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Intro; Preface; References; About the Book; Contents; About the Author; 1 Asymptotic Analysis of Dynamic Elasticity Problems for a Hollow Cylinder of Finite Length; Abstract; 1.1 Construction of Homogeneous Solutions; 1.2 Analysis of the Roots of the Dispersion Equation; 1.3 Construction of Asymptotic Formulas for Displacements and Stresses; 1.4 Generalized Orthogonality Condition of Homogeneous Solutions: Satisfaction of Boundary Conditions at the Cylinder Ends; 1.5 Construction of Dynamic Refined Applied Theories of a Hollow Cylinder; 1.6 Torsional Vibrations of an Isotropic Hollow Cylinder.
1.7 Elastic Vibrations of a Hollow Cylinder with a Fixed Side Surface1.8 Forced Vibrations of a Hollow Cylinder with Mixed Boundary Conditions on the Side Surface; References; 2 Asymptotic Analysis of Dynamic Elasticity Problem for a Hollow Sphere; Abstract; 2.1 The General Representation of the Solution to the Equations of Axisymmetric Dynamic Elasticity Theory in Spherical Coordinates; 2.2 Inhomogeneous Solutions; 2.3 Construction of Homogeneous Solutions; 2.4 Asymptotic Analysis of the Dispersion Equation; 2.5 Asymptotic Analysis of Homogeneous Solutions for a Spherical Shell.
2.6 Dynamical Torsion of a Spherical Layer2.7 Non-axisymmetric Dynamic Problems of Elasticity Theory for a Hollow Sphere; References; 3 Free Vibrations of Isotropic Hollow Cylinder and Closed Hollow Sphere; Abstract; 3.1 Free Vibrations of an Isotropic Hollow Cylinder; 3.2 Analysis of the Frequency Equation and Vibration Forms of a Cylinder; 3.3 Axisymmetric Free Vibrations of a Hollow Sphere; References; 4 Asymptotic Analysis of Stress-Strain State of a Truncated Hollow Cone; Abstract; 4.1 Construction of Homogeneous Solutions; 4.2 Analysis of the Roots of the Characteristic Equation.
4.3 Analysis of the Stress-Strain State4.4 Reduction to Infinite Systems; 4.5 Construction of Refined Applied Theories for a Conical Shell; 4.6 Axisymmetric Problem for a Plate of Variable Thickness; 4.7 Analysis of the Characteristic Equation for a Plate of Variable Thickness; 4.8 Analysis of Stress-Strain State of a Plate; 4.9 Reduction of a Boundary Value Problem for a Plate of Variable Thickness and Infinite Systems at Given Stresses; 4.10 Construction of Applied Theories for the Plates of Variable Thickness.
4.11 Investigation of Elastic Equilibrium of a Hollow Cone with a Fixed Side Surface and Mixed Boundary Conditions on the Side Surface4.12 Asymptotic Analysis of the Solutions of Some Axisymmetric Problems for Plates of Variable Thickness; 4.13 Asymptotic Analysis of the Characteristic Equation; 4.14 Construction of Asymptotic Formulas for Displacements and Stresses; 4.15 Kirsch Problem for Plates of Variable Thickness; 4.16 Torsional Vibrations of a Conical Shell of Variable Thickness; References; Appendix; References.
1.7 Elastic Vibrations of a Hollow Cylinder with a Fixed Side Surface1.8 Forced Vibrations of a Hollow Cylinder with Mixed Boundary Conditions on the Side Surface; References; 2 Asymptotic Analysis of Dynamic Elasticity Problem for a Hollow Sphere; Abstract; 2.1 The General Representation of the Solution to the Equations of Axisymmetric Dynamic Elasticity Theory in Spherical Coordinates; 2.2 Inhomogeneous Solutions; 2.3 Construction of Homogeneous Solutions; 2.4 Asymptotic Analysis of the Dispersion Equation; 2.5 Asymptotic Analysis of Homogeneous Solutions for a Spherical Shell.
2.6 Dynamical Torsion of a Spherical Layer2.7 Non-axisymmetric Dynamic Problems of Elasticity Theory for a Hollow Sphere; References; 3 Free Vibrations of Isotropic Hollow Cylinder and Closed Hollow Sphere; Abstract; 3.1 Free Vibrations of an Isotropic Hollow Cylinder; 3.2 Analysis of the Frequency Equation and Vibration Forms of a Cylinder; 3.3 Axisymmetric Free Vibrations of a Hollow Sphere; References; 4 Asymptotic Analysis of Stress-Strain State of a Truncated Hollow Cone; Abstract; 4.1 Construction of Homogeneous Solutions; 4.2 Analysis of the Roots of the Characteristic Equation.
4.3 Analysis of the Stress-Strain State4.4 Reduction to Infinite Systems; 4.5 Construction of Refined Applied Theories for a Conical Shell; 4.6 Axisymmetric Problem for a Plate of Variable Thickness; 4.7 Analysis of the Characteristic Equation for a Plate of Variable Thickness; 4.8 Analysis of Stress-Strain State of a Plate; 4.9 Reduction of a Boundary Value Problem for a Plate of Variable Thickness and Infinite Systems at Given Stresses; 4.10 Construction of Applied Theories for the Plates of Variable Thickness.
4.11 Investigation of Elastic Equilibrium of a Hollow Cone with a Fixed Side Surface and Mixed Boundary Conditions on the Side Surface4.12 Asymptotic Analysis of the Solutions of Some Axisymmetric Problems for Plates of Variable Thickness; 4.13 Asymptotic Analysis of the Characteristic Equation; 4.14 Construction of Asymptotic Formulas for Displacements and Stresses; 4.15 Kirsch Problem for Plates of Variable Thickness; 4.16 Torsional Vibrations of a Conical Shell of Variable Thickness; References; Appendix; References.