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Impact Mechanics - W. J. Stronge

Paperback Published: 5th July 2004
ISBN: 9780521602891
Number Of Pages: 304

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Impact mechanics is concerned with the reaction forces that develop during a collision and the dynamic response of structures to these reaction forces. The subject has a wide range of engineering applications, from designing sports equipment to improving the crashworthiness of automobiles. This book develops several different methodologies for analysing collisions between structures. These range from rigid body theory for structures that are stiff and compact, to vibration and wave analyses for flexible structures. The emphasis is on low-speed impact where damage is local to the small region of contact between the colliding bodies. The analytical methods presented give results that are more robust or less sensitive to initial conditions than have been achieved hitherto. As a text, Impact Mechanics builds upon foundation courses in dynamics and strength of materials. It includes numerous industrially relevant examples and end-of-chapter homework problems drawn from industry and sports. Practising engineers will also find the methods presented in this book useful in calculating the response of a mechanical system to impact.

'A delightful book, it is clear and beautifully prepared in a stimulating manner, which will encourage frequent reference and further reading in the several references provided. Practising engineers will also find the methods presented in this book very useful in calculating the response of mechanical systems to impact.' Current Engineering Practice '... the book is unsurpassed in the masterly cogent treatment of intricate problems. We may paraphrase the words of the Spanish poet Garcia Lorca, when we predict that a considerable period will elapse before a book of comparable excellence will be published on impact theory.' Piero Villaggio, Zentralblatt fur Mathematik

List of Symbolsp. xiii
Prefacep. xvii
Introduction to Analysis of Low Speed Impactp. 1
Terminology of Two Body Impactp. 2
Configuration of Colliding Bodiesp. 2
Relative Velocity at Contact Pointp. 3
Interaction Forcep. 3
Classification of Methods for Analyzing Impactp. 3
Description of Rigid Body Impactp. 5
Description of Transverse Impact on Flexible Bodiesp. 9
Description of Axial Impact on Flexible Bodiesp. 9
Applicability of Theories for Low Speed Impactp. 9
Principles of Dynamicsp. 11
Particle Kineticsp. 11
Kinetics for a Set of Particlesp. 13
Kinetic Equations for a Rigid Bodyp. 14
Rate of Change for Moment of Momentum of a System about a Point Moving Steadily Relative to an Inertial Reference Framep. 17
Decomposition of a Vectorp. 18
Vectorial and Indicial Notationp. 19
Rigid Body Theory for Collinear Impactp. 21
Equation of Relative Motion for Direct Impactp. 21
Compression and Restitution Phases of Collisionp. 23
Kinetic Energy of Normal Relative Motionp. 25
Work of Normal Contact Forcep. 26
Coefficient of Restitution and Kinetic Energy Absorbed in Collisionp. 26
Velocities of Contact Points at Separationp. 28
Partition of Loss of Kinetic Energyp. 30
Rigid Body Theory for Planar or 2D Collisionsp. 35
Equations of Relative Motion at Contact Pointp. 35
Impact of Smooth Bodiesp. 37
Friction from Sliding of Rough Bodiesp. 40
Amontons-Coulomb Law of Dry Frictionp. 40
Equations of Planar Motion for Collision of Rough Bodiesp. 41
Contact Processes and Evolution of Sliding during Impactp. 42
Work of Reaction Impulsep. 44
Total Work Equals Change in Kinetic Energyp. 44
Partial Work by Component of Impulsep. 45
Energetic Coefficient of Restitutionp. 46
Terminal Impulse p[subscript f] for Different Slip Processesp. 47
Friction in Collinear Impact Configurationsp. 55
Friction in Noncollinear Impact Configurationsp. 59
Planar Impact of Rigid Bar on Rough Half Spacep. 59
3D Impact of Rough Rigid Bodiesp. 63
Collision of Two Free Bodiesp. 64
Law of Friction for Rough Bodiesp. 67
Equation of Motion in Terms of the Normal Impulsep. 67
Sliding that Halts during Collisionp. 68
Terminal Normal Impulse from Energetic Coefficient of Restitutionp. 69
Oblique Collision of a Rotating Sphere on a Rough Half Spacep. 70
Slender Rod that Collides with a Rough Half Spacep. 72
Slip Trajectories or Hodographsp. 74
Equilateral Triangle Colliding on a Rough Half Spacep. 75
Slip Trajectories and Hodograph for Equilateral Triangle Inclined at [theta] = [pi]/4p. 77
Spherical Pendulum Colliding on a Rough Half Spacep. 79
Numerical Results for [theta] = [pi]/3 and [pi]/4p. 82
General 3D Impactp. 83
Rigid Body Impact with Discrete Modeling of Compliance for the Contact Regionp. 86
Direct Impact of Viscoelastic Bodiesp. 86
Linear Viscoelasticity-the Maxwell Modelp. 87
Simplest Nonlinear Viscoelastic Deformable Elementp. 89
Hybrid Nonlinear Viscoelastic Element for Spherical Contactp. 91
Parameters of the Hybrid Nonlinear Element for Impact on a Golf Ballp. 93
Tangential Compliance in Planar Impact of Rough Bodiesp. 93
Dynamics of Planar Collision for Hard Bodiesp. 94
Slip Processesp. 100
Oblique Impact of an Elastic Sphere on a Rough Half Spacep. 104
Dissipation of Energyp. 109
Effects of Tangential Compliancep. 111
Bounce of a Superballp. 112
Continuum Modeling of Local Deformation Near the Contact Areap. 116
Quasistatic Compression of Elastic-Perfectly Plastic Solidsp. 117
Elastic Stresses-Hertzian Contactp. 117
Indentation at Yield of Elastic-Plastic Bodiesp. 119
Quasistatic Elastic-Plastic Indentationp. 120
Fully Plastic Indentationp. 123
Elastic Unloading from Maximum Indentationp. 124
Resolved Dynamics of Planar Impactp. 126
Direct Impact of Elastic Bodiesp. 126
Eccentric Planar Impact of Rough Elastic-Plastic Bodiesp. 129
Coefficient of Restitution for Elastic-Plastic Solidsp. 131
Partition of Internal Energy in Collision between Dissimilar Bodiesp. 132
Composite Coefficient of Restitution for Colliding Bodies with Dissimilar Hardnessp. 132
Loss of Internal Energy to Elastic Wavesp. 134
Applicability of the Quasistatic Approximationp. 137
Transverse Impact of Rough Elastic-Plastic Cylinders-Applicability of Energetic Coefficient of Restitutionp. 137
Elastic Normal Compliancep. 138
Yield for Plane Strain Deformationp. 139
Elastic-Plastic Indentationp. 139
Fully Plastic Indentationp. 140
Analyses of Contact Forces for Oblique Impact of Rough Cylindersp. 140
Loss of Internal Energy to Elastic Waves for Planar (2D) Collisionsp. 142
Synopsis for Spherical Elastic-Plastic Indentationp. 143
Axial Impact on Slender Deformable Bodiesp. 146
Longitudinal Wave in Uniform Elastic Barp. 146
Initial Conditionsp. 147
Reflection of Stress Wave from Free Endp. 150
Reflection from Fixed Endp. 152
Reflection and Transmission at Interface-Normal Incidencep. 152
Spall Fracture Due to Reflection of Stress Wavesp. 153
Planar Impact of Rigid Mass against End of Elastic Barp. 156
Boundary Condition at Impact Endp. 157
Boundary Condition at Dashpot Endp. 157
Distribution of Stress and Particle Velocityp. 158
Experimentsp. 159
Impact, Local Indentation and Resultant Stress Wavep. 160
Wave Propagation in Dispersive Systemsp. 162
Group Velocityp. 163
Transverse Wave in a Beamp. 164
Euler-Bernoulli Beam Equationp. 164
Rayleigh Beam Equationp. 165
Timoshenko Beam Equationp. 166
Comparison of Euler-Bernoulli, Rayleigh and Timoshenko Beam Dynamicsp. 168
Impact on Assemblies of Rigid Elementsp. 173
Impact on a System of Rigid Bodies Connected by Noncompliant Bilateral Constraintsp. 174
Generalized Impulse and Equations of Motionp. 174
Equations of Motion Transformed to Normal and Tangential Coordinatesp. 177
Impact on a System of Rigid Bodies Connected by Compliant Constraintsp. 182
Comparison of Results from Alternative Analytical Approximations for Multibody Systems with Unilateral Constraintsp. 183
Numerical Simulation and Discussion of Multibody Impactp. 188
Spatial Gradation of Normal Contact Stiffness [kappa subscript j] = [chi superscript kappa]p. 190
Applicability of Simultaneous Impact Assumptionp. 198
Collision against Flexible Structuresp. 201
Free Vibration of Slender Elastic Bodiesp. 201
Free Vibration of a Uniform Beamp. 201
Eigenfunctions of a Uniform Beam with Clamped Endsp. 202
Rayleigh-Ritz Mode Approximationp. 203
Single Degree of Freedom Approximationp. 205
Transverse Impact on an Elastic Beamp. 206
Forced Vibration of a Uniform Beamp. 207
Impact of a Perfectly Plastic Missilep. 207
Effect of Local Compliance in Structural Response to Impactp. 209
Impact on Flexible Structures - Local or Global Response?p. 214
Propagating Transformations of State in Self-Organizing Systemsp. 219
Systems with Single Attractorp. 220
Ball Bouncing down a Flight of Regularly Spaced Stepsp. 220
Systems with Two Attractorsp. 222
Prismatic Cylinder Rolling down a Rugh Inclined Planep. 222
The Domino Effect - Independent Interaction Theoryp. 228
Domino Toppling - Successive Destabilization by Cooperative Neighborsp. 235
Wavefront Stability for Multidimensional Domino Effectsp. 240
Approach to Chaos - an Unbounded Increase in Number of Attractorsp. 242
Periodic Vibro-impact of Single Degree of Freedom Systemsp. 242
Period One Orbitsp. 244
Poincare Section and Return Mapp. 244
Stability of Orbit and Bifurcationp. 245
Role of Impact in the Development of Mechanics During the Seventeenth and Eighteenth Centuriesp. 248
Historical Referencesp. 264
Glossary of Termsp. 266
Answers to Some Problemsp. 269
Referencesp. 271
Indexp. 277
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521602891
ISBN-10: 0521602890
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 304
Published: 5th July 2004
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.6 x 18.9  x 1.8
Weight (kg): 0.56