Book contents
- Frontmatter
- Contents
- List of Symbols
- Preface
- Chapter 1 Introduction to Analysis of Low Speed Impact
- Chapter 2 Rigid Body Theory for Collinear Impact
- Chapter 3 Rigid Body Theory for Planar or 2D Collisions
- Chapter 4 3D Impact of Rough Rigid Bodies
- Chapter 5 Rigid Body Impact with Discrete Modeling of Compliance for the Contact Region
- Chapter 6 Continuum Modeling of Local Deformation Near the Contact Area
- Chapter 7 Axial Impact on Slender Deformable Bodies
- Chapter 8 Impact on Assemblies of Rigid Elements
- Chapter 9 Collision against Flexible Structures
- Chapter 10 Propagating Transformations of State in Self-Organizing Systems
- Appendix A Role of Impact in the Development of Mechanics During the Seventeenth and Eighteenth Centuries
- Appendix B Glossary of Terms
- Answers to Some Problems
- References
- Index
Chapter 7 - Axial Impact on Slender Deformable Bodies
Published online by Cambridge University Press: 08 January 2010
- Frontmatter
- Contents
- List of Symbols
- Preface
- Chapter 1 Introduction to Analysis of Low Speed Impact
- Chapter 2 Rigid Body Theory for Collinear Impact
- Chapter 3 Rigid Body Theory for Planar or 2D Collisions
- Chapter 4 3D Impact of Rough Rigid Bodies
- Chapter 5 Rigid Body Impact with Discrete Modeling of Compliance for the Contact Region
- Chapter 6 Continuum Modeling of Local Deformation Near the Contact Area
- Chapter 7 Axial Impact on Slender Deformable Bodies
- Chapter 8 Impact on Assemblies of Rigid Elements
- Chapter 9 Collision against Flexible Structures
- Chapter 10 Propagating Transformations of State in Self-Organizing Systems
- Appendix A Role of Impact in the Development of Mechanics During the Seventeenth and Eighteenth Centuries
- Appendix B Glossary of Terms
- Answers to Some Problems
- References
- Index
Summary
Alice laughed. ‘There's no use trying,’ she said, ‘one can't believe impossible things.’ ‘I daresay you haven't had much practice,’ said the Queen. ‘When I was your age, I always did it for half-an-hour a day. Why, sometimes I've believed as many as six impossible things before breakfast.’
Lewis Carroll, Through the Looking Glass (1872)Axial impact on a deformable body results in a disturbance which initially propagates away from the impact site at a specific speed. This disturbance is a pulse or wave of particle displacement (and consequent stress). Wave propagation relates to propagation of a coherent pulse of stress and particle displacement through a medium at a finite speed. Familiar manifestations of this phenomenon are the transmission of sound through air, water waves across the surface of the sea and seismic tremors through the earth; thus, waves exist in gases, liquids and solids. Sources of excitation may be either concentrated or distributed spatially, and brief or extended functions of time. The unifying characteristic of waves is propagation of a disturbance through a medium. Properties of the medium that result in waves and determine the speeds of propagation are the density ρ and moduli of deformability (Young's modulus E, shear modulus G, bulk modulus K, etc.).
Longitudinal Wave in Uniform Elastic Bar
Consider a uniform slender elastic bar of cross-sectional are A, elastic modulus E and density ρ; the bar contains a region with axial stress σ(x, t) that is propagating in the positive x direction as shown in Fig. 7.1.
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- Impact Mechanics , pp. 146 - 172Publisher: Cambridge University PressPrint publication year: 2000
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