Mechanical Waves: Free, Forced, and Transition

Waves are a universal manifestation of matter, ranging from surface waves on water and seismic waves to light and gravity, and from waves in media and structures to the microscopic behavior of particles. Unlike gravitational waves, mechanical waves depend on the properties of the medium and the structure through which they propagate. It is therefore not surprising that the diversity of media leads to a wide variety of mechanical wave types. This book presents a comprehensive and unified framework for understanding mechanical wave phenomena. Covering both classical foundations and advanced developments, it systematically addresses general wave properties and the specific characteristics of waves in a wide range of media and structures—both continuous and discrete. The text is organized into eight parts, beginning with a concise introduction, On Waves in Brief, which highlights key concepts such as wave types, phase and group velocities, and wave propagation in different media. As the first level of wave theory, this introductory section is designed to be accessible to a broad readership, while the subsequent chapters examine specialized topics intended for researchers, engineers, and graduate students. Core themes include wave energy, mass, and momentum, with particular attention to novel topics such as wave energy partitioning, the modern formulation of wave momentum, and its implications for wave dynamics. The book also explores wave dispersion, orthogonality and localization, general dynamic elasticity, and nonlinear effects in mechanical systems. In addition, the treatment of forced waves provides new insights into excitation mechanisms, phase shifts, resonance phenomena, and the manifestation of the causality principle. By integrating classical results with recent advances—some presented here for the first time—this book offers a coherent theoretical framework that connects mechanical waves with broader wave phenomena, from gravitational and electromagnetic waves to localized vibrations in structured materials. It serves as a valuable reference for researchers in wave mechanics, materials science, and applied physics, as well as for graduate students seeking a deeper understanding of mechanical wave theory.

Table of Contents:
On waves in brief: Light, Gravitational wave and Mechanical waves.- Phase and group velocities.- Waves in media and structures.- Wave energy, mass and momentum: Energy partition.- Group velocity and momentum.- Longitudinal and flexural waves.- Wave orthogonality and localization: Generalized conditions.- Betti's theorem.- 1D and 2D waves.- Waves and Ripples.- Dynamic elasticity: Longitudinal, shear, surface Gravity and Rayleigh waves.- Lattices and  Fourier transform related.- Wave dispersion: The wave quasi front.- Wave at zero group velocity.- Some Nonlinear waves: Longitudinal waves.- Waves in strings, beams, and solitary waves.- Forced waves: Wave excitation and the phase shift.- Steady state limit and the causality principle.- Resonant waves.- Some general relations: Fundamentals.- Generalized functions and Integral transforms.

About the Author :
Leonid I. Slepyan is Professor Emeritus at Tel Aviv University, where he served as Professor of Mechanical Engineering from 1992 to 2000. He graduated from the Higher Naval Engineering School and the Naval Academy in St. Petersburg and later earned his Ph.D. (1961) and D.Sc. (1965). Over the course of his career, he held senior research and academic positions at the Research Institute of the Navy, and the Marine Technical University in St. Petersburg, where he was Professor and Head of Department. He also served as a Marie Curie Professor at Aberystwyth University, UK.   Professor Slepyan has published more than 150 research papers in leading international journals, including Physical Review Letters, Journal of the Mechanics and Physics of Solids, International Journal of Engineering Science, and Proceedings of the Royal Society A.