LEADER 04760nam 2200721 450 001 9910460418903321 005 20210511022202.0 010 $a3-11-055536-0 010 $a1-5231-0464-3 010 $a3-11-031657-9 010 $a3-11-038973-8 024 7 $a10.1515/9783110316575 035 $a(CKB)3710000000405812 035 $a(EBL)2035732 035 $a(OCoLC)908512710 035 $a(SSID)ssj0001497977 035 $a(PQKBManifestationID)11810686 035 $a(PQKBTitleCode)TC0001497977 035 $a(PQKBWorkID)11499204 035 $a(PQKB)10506833 035 $a(MiAaPQ)EBC2035732 035 $a(DE-B1597)209909 035 $a(OCoLC)910582789 035 $a(DE-B1597)9783110316575 035 $a(Au-PeEL)EBL2035732 035 $a(CaPaEBR)ebr11049755 035 $a(CaONFJC)MIL807813 035 $a(EXLCZ)993710000000405812 100 $a20150511h20152015 uy| 0 101 0 $aeng 135 $aurnnu---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aNonlinear dynamics $emathematical models for rigid bodies with a liquid /$fIvan A. Lukovsky ; translated by Peter V. Malyshev 210 1$aBerlin :$cDe Gruyter,$d[2015] 210 4$dİ2015 215 $a1 online resource (410 p.) 225 1 $aDe Gruyter studies in mathematical physics,$x2194-3532 ;$v27 300 $aDescription based upon print version of record. 311 $a3-11-031658-7 311 $a3-11-031655-2 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tForeword to English Edition --$tForeword to Russian Edition --$tContents --$tIntroduction --$tChapter 1. Governing equations and boundary conditions in the dynamics of a bounded volume of liquid --$tChapter 2. Direct methods in the nonlinear problems of the dynamics of bodies containing liquids --$tChapter 3. Hydrodynamic theory of motions of the ships transporting liquids --$tChapter 4. Nonlinear differential equations of space motions of a rigid body containing an upright cylindrical cavity partially filled with liquid --$tChapter 5. Nonlinear modal equations for noncylindical axisymmetric tanks --$tChapter 6. Derivation of the nonlinear equations of space motions of the body-liquid system by the method of perturbation theory --$tChapter 7. Equivalent mechanical systems in the dynamics of a rigid body with liquid --$tChapter 8. Forced finite-amplitude liquid sloshing in moving vessels --$tBibliography --$tIndex --$tBackmatter 330 $aThis book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid. The methods are normally based on the Bateman-Luke variational formalism combined with perturbation theory. The derived approximate equations of spatial motions of the body-liquid mechanical system (these equations are called mathematical models in the title) take the form of a finite-dimensional system of nonlinear ordinary differential equations coupling quasi-velocities of the rigid body motions and generalized coordinates responsible for displacements of the natural sloshing modes. Algorithms for computing the hydrodynamic coefficients in the approximate mathematical models are proposed. Numerical values of these coefficients are listed for some tank shapes and liquid fillings. The mathematical models are also derived for the contained liquid characterized by the Newton-type dissipation. Formulas for hydrodynamic force and moment are derived in terms of the solid body quasi-velocities and the sloshing-related generalized coordinates. For prescribed harmonic excitations of upright circular (annular) cylindrical and/or conical tanks, the steady-state sloshing regimes are theoretically classified; the results are compared with known experimental data. The book can be useful for both experienced and early-stage mechanicians, applied mathematicians and engineers interested in (semi-)analytical approaches to the "fluid-structure" interaction problems, their fundamental mathematical background as well as in modeling the dynamics of complex mechanical systems containing a rigid tank partly filled by a liquid. 410 0$aDe Gruyter studies in mathematical physics ;$v27. 606 $aDynamics 606 $aDynamics, Rigid 606 $aNonlinear theories 608 $aElectronic books. 615 0$aDynamics. 615 0$aDynamics, Rigid. 615 0$aNonlinear theories. 676 $a003.75 700 $aLukovsky$b Ivan A.$01055970 702 $aMalyshev$b Peter V. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910460418903321 996 $aNonlinear dynamics$92489966 997 $aUNINA