Dynamics of Solid Structures: Methods using Integrodifferential Relations

Georgy Viktorovich Kostin; Vasily V. Saurin

Published by De Gruyter 2018

Dynamics of Solid Structures

Methods using Integrodifferential Relations

Georgy Viktorovich Kostin and Vasily V. Saurin

https://doi.org/10.1515/9783110516449

Overview
Contents

About this book

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.

Contents
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 / Editor information

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

Reviews

"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

Topics

Frontmatter Publicly Available Download PDF	I
Preface Requires Authentication Unlicensed Licensed Download PDF	VII
Basic notation Requires Authentication Unlicensed Licensed Download PDF	XI
Contents Publicly Available Download PDF	XIII
1. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
2. Generalized formulations of parabolic and hyperbolic problems Requires Authentication Unlicensed Licensed Download PDF	9
3. Variational principles in linear elasticity Requires Authentication Unlicensed Licensed Download PDF	31
4. Variational statements in structural mechanics Requires Authentication Unlicensed Licensed Download PDF	53
5. Ritz method for initial-boundary value problems Requires Authentication Unlicensed Licensed Download PDF	71
6. Variational and projection techniques with semi-discretization Requires Authentication Unlicensed Licensed Download PDF	113
7. Integrodifferential approach to eigenvalue problems Requires Authentication Unlicensed Licensed Download PDF	129
8. Spatial vibrations of elastic beams with convex cross-sections Requires Authentication Unlicensed Licensed Download PDF	165
9. Double minimization in optimal control problems Requires Authentication Unlicensed Licensed Download PDF	197
10. Semi-discrete approximations in inverse dynamic problems Requires Authentication Unlicensed Licensed Download PDF	229
11. Modeling and control in mechatronics Requires Authentication Unlicensed Licensed Download PDF	259
A. Vectors and tensors Requires Authentication Unlicensed Licensed Download PDF	275
B. Sobolev spaces Requires Authentication Unlicensed Licensed Download PDF	279
Bibliography Requires Authentication Unlicensed Licensed Download PDF	281
Index Requires Authentication Unlicensed Licensed Download PDF	287

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Mechanical Engineers, Material Scientists, Applied Mathematicians, Physicists.
Pages
- Front matter: 17
- Main content: 288
Illustrations
- Illustrations: 130

eBook

Published: November 20, 2017
ISBN: 9783110516449

Hardcover

Published: November 20, 2017
ISBN: 9783110516234