 Mathematical Model 233
8.6.2 The Finite Element Carrying the Moving Mass Particle . 235
8.6.3 Accelerating Mass—Examples 238
8.7 Conclusions 239X Contents
9 Meshfree Methods in Moving Load Problems 241
9.1 Meshless Methods (Element-Free Galerkin Method) 241
9.2 Results 243
10 Examples of Applications 247
10.1 Dynamics of the Classical Vehicle–Track System . 249
10.2 Dynamics of the System Vehicle—Y-Type Track . 253
10.3 Dynamics of Subway Track . 262
10.4 Vibrations of Airport Runways 266
Appendix . 271
A Computer Programs . 271
A.1 String—Space–Time Element Method 271
A.2 Timoshenko Beam—Newmark Method . 274
A.3 Mindlin Plate—Space–Time Element Method 277
A.4 Kirchhoff Plate — Space-Time Element Method . 283
References 285
Index
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