Nonlinear Dynamics

Mathematical Models for Rigid Bodies with a Liquid

Ivan A. Lukovsky (Autor)

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XVI, 394 Seiten | Ausstattung: eBook & Hardcover

2015
De Gruyter
9783110316582 (ISBN)

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This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid. The methods are normally based on the Bateman-Luke variational formalism combined with perturbation theory. The derived approximate equations of spatial motions of the body-liquid mechanical system (these equations are called mathematical models in the title) take the form of a finite-dimensional system of nonlinear ordinary differential equations coupling quasi-velocities of the rigid body motions and generalized coordinates responsible for displacements of the natural sloshing modes. Algorithms for computing the hydrodynamic coefficients in the approximate mathematical models are proposed. Numerical values of these coefficients are listed for some tank shapes and liquid fillings. The mathematical models are also derived for the contained liquid characterized by the Newton-type dissipation. Formulas for hydrodynamic force and moment are derived in terms of the solid body quasi-velocities and the sloshing-related generalized coordinates. For prescribed harmonic excitations of upright circular (annular) cylindrical and/or conical tanks, the steady-state sloshing regimes are theoretically classified; the results are compared with known experimental data. The book can be useful for both experienced and early-stage mechanicians, applied mathematicians and engineers interested in (semi-)analytical approaches to the “fluid-structure” interaction problems, their fundamental mathematical background as well as in modeling the dynamics of complex mechanical systems containing a rigid tank partly filled by a liquid.

Ivan A. Lukovsky, National Academy of Sciences of Ukraine, Kiev, Ukraine.

Reihe/Serie	De Gruyter Studies in Mathematical Physics ; 27
Übersetzer	Peter V. Malyshev
Zusatzinfo	Includes a print version and an ebook
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Dynamics • Dynamics, Mathematics • Dynamik • Fluid-Struktur-Wechselwirkung • Lagrange formalism for hydrodynamic and hybrid mechanical systems, fluid-structure interaction, nonlinear sloshing, coupled `rigid tank-contained liquid' dynamics, spacecraft and land-based applications • Lagrange formalism for hydrodynamic and hybrid mechanical systems, fluid-structure interaction, nonlinear sloshing, coupled `rigid tank-contained liquid’ dynamics, spacecraft and land-based applications • Nichtlineare Dynamik • Nonlinear Theories • Nonlinear theories, Mathematics
ISBN-13	9783110316582 / 9783110316582
Zustand	Neuware