Dynamics of Thin Walled Elastic Bodies

Written by a well-known group of researchers from Moscow, this book is a study of the asymptotic approximations of the 3-D dynamical equations of elasticity in the case of thin elastic shells of an arbitrary shape. Vibration of shells is a very useful theory in space techniques, submarine detection, and other high-tech domains. Dynamics of Thin Walled Elastic Bodies shows that refined shell theories used in engineering practice give a distorted picture of the high-frequency or non-stationary dynamics of shells, and offers new, mathematically more consistent ways of describing the dynamics of shells.

Key Features
• Studies the asymptotic approximations of the 3-D dynamical equations of elasticity
• Vibration of shells is a very useful theory in space techniques, submarine detection, and other high-tech domains
• Shows that refined shell theories used in engineering practice give a distorted picture of the high-frequency or non-stationary dynamics of shells
• Offers new, mathematically more consistent ways of describing the dynamics of shells

Audience: Researchers at naval research establishments and aerospace facilities, as well as civil (structural) engineers and researchers in the fields of mechanics, acoustics, and applied mathematics.

Vibration of shells is a very useful theory in space techniques, submarine detection, and other high-tech domains. This book is an exposition of the dynamic theory of thin walled linear elastic bodies, treated as an asymptotic branch of 3D elasticity, free of ad hoc assumptions.

The authors' analysis shows that shell theories used in engineering practice give a distorted picture of the high-frequency or non-stationary dynamics of shells. Their theory takes into consideration phenomena characterized by the wavelength having the order of a body's thickness and by the time scale being the time taken for elastic waves to propagate the distance equal to the body's thickness. It is evident that the classical Kirchoff-Love theory of shells, as well as its refinements, is not adequate to describe such phenomena.

This is an important book for researchers in mechanics, applied mathematics and acoustics. Structural engineers and those at naval research establishments and aerospace facilities will also find this theory invaluable.

Booknews

Explains the dynamic theory of thin-walled linearly elastic bodies, which are treated as an asymptotic branch of 3D elasticity free of ad hoc assumption. The theory takes into consideration phenomena characterized by the wavelength having the order of the thickness of a body and by the time scale of the order of the time elastic waves take to propagate the distance equal to the thickness. The authors focus on the derivation of asymptotic approximations of the 3D dynamic equations of elasticity as the thickness tends to zero. Annotation c. by Book News, Inc., Portland, Or.

Professor J D Kaplunov is a senior scientist at the Institute for Problems in Mechanics, Russian Academy of Sciences. His research interests are in solid mechanics, acoustics and asymptotic methods.

Professor L Yu Kossovich is Dean of the Faculty of Mathematics and Mechanics and Head of the Department of Mathematical Theory of Elasticity and Biomechanics at Saratov State University, Russia. His research interests are in solid mechanics, wave propagation and asymptotic methods.

Dr E V Nolde is a researcher at the Institute for Problems in Mechanics, Russian Academy of Sciences. Her research interests are in shell theory, acoustics and asymptotic methods.