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Dynamics of thin walled elastic bodies (Online)
1 online resource (vii, 226 pages :) illustrations
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.
Front Cover; Dynamics of Thin Walled Elastic Bodies; Copyright Page; Table of Contents; Dedication; Introduction; Chapter 1. Statement of the Problem and Model Examples; 1.1 Governing Equations and Basic Definitions; 1.2 The Vibration Modes of an Elastic Layer; 1.3 Asymptotic Derivation of Approximate Equations of Plate Bending (1D Case); 1.4 A Symbolic Notation for the Solutions to the Dynamic Equations of Elasticity; Chapter 2. Low-Frequency Approximations; 2.1 Tangential Low-Frequency Approximations; 2.2 Transverse Low-Frequency Approximations
2.3 The Equations of the Leading Low-Frequency Approximations in Stress Resultants and Stress CouplesChapter 3. Long-Wave High-Frequency Approximations; 3.1 Transverse High-Frequency Approximations; 3.2 Tangential High-Frequency Approximations; 3.3 Special Cases of Long-Wave High-Frequency Approximations; Chapter 4. Short-Wave Approximations. The Error Estimate in Dynamics of Thin Walled Bodies; 4.1 Short-Wave Approximations; 4.2 The Error Estimate of Propagating Modes; 4.3 The Ranges of Applicability of Leading Approximations and Overlap Regions; Chapter 5. Vibrations of a Body of Revolution
7.3 The Error Estimate of Boundary Value Problems7.4 The Theories of Plates and Shells with Modified Inertia; 7.5 The Classical Theories with Modified Inertia in the Stationary Case; Chapter 8. Long-Wave High-Frequency Vibrations of a Thin Walled Body Immersed in a Continuum; 8.1 Long-Wave High-Frequency Vibrations in an Acoustic Medium; 8.2 Long-Wave High-Frequency Vibrations of a Thin Walled Body with Fixed Faces. Interaction of a Thin Walled Body with a Dense Stiff Elastic Medium; Chapter 9. Radiation and Scattering by a Thin Walled Body
9.1 Radiation of an Elastic Layer into an Acoustic Half-Space (Plane Problem)9.2 Scattering of a Plane Acoustic Wave by a Thin Walled Cylinder. Application of the Shell Theories with Modified Inertia; 9.3 Scattering of a Plane Acoustic Wave by a Thin Walled Cylinder. Application of High-Frequency Approximations; 9.4 Scattering of a Plane Acoustic Wave by a Spherical Shell; Chapter 10. Non-Stationary Wave Propagation; 10.1 Formulation of the Problem and the Method Employed; 10.2 The Boundary Layer in the Vicinity of the Dilatation Wave Front
by J.D. Kaplunov, L.Yu. Kossovich, E.V. Nolde.
Includes bibliographical references and index.
San Diego, Calif. : Academic Press, ©1998