Transient Aerohydroelasticity of Spherical Bodies

1. Basic Theory of Transient Aerohydroelasticity of Spherical Bodies.- 1.1 Equations of Motion of Elastic Media.- 1.2 An Acoustic Medium.- 1.3 Equations of Motion of Thin-Walled Shells.- 1.4 Conditions of Contact for Interacting Media.- 1.5 General Integral of the Wave Equation in the Spherical Coordinates.- 2. Radial Vibrations of Media with Spherical Interfaces.- 2.1 Propagation of Disturbances from a Cavity.- 2.2 Vibrations of Thin-Walled Isotropic Shells Contacting Elastic Media.- 2.3 Vibrations of a Thick-Walled Sphere in an Elastic Medium.- 2.4 Limiting Cases in Problems of Vibrations of Thick-Walled Sphere.- 2.5 Separation of Discontinuities in Solutions.- 2.6 Vibrations of a Piecewise Homogeneous Elastic Space with Concentric Spherical Interfaces.- 3. Diffraction of Waves by Elastic Spherical Bodies.- 3.1 Statement of the Problem.- 3.2 The Laplace Transform.- 3.3 Representation of the Solution in the Form of Superposition of Generalized Spherical Waves.- 3.4 Diffraction Problems for an Acoustic Medium.- 3.5 Numerical Examples.- 4. Axially Symmetric Vibrations of Elastic Media Having a Spherical Cavity or a Stiff Inclusion.- 4.1 Interaction Forces.- 4.2 Propagation of Disturbances from a Cavity.- 4.3 Diffraction of Waves by a Cavity or by an Immovable Spherical Inclusion.- 4.4 The Resultant Force at an Immovable Sphere.- 5. Diffraction of Plane (Spherical) Waves by a Spherical Barrier Supported by a Thin-Walled Shell.- 5.1 Propagation of Disturbances from a Supported Spherical Cavity.- 5.2 Diffraction of Elastic Waves by a Thin-Walled Shell Occupied by an Elastic Medium.- 5.3 Internal Problems on Interaction of Waves with a Thin-Walled Spherical Shell.- 5.4 Interaction Between Shells and Acoustic Media.- 5.5 External Problem of Interaction of Waves with a HollowShell.- 5.6 Internal Problems in the Absence of Surrounding Medium.- 6. Translational Motion of a Sphere in Elastic and Acoustic Media.- 6.1 Response of a Surrounding Medium to a Sphere's Motion at a Predetermined Law.- 6.2 Motion of a Perfectly Rigid Spherical Inclusion Under Action of Predetermined Forces.- 6.3 Diffraction of Elastic Waves by a Perfectly Rigid Sphere Having Internal Elements.- 6.4 Displacement of the Center of Mass of an Elastic Spherical Obstacle.- 6.5 A Perfectly Rigid Spherical Shell Filled with an Elastic Medium.- 7. Penetration of Spherical Bodies into a Fluid Half-Space.- 7.1 Penetration of Spherical Shells into a Compressible Fluid.- 7.2 Penetration of Spherical Shells into an Incompressible Fluid.- 7.3 Penetration of Rigid Spherical Bodies into a Fluid Half-Space.- 8. Spherical Waves in Media with Complicated Properties.- References.