In almost all materials, the amplitudes of plane waves decay due to energy absorption during its propagation. The energy loss can be attributed to viscous damping, vibrational loss and other energy sink mechanisms. This phenomena is broadly classified as dissipation. Mathematically, both the amplitudes and wave numbers of these waves are complex vectors, so that the planes of constant phase differ from the planes of constant amplitude. The book deals with the various aspects of such waves known as inhomogeneous waves.
Using the principles of continuum mechanics, the book begins with the mathematical theory of inhomogeneous waves. Viscoelastic media possessing dissipative natures are modeled in chapter 2. No thermal effects have been included here. Various types of media have been considered for the propagation of inhomogeneous waves including unbounded medium (chapter 3), semi-infinite medium (chapter 4) and multiple layered medium (chapter 6). In chapters 4 and 5, the usual Snell’s law of reflection and transmission have been extended to the case of inhomogeneous waves. Propagation of inhomogeneous, surface waves including free surface Rayleigh waves and interfacial Stoneley waves has been discussed in chapter 5. The effect of body forces on the surface wave has been included in the analysis. Chapter 7 deals with the phenomena of wave scattering due to inhomogeneity which may be due to inclusions of dissimilar materials or internal voids. An integral representation of inhomogeneous waves as well as the analogue of radiation condition are presented here. In chapters 8 and 9, the propagation of inhomogeneous waves in heterogeneous media is discussed. Born approximations, WKB methods and asymptotic ray methods are included in the discussion.
The book offers a well planned, systematic development of the theory of propagation of inhomogeneous waves in dissipative and prestressed media. The importance of thermodynamic conditions to the propagation characteristics has been emphasized. Readers will find a wealth of information on advanced research materials in the book due to its inclusions of many applications from various applied disciplines e.g., seismology, NDE, and ocean acoustics.