Dynamics with Friction Modeling, Analysis and Experiment – Part II

Dynamics with Friction Modeling, Analysis and Experiment – Part II
اسم المؤلف
Ardeshir Guran, Friedrich Pfeiffer, Karl Popp
التاريخ
21 أكتوبر 2021
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Dynamics with Friction Modeling, Analysis and Experiment – Part II
Editors
Ardeshir Guran
Institute of Structronics, Canada
Friedrich Pfeiffer
Technical University of Munich, Germany
Karl Popp
University of Hannover, Germany
Contents
Preface ix
Ardeshir Guran, Friedrich Pfeiffer and Karl Popp
Contributors xi
D Y N A M I C S W I T H F R I C T I O N : M O D E L I N G , A N A L Y S I S A N D
E X P E R I M E N T S , P A R T II
Chapter 1: Interaction of Vibration and Friction at D r y Sliding C o n t a c t s 1
Daniel P. Hess

  1. Introduction 1
  2. Normal Vibration and Friction at Hertzian Contacts 3
  3. Normal Vibration and Friction at Rough Planar Contacts 7
  4. Normal and Angular Vibrations at Rough Planar Contacts 9
  5. Stability Analysis 13
  6. Chaotic Vibration and Friction 20
  7. Conclusions 25
  8. References 26
    Chapter 2: Vibrations and Friction-Induced Instability in Discs 29
    John E. Mottershead
  9. Introduction 29
  10. Disc Vibrations and Critical Speeds 30
    2.1 Flexural vibrations 30
    2.2 Vibration of a spinning membrane 32
    2.3 Combined effects of centrifugal and flexural rigidity 33
    2.4 Travelling waves and critical speeds 34
    2.5 Imperfect discs 36
  11. Excitation by a Transverse-Spring-Damper System 39
    3.1 Stationary disc with a rotating mass-spring-damper system 40
    3.2 Rotating disc with a stationary mass-spring-damper system 45
    3.3 Instability mechanisms 46
  12. Follower Force Friction Models 48
    4.1 Follower force analysis in brake design 48
    4.2 Sensitivity analysis 49
    4.3 Distributed frictional load 50
    4.4 Friction with a negative /z-velocity characteristic 51
  13. Friction-Induced Parametric Resonances 52
    xiiixiv Contents
    5.1 Discrete transverse load 53
    5.1.1 Simulated example 57
    5.2 Distributed load system 59
    5.2.1 Simulated example 63
  14. Parametric Excitation by a Prictional Follower Force with a
    Negative fi-Velocity Characteristic 66
    6.1 Simulated example 70
  15. Closure 70
    Acknowledgment 73
    References 73
    Chapter 3: Dynamics of Flexible Links in Kinematic Chains 75
    Dan B. Marghitu and Ardeshir Guran
  16. Introduction 75
  17. Kinematics and Kinetics of Flexible Bodies in General Motion 77
    2.1 Small deformations 77
    2.2 Large deformations 80
  18. Equations of Motion for Small Deformations in Rectilinear Elastic Links 81
  19. Equations of Motion for Large Deformations in Rectilinear Elastic Links 83
    4.1 Planar equations of motion 84
  20. The Dynamics of Viscoelastic Links 85
    5.1 Application 86
    5.2 Computing algorithm 89
  21. The Vibrations of a Flexible Link with a Lubricated Slider Joint 89
    6.1 Reynolds equation of lubrication 89
    6.2 Cavitation 91
    6.3 Solution method for an elastic link in a rigid mechanism 92
    6.4 Application to a slider mechanism 94
  22. References 97
    Chapter 4: Solitons, Chaos and Modal Interactions in Periodic Structures 99
    M. A. Davies and F. C. Moon
  23. Introduction 99
  24. Experiment 102
  25. Numerical Model 103
  26. Forced Vibrations and Modal Interactions 108
    4.1 Numerical experiment — Modal trading 108
    4.2 Forced vibrations of the experimental structure 110Contents xv
  27. Impact Response 115
    5.1 Comparison of experiment and model 115
    5.2 Calculation of nonlinear wave speeds 119
  28. Conclusions 120
  29. Acknowledgments 122
  30. References 122
    Chapter 5: Analysis and Modeling of an Experimental Frictionally
    Excited B e a m 125
    R. V. Kappagantu and B. F. Feeny
  31. Introduction 125
  32. Experimental Setup 126
  33. Friction Measurement 128
  34. Displacement Measurement 133
    4.1 From strain to displacement 133
  35. Dynamical Responses 135
  36. Proper Orthogonal Modes 138
  37. Mathematical Model 141
  38. Numerical Simulations and Validation 143
  39. Discussion and Elaboration 147
  40. Conclusions 150
  41. Acknowledgments 151
    References 151
    Chapter 6: Transient Waves in Linear Viscoelastic Media 155
    Francesco Mainardi
    Introduction 155
  42. Statement of the Problem by Laplace Transform 156
  43. The Structure of Wave Equations in the Space-Time Domain 159
  44. The Complex Index of Refraction: Dispersion and Attenuation 162
  45. The Signal Velocity and the Saddle-Point Approximation 167
  46. The Regular Wave-Front Expansion 172
  47. The Singular Wave-Front Expansion 178
    Conclusions 186
    Acknowledgments 186
    References 186xvi Contents
    Chapter 7: Dynamic Stability and Nonlinear Parametric Vibrations
    of Rectangular Plates 191
    G. L. Ostiguy
  48. Introduction 191
  49. Theoretical Analysis 194
    2.1 Analytical model 194
    2.2 Basic equations 195
    2.3 Boundary conditions 195
    2.4 Method of solution 197
  50. Solution of the Temporal Equations of Motion 199
  51. Stationary Response 199
    4.1 Principal parametric resonances 201
    4.2 Simultaneous resonances 202
    4.3 Combination resonances 203
  52. Nonstationary Responses 204
  53. Results and Discussion 205
    Acknowledgments 222
    References 223
    Chapter 8: Friction Modelling and D y n a m i c C o m p u t a t i o n 227
    J. P. Meijaard
  54. Introduction 227
  55. Phenomenological Models 229
    2.1 Models without memory effects 230
    2.2 Models with memory effects 235
    2.3 Stability of stationary sliding 236
    2.4 Two-dimensional sliding 240
  56. Analysis of Systems of Several Rigid Bodies 240
    3.1 Analysis of mechanical systems 240
    3.2 Arch loaded by a horizontal base motion 244
    3.3 Four-bar linkage under gravity loading 247
    References 250
    Chapter 9: Damping through Use of Passive and Semi-Active D r y
    Friction Forces 253
    Aldo A. Ferri
  57. Introduction 253
  58. Passive Mechanisms 254Contents xvii
    2.1 Background 254
    2.2 Linear-Coulomb damping 256
    2.3 Profiled block 265
    2.4 Shock and vibration isolation 269
    2.5 In-plane slip 273
  59. Semi-Active Friction 280
    3.1 Semi-active damping 281
    3.2 Semi-active friction damping in a SDOF system 282
    3.3 Structural vibration control 283
    3.4 Semi-active automative suspension 295
  60. Conclusions 297
  61. Acknowledgment 298
  62. References 298
    Subject Index 309
    Author Index

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