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Dynamics of Solid Structures

Methods using Integrodifferential Relations

This monograph covers new variational and projection methods to study the dynamics within solid structures. To cope with the underlying initial-boundary value problems, the method of integrodifferential relations is employed. Applications and examples in physics, mechanics and control engineering range from natural vibrations or forced motions of elastic and viscoelastic bodies to heat and mass transfer processes.

Generalized formulations of parabolic and hyperbolic problems
Variational principles in linear elasticity
Variational statements in structural mechanics
Ritz method for initial-boundary value problems
Variational and projection techniques with semi-discretization
Integrodifferential approach to eigenvalue problems
Spatial vibrations of elastic beams with convex cross-sections
Double minimization in optimal control problems
Semi-discrete approximations in inverse dynamic problems
Modeling and control in mechatronics

Author Information

Georgy V. Kostin and Vasily V. Saurin, Institute for Problems in Mechanics, Russia.


"The book is well written and includes numerical examples at the end of each chapter. The book will be useful to teachers, students and researchers."
Girish Kumar Ramaiah in: Zentralblatt MATH 1406.74001

"In summary, this book will be of interest to researchers in theoretical and computational solid mechanics. It is perhaps less appropriate for a crystallography audience."
Gregory Chirikjian in: Acta Cryst. (2019). A75, 657

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Audience: Mechanical Engineers, Material Scientists, Applied Mathematicians, Physicists.