Book contents
- Frontmatter
- Contents
- Preface
- 1 One-Dimensional Viscoelasticity
- 2 Three-Dimensional Viscoelasticity
- 3 Viscoelastic P, SI, and SII Waves
- 4 Framework for Single-Boundary Reflection–Refraction and Surface-Wave Problems
- 5 General P, SI, and SII Waves Incident on a Viscoelastic Boundary
- 6 Numerical Models for General Waves Reflected and Refracted at Viscoelastic Boundaries
- 7 General SI, P, and SII Waves Incident on a Viscoelastic Free Surface
- 8 Rayleigh-Type Surface Wave on a Viscoelastic Half Space
- 9 General SII Waves Incident on Multiple Layers of Viscoelastic Media
- 10 Love-Type Surface Waves in Multilayered Viscoelastic Media
- 11 Appendices
- References
- Additional Reading
- Index
5 - General P, SI, and SII Waves Incident on a Viscoelastic Boundary
Published online by Cambridge University Press: 29 October 2009
- Frontmatter
- Contents
- Preface
- 1 One-Dimensional Viscoelasticity
- 2 Three-Dimensional Viscoelasticity
- 3 Viscoelastic P, SI, and SII Waves
- 4 Framework for Single-Boundary Reflection–Refraction and Surface-Wave Problems
- 5 General P, SI, and SII Waves Incident on a Viscoelastic Boundary
- 6 Numerical Models for General Waves Reflected and Refracted at Viscoelastic Boundaries
- 7 General SI, P, and SII Waves Incident on a Viscoelastic Free Surface
- 8 Rayleigh-Type Surface Wave on a Viscoelastic Half Space
- 9 General SII Waves Incident on Multiple Layers of Viscoelastic Media
- 10 Love-Type Surface Waves in Multilayered Viscoelastic Media
- 11 Appendices
- References
- Additional Reading
- Index
Summary
A theoretical closed-form solution for the problem of a general P, SI, or SII wave incident on a plane welded boundary between HILV media, V and V′, is one for which the characteristics of the reflected and refracted waves are expressed in terms of the assumed characteristics of the incident wave. Application of the boundary conditions at the boundary allows the amplitude and phase for the reflected and refracted waves to be expressed in terms of the properties of the media and those given for the incident wave. The directions of the propagation and attenuation vectors for the reflected and refracted waves are determined in terms of those of the incident wave by showing that the complex wave number for each solution must be the same. For problems involving incident P and SI waves, the boundary conditions are most readily applied using the solutions involving displacement potentials, namely, (4.2.1), (4.2.2), (4.2.16), and (4.2.17). For problems involving incident SII waves, the boundary conditions can be applied most easily using solutions involving only one component of the displacement field, namely (4.2.26) and (4.2.27).
Boundary-Condition Equations for General Waves
The welded boundary between media V and V′ is specified mathematically by requiring that the stress and displacement are continuous across the boundary. For purposes of brevity, application of these boundary conditions to the general solutions specifying each type of wave as incident, reflected, or refracted allows a general set of equations to be derived from which a particular problem of interest can be solved by choosing the incident wave of interest.
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- Viscoelastic Waves in Layered Media , pp. 107 - 142Publisher: Cambridge University PressPrint publication year: 2009