Fundamental Solutions in Elastodynamics
Fundamental Solutions in Elastodynamics
This work is a compilation of fundamental solutions (or Green's functions) for classical or canonical problems in elastodynamics presented with a common format and notation. These formulas describe the displacements and stresses elicited by dynamic sources in solid elastic media like full spaces, half-spaces, strata and plates in both two and three dimensions, using the three major coordinate systems (Cartesian, cylindrical and spherical), and also for transient and harmonic motions. Such formulas are useful for numerical methods and practical application to problems of wave propagation in elasticity, soil dynamics, earthquake engineering, mechanical vibration, or geophysics. These formulas were heretofore only found scattered throughout the literature. The solutions are tabulated without proof, but giving reference to appropriate modern papers and books containing full derivations. Most formulas in the book have been programmed and tested within the MATLAB environment. The program listings are available for free download on the book's website.
- First accessible compilation of fundamental solutions in elastodynamics
- Formulas are available in MATLAB files which are listed in the appendix and available free for download on the book's website
- Solutions appear for the first time in common format and with common notation
Reviews & endorsements
'[This book] presents a concise treatment of fundamental solutions of a variety of problems arising in elastodynamics … It should be useful to students and researchers in applied mathematics, geophysics, engineering and other applied sciences.' Fiazud Din Zaman, Zentralblatt MATH
Product details
July 2011Paperback
9780521375993
262 pages
254 × 178 × 14 mm
0.46kg
Available
Table of Contents
- Preface
- Part I. Preliminaries:
- 1. Fundamentals
- 2. Dipoles
- Part II. Full Space Problems:
- 3. Two-dimensional problems in full, homogeneous spaces
- 4. Three-dimensional problems in full, homogeneous spaces
- Part III. Half-Space Problems:
- 5. Two-dimensional problems in homogeneous half-spaces
- 6. Three-dimensional problems in homogeneous half-spaces
- Part IV. Plates and Strata:
- 7. Two-dimensional problems in homogeneous plates and strata
- Part V. Analytical and Numerical Methods:
- 8. Solutions to the Helmholtz and wave equations
- 9. Integral transform method
- 10. Stiffness (impedance) matrix method
- Part VI. Appendices:
- 11. Basic properties of mathematical functions
- 12. Brief table of integral transforms
- 13. MATLAB(R) program listings.
