By I.M. Rapoport

The motions of beverages in relocating packing containers represent a vast category of difficulties of significant functional value in lots of technical fields. The impression of the dynamics of the liquid at the motions of the box itself is a best and intricate element of the final topic, no matter if one considers in basic terms the rigid-body motions of the box or its elastic motions in addition. it truly is such a lot becoming accordingly that this translation of Professor Rapoport's e-book has been undertaken so in a timely fashion following its unique book, so one can make on hand this relatively specific account of the mathematical foundations underlying the remedy of such prob lems. on the grounds that so much of this giant physique of research has been constructed during the last decade via scientists within the USSR, and has as a result been largerly unavailable to these not able to learn Russian, this quantity will unquestionably be of significant worth to many folks. H.

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**Extra resources for Dynamics of Elastic Containers: Partially Filled with Liquid**

**Example text**

Leti7(x, y, z, t) and p (x, y, z, t) be functions found from Eqs. 19) for the given acceleration ;0 We shall show that when we replace the above (t). 38) According to Eqs. 19), we must establish the presence of identities V2 p* = 0 in V fV ; op' [ - * - d; 02U~] - - = - Q , (wo-g)·n+-·(rxn)+on dt ot2 onStv; op' o2p* -+- - m ~ ~ - = -Q, ~ 2C*] - d' on dt2 cr· '" [ -. 39) Cavities Partially Filled with an Ideal Fluid 51 and also of identities grad (~diV U*)+2div(G gradZ;*)+ 1-20 -. t* (-+:;: -. 42) Setting f= 1 in the first of Eqs.

2, supplementing this system of equations by the equations of the theory of elasticity (relating the latter function with the surface and volume Dynamics of Elastic Containers 30 forces aCing on the elastic body), we obtain a boundary-value problem which uniquely defines the functions u(x, g, z, t),p(x, g, z, t). W"o(t), and d;(t) according to the specified external forces, provided dt that certain boundary conditions are specified for the unknown functions u(x, g, z, t) and p{x, g, z, t). Let us consider the particular case when the solid body is absolutely rigid and its cavities contain nondeforming partitions which are placed in the cross sections of cavities O't.

17) (cont'd) According to Eqs. 17). Eqs. 10) can be written in the form [s JS QdV+~Q. (MJ dv+~I Pnds +~~' f. ds )] X X(g-;o)-~ X (SJS ~Qdv+ ~Q' IfJrd'V)- {SJS~~ Qdv+ ~ Q. ) X xiJ2jot2• dS]}+Fo+F(t)=O. 18) Q. :: ds-[SiS~x ~~ Qdv+ ~Q'x X (SS~o;~n ds+ SS;O;~; dS)] +M (t)=0 Stv cr. We now introduce vectorial functions of time grad 08at S~........ ) X ' on at + cr. 0-ot2' ds; 2 -+ -+ S tv StV -+ -+ 2/ cr. 08at dv= SS cp02uot2 ds+ anot ds= SS _n +Sj' . ot2 ds X grad-- -+ iJ28 Stv+ cr • -+ cr. cp -+ Stv 02/.