Hagedorn P., DasGupta A. Vibrations and Waves in Continuous Mechanical Systems

John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, England, 2007. 388 p. — ISBN: 978-0470-051738-3.This book provides a first course on the vibrations of continuous systems that will be suitable for students of continuous system dynamics, at senior undergraduate and graduate levels, in mechanical, civil and aerospace engineering. It will also appeal to researchers developing theory and analysis within the field.Starting from an elementary level, this book helps develop a comprehensive understanding of the theory of these systems and the tools with which to analyse them, before progressing to more advanced topics.Presents dynamics and analysis techniques for a wide range of continuous systems including strings, bars, beams, membranes, plates, fluids and elastic bodies in one, two and three dimensions.
Covers special topics such as the interaction of discrete and continuous systems, vibrations in translating media, and sound emission from vibrating surfaces, among others.
Develops the reader’s understanding by progressing from very simple results to more complex analysis without skipping the key steps in the derivations.
Offers a number of new topics and exercises that form essential steppingstones to the present level of research in the field.
Includes exercises at the end of the chapters based on both the academic and practical experience of the authors.Vibrations of strings and bars
One-dimensional wave equation: d'Alembert’s solution
Vibrations of beams
Vibrations of membranes
Vibrations of plates
Boundary value and eigenvalu eproblems in vibrations
Waves in fluids
Waves in elastic continua
Appendix A: The variational for mu lationof dynamics
Appendix B: Harmonic waves and dispersion relation
Appendix C: Variational formulation for dynamics of plates