Elastic Waves: High Frequency Theory

ISBN-13: 9781138033061 / Angielski / Twarda / 2018 / 286 str.

Vassily Babich; Aleksei Kiselev

Opis

This book is concerned with mathematical aspects of theory of high-frequency elastic waves, which is also known as the ray method. The aim of the book is to present a clear systematic description of the ray method, and at the same time to emphasize its mathematical beauty.

Spis treści

Preface. Introduction. Chapter 1. Basic notions of elastodynamics. Chapter 2. Plane waves. Chapter 3. Point sources and spherical waves in homogeneous isotropic media. Chapter 4. The ray method for volume waves in isotropic media. Chapter 5. The ray method for volume waves in anisotropic media. Chapter 6. Point sources in inhomogeneous isotropic media. The wave S from a center of expansion. The wave P from a center of rotation. Chapter 7. The "nongeometrical" wave S *. Chapter 8. The ray method for Rayleigh waves. A.1. Definition of tensor. A.2. Simple operations with tensors. A.3. Metric tensor. Raising and lowering indices. A.4. Coordinates (q1, q2, n) associated with a surface in R3. The first and second fundamental forms. A.5. Covariant derivative. Divergence