Kaplunov J.D., Kossovitch L.Y., Nolde E.V. Dynamics of Thin Walled Elastic Bodies

Academic Press, 1998. — 226 p.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.
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 shellsStatement of the Problem and Model Examples
Low-Frequency Approximations
Long-Wave High-Frequency Approximations
Short-Wave Approximations. The Error Estimate in Dynamics of Thin Walled Bodies
Vibrations of a Body of Revolution
A Thin Walled Body under Surface Loading
Higher Order Theories of Plates and Shells
Long-Wave High-Frequency Vibrations of a Thin Walled Body Immersed in a Continuum
Radiation and Scattering by a Thin Walled Body
Non-Stationary Wave Propagation
General Notation