scholarly journals Combined motion of reservoir with liquid for angular motions of carrying body

2009 ◽  
Vol 31 (2) ◽  
pp. 103-121
Author(s):  
Oleg S. Limarchenko
Keyword(s):  
Free Surface ◽  
Variational Principle ◽  
Boundary Conditions ◽  
Variational Formulation ◽  
Discrete Model ◽  
Wave Motion ◽  
Ideal Liquid ◽  
Combined Motion ◽  
Liquid Free Surface ◽  
Pendulum Suspension

We consider peculiarities of the modeling of wave motion of ideal liquid in a reservoir, which performs inclined motions. For description of behavior of the system we use variational formulation of the problem on the basis of the Hamilton-Ostrogradskiy variational principle with preliminary satisfying all kinematic boundary conditions of the problem. It is shown that this approach makes it possible to reduce considerably the number of unknowns of the problem and reduce it description only to parameters of motion of a liquid free surface and parameters of motion of a carrying body. The constructed nonlinear discrete model of the system was applied for investigation of motion of a reservoir with liquid on pendulum suspension, on taking into account liquid outflow and other problems, which have theoretical and applied meaning.

scholarly journals Incorporating arbitrary basal topography in the variational formulation of ice-sheet models

2011 ◽  
Vol 57 (203) ◽  
pp. 461-467 ◽  
Author(s):  
John K. Dukowicz ◽  
Stephen F. Price ◽  
William H. Lipscomb
Keyword(s):  
Boundary Condition ◽  
Variational Principle ◽  
Boundary Conditions ◽  
Variational Formulation ◽  
Ice Sheet ◽  
Approximate Model ◽  
Dirichlet Condition ◽  
Natural Boundary Condition ◽  
Natural Boundary ◽  
Basal Sliding

AbstractThere are many advantages to formulating an ice-sheet model in terms of a variational principle. In particular, this applies to the specification of boundary conditions, which might otherwise be problematic to implement. Here we focus primarily on the frictional basal sliding boundary condition in a non-Newtonian Stokes model. This type of boundary condition is particularly difficult because it is heterogeneous, requiring both a Dirichlet (no-penetration) condition normal to the bed, and a Neumann (frictional sliding) condition tangential to the bed. In general, Neumann conditions correspond to natural boundary conditions in a variational principle; that is, they arise naturally in the variational formulation and thus need not be explicitly specified. While the same is not necessarily true of Dirichlet conditions, it is possible to enforce a no-penetration condition using Lagrange multipliers within the variational principle so that the Dirichlet condition becomes a natural boundary condition. Thus, in the case of ice sheets, all relevant boundary conditions may be incorporated in the variational functional, making them particularly easy to discretize. For the Stokes model, the resulting basal boundary condition is valid for arbitrary topographic slopes. Here we apply the same methodology to the Blatter– Pattyn higher-order approximate model, which is ordinarily limited to small basal slopes by the smallaspect-ratio approximation. We introduce a modification that improves on the accuracy of the standard Blatter–Pattyn model for all values of the basal slope, as we demonstrate in the slow sliding regime for which analytical results are available. The remaining error is due to the effects of the small-aspect-ratio approximation in the Blatter–Pattyn model.

Effect of Gravity on a Free-Free Fluid-Structure System

2002 ◽  
Author(s):  
Jean-Se´bastien Schotte´ ◽  
Roger Ohayon
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Gravity Field ◽  
Strong Coupling ◽  
Variational Formulation ◽  
Free Fluid ◽  
Inviscid Liquid ◽  
Liquid Free Surface ◽  
Rigid Body Modes ◽  
Elastic Tank

In this paper, we propose a symmetric variational formulation for the eigenmode computation of a free-free elastic tank partially filled with an incompressible inviscid liquid in presence of a gravity field. The originality of this model is to take into account the strong coupling between the sloshing of the liquid free surface and the hydroelastic deformations of the tank. We will show that this allows the rigid body modes of the system to be predicted correctly.

scholarly journals A NEW VARIATIONAL FORMULATION FOR CONVEX HAMILTONIAN SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS

2011 ◽  
Vol 84 (2) ◽  
pp. 186-204 ◽  
Author(s):  
MARK LEWIS ◽  
ABBAS MOAMENI
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Hamiltonian Systems ◽  
Variational Formulation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Second Order ◽  
Second Order Hamiltonian Systems ◽  
New Formulation

AbstractA variational principle is established to provide a new formulation for convex Hamiltonian systems. Using this formulation, we obtain some existence results for second-order Hamiltonian systems with a variety of boundary conditions, including nonlinear ones.

scholarly journals Acoustic radiation force effect on a spherical drop placed in the vicinity of an ideal liquid free surface

2019 ◽  
pp. 50-53
Author(s):  
O. P. Zhuk ◽  
Y. A. Zhuk
Keyword(s):  
Free Surface ◽  
Sound Wave ◽  
Incident Wave ◽  
Acoustic Pressure ◽  
Acoustic Radiation ◽  
Radiation Force ◽  
Ideal Liquid ◽  
Acoustic Radiation Force ◽  
Spherical Drop ◽  
Liquid Free Surface

Acoustic radiation force effect on a liquid spherical drop placed in the vicinity of an ideal liquid free surface is studied. The problem of determination of the radiation forces acting on an obstacle in ideal liquid is formulated with respect to the Lagrange coordinate system. Thus, the radiation pressure is defined as time-averaged value of the acoustic pressure over the obstacle surface. This approach is adequate if, at determining of the acoustic pressure in a fluid, the deviation of the pressure from the harmonic law in time domain is taken into account in the obstacle vicinity. An action of the acoustic radiation force on a spherical drop of ideal liquid placed in turn in a liquid by its free plane surface is studied here for the case of the incident plane sound wave propagating perpendicularly to the liquid boundary. As a result, the liquid sphere is appeared to be located in the standing sound wave of pressure which has its displacement node at the free surface. Problem solution is obtained as a three step procedure. Initially, solution of the problem of an incident wave scattering at the drop is derived. With making use of the results obtained, the second step encompasses determining of hydrodynamic forces acting on the liquid spherical drop with their subsequent averaging over the suitable time interval at the third step. It is found there frequencies of the incident wave exist that provide zero radiation force acting on the drop which is immobile in this case. These equilibrium positions of the spherical drop could be stable or unstable with respect to the incident wave frequency variation.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

scholarly journals Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 461
Author(s):  
Kenta Oishi ◽  
Yoshihiro Shibata
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mhd Flow ◽  
Transmission Conditions ◽  
Well Posedness ◽  
Anisotropic Space ◽  
Free Boundary Conditions ◽  
Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On the free surface, free boundary conditions for MHD flow and transmission conditions for electromagnetic fields are imposed. We proved the local well-posedness in the general setting of domains from a mathematical point of view. The solutions are obtained in an anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) for the velocity field and in an anisotropic space Hp1((0,T),Lq)∩Lp((0,T),Hq2) for the magnetic fields with 2<p<∞, N<q<∞ and 2/p+N/q<1. To prove our main result, we used the Lp-Lq maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions, which have been obtained by Frolova and the second author.

scholarly journals Numerical Modeling of the Motion of the Flat Textile Structures

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Piotr Szablewski
Keyword(s):  
Numerical Modeling ◽  
Boundary Conditions ◽  
Discrete Model ◽  
Gravity Force ◽  
Dynamic Conditions ◽  
Textile Structure ◽  
Sewing Thread ◽  
Lagrange’S Equations ◽  
Lagrange's Equations ◽  
Time Boundary

In many problems from the field of textile engineering (e.g., fabric folding, motion of the sewing thread) it is necessary to investigate the motion of the objects in dynamic conditions, taking into consideration the influence of the forces of inertia and changing in the time boundary conditions. This paper deals with the model analysis of the motion of the flat textile structure using Lagrange's equations in two variants: without constraints and with constraints. The motion of the objects is under the influence of the gravity force. Lagrange's equations have been used for discrete model of the structure.

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