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Nonlinear Dynamics : Mathematical Models for Rigid Bodies with a Liquid.
This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid. It combines several methods and compares the results with experimental data. It is useful for experienced and early-stage readers interested in analytical approac...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Berlin/Boston :
De Gruyter,
2015.
©2015 |
| Colección: | De Gruyter studies in mathematical physics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Foreword to English Edition; Foreword to Russian Edition; Contents; Introduction; 1 Governing equations and boundary conditions in the dynamics of a bounded volume of liquid; 1.1 Conservation laws. Governing equations; 1.2 Stress tensors, strain rates, and their links; 1.3 Mathematical and physical models; 1.4 Boundary and initial conditions; 1.5 Formulation of the main boundary-value problem in a curvilinear coordinate system; 2 Direct methods in the nonlinear problems of the dynamics of bodies containing liquids.
- 2.1 Variational formulation of the free-surface problem of liquid sloshing in an immobile basin2.2 Multimodal method for an immobile basin; 2.3 Modal equations for noncylindrical basins; 2.4 Linear modal equations for an immobile tank; 2.5 Bateman-Luke principle for the nonlinear sloshing problem in a tank performing prescribed motions; 2.6 Multimodal method for a tank performing prescribed motions; 2.7 Evaluation of the Stokes-Zhukovsky potentials by the variationa method; 2.8 Resulting hydrodynamic forces and moments; 2.9 Nonlinear dynamic equations of the body-liquid system.
- 3 Hydrodynamic theory of motions of the ships transporting liquids3.1 Statement of the problem; 3.2 Bateman-Luke variational principle for floating bodies containing tanks filled with liquids; 3.3 Hydrodynamic forces and moments acting upon the floating rigid body; 4 Nonlinear differential equations of space motions of a rigid body containing an upright cylindrical cavity partially filled with liquid; 4.1 Nonlinear modal equations of liquid sloshing in cylindrical vessels with circular and annular cross sections; 4.2 Nonlinear modal equations for "viscous" liquid.
- 4.3 Hydrodynamic coefficients for circular cylindrical tanks with nonflat bottoms4.4 Hydrodynamic coefficients for the upright cylindrical tank of elliptic cross section; 4.5 Stokes-Zhukovsky potentials for coaxial cylindrical tanks; 4.6 Hydrodynamic parameters connected with motions of the rigid body; 4.7 Scalar equations in some special cases; 4.8 Nonlinear equations of perturbed motion of the body containing a cylindrical cavity partially filled with liquid; 5 Nonlinear modal equations for noncylindical axisymmetric tanks; 5.1 Natural sloshing modes for the nontruncated conical tank.
- 5.2 Natural sloshing modes for truncated conical tanks5.3 Nonlinear modal equations for nontruncated conical tanks; 5.4 Nonlinear modal equations for truncated conical tanks; 5.5 Spherical vessel; 6 Derivation of the nonlinear equations of space motions of the body-liquid system by the method of perturbation theory; 6.1 Reduction to a sequence of linear boundary-value problems; 6.2 Vector form of the nonlinear equations of space motions of the body-liquid system; 6.3 Main boundary-value problems for axially symmetric cylindrical cavities near the free surface.