The problems of transient interaction of deformable bodies with surrounding media are of great practical and theoretical importance. When solving the problems of this kind, the main difficulty is in the necessity to integrate jointly the system of equations which describe motion of the body and the system of equations which describe motion of the medium under the boundary conditions predetermined at the unknown (movable) curvilinear interfaces. At that, the position of these interfaces should be determined as part of the solution process. That is why, the known exact solutions in this area of mechanics of continuum have been derived mainly for the cases of idealized rigid bodies. Different aspects of the problems of transient interaction of bodies and structures with continuum (derivation of the efficient mathematical mod­ els for the phenomenon, development of the theoretical and experimental methods to be used for study of the transient problems of mechanics, etc.) were considered in the books by S.U. Galiev, A.N. Guz, V.D. Kubenko, V.B. Poruchikov, L.L Slepyan, A.S. Volmir, and Yu.S. Yakovlev. The results presented by these authors make interest when solving a great variety of problems and show a necessity of joint usage of the results obtained in differ­ ent areas: aerohydrodynamics, theory of elasticity and plasticity, mechanics of soils, theory of shells and plates, applied and computational mathemat­ ics, etc.

Inhalt

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.- 2.4.1 External and Internal Acoustic Media (K0 = K1 = 1).- 2.4.2 The Absence of Internal Medium (?0 = 0).- 2.4.3 A Solid Sphere in an Elastic Medium.- 2.4.4 Propagation of Disturbances from a Cavity.- 2.4.5 Reflection of an Elastic Wave from Walls of an Absolutely Rigid Reservoir.- 2.4.6 Free Internal Surface r = r1.- 2.4.7 Absolutely Rigid Fixture at the Internal Surface r = r1. External Problem (?2 = ?, ?2 = 0).- 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 Hollow Shell.- 5.6 Internal Problems in the Absence of Surrounding Medium.- 5.6.1 An Elastic Shell Occupied by an Acoustic Medium.- 5.6.2 An Absolutely Stiff Spherical Shell Occupied by an Elastic Medium.- 5.6.3 A Stiff Reservoir Occupied by an Acoustic Medium.- 5.6.4 An Elastic Sphere Having a Free External Sur face.- 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.