Dynamics of Elastic Containers

The motions of liquids in moving containers constitute a broad class of problems of great practical importance in many technical fields. The influence of the dynamics of the liquid on the motions of the container itself is a most interesting and complex aspect of the general subject, whether one considers only the rigid-body motions of the container or its elastic motions as well. It is most fitting therefore that this translation of Professor Rapoport's book has been undertaken so promptly following its original publication, so as to make readily available this rather detailed account of the mathematical foundations underlying the treatment of such prob lems. Since most of this vast body of analysis has been developed over the past decade by scientists in the USSR, and has therefore been largerly unavailable to those unable to read Russian, this volume will undoubtedly be of great value to many of us. H.

Contenu
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.