Dynamics of Elastic Containers

1 Fluid Pressure on the Wetted Surface of the Cavity.- [1] The Velocity Potential.- [2] Pressure in Regions Occupied by the Fluid Masses.- [3] The Force Equation and the Moment Equation.- [4] Moments of Inertia of a Solid Body Containing Fluid Masses.- 2 Equations of Motion of an Elastic Body with Cavities Partially Filled with an Ideal Fluid.- [1] Elastic Displacements $$\vec u\left( {x,{\text{ }}y,{\text{ }}z,{\text{ }}t} \right)$$.- [2] Steady Motion.- [3] Disturbances of Steady Motion.- [4] Disturbances Brought About by Changes in Initial Conditions.- [5] Impulsive Disturbances of Steady Motion.- [6] Integro-Differential Equations of Motion.- [7] Reducing Several Boundary-Value Problems to One, Principal Boundary-Value Problem.- 3 The Basic Boundary-value Problem.- [1] The Homogeneous Boundary-Value Problem.- [2] The Nonhomogeneous Boundary-Value Problem.- [3] Variational Statement of the problem.- [4] Asymptotic Expansion of the Basic Functional.- [5] Refining the Basic Equations of the Strength of Materials.- [6] Approximate Solution of the Basic Boundary-Value Problem.- 4 Vibrations of an Elastic Body Containing Fluid Masses.- [1] Natural Vibrations of an Elastic Body Containing Fluid Masses.- [2] Stability of the Steady Motion.- [3] Uniqueness of the Solution of Cauchy’s Problem for the Elastic Displacements $$\vec u\left( {x,{\text{ }}y,{\text{ }}z,{\text{ }}t} \right)$$ and the Pressure p(x, y, z, t).- [4] The Conjugate Boundary-Value Problem, Biorthogonal System of Eigenfunctions.- [5] Forced Vibrations of a Fluid-Filled Elastic Body.- [6] Ordinary Differential Equations of Motion.- 5 The Case When the Elastic Body Is Symmetrical with Respect to Two Mutually Perpendicular Planes.- [1] Transformation of The Basic Boundary-Value Problem.- [2] Determinant D(?).- [3] Longitudinal and Flexural Vibrations of an Elastic Body Containing Fluid.- [4] Natural Flexural Vibrations and Their Stability.- References.