Control of a Rotating Rigid Body Containing a Fluid with Free Surface

2013 ◽  
pp. 49-72
Keyword(s):  
Free Surface ◽  
Rigid Body

Boussinesq's problem for a flat-ended cylinder

1946 ◽  
Vol 42 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Elastic Medium ◽  
Normal Displacement ◽  
Full Account ◽  
Elastic Stresses ◽  
Special Cases ◽  
Cylindrical Punch ◽  
Distribution Of Stress ◽  
Boussinesq’S Problem

1. In a recent paper(1) expressions were found for the elastic stresses produced in a semi-infinite elastic medium when its boundary is deformed by the pressure against it of a perfectly rigid body. In deriving the solution of this problem—the ‘Boussinesq’ problem—it was assumed that the normal displacement of a point within the area of contact between the elastic medium and the rigid body is prescribed and that the distribution of pressure over that area is determined subsequently. The solutions for the special cases in which the free surface was indented by a cone, a sphere and a flat-ended cylindrical punch were derived, but no attempt was made to give a full account of the distribution of stress in the interior of the medium in any of these cases.

Validation of Open-Source SPH Code DualSPHysics for Numerical Simulations of Water Entry and Exit of a Rigid Body

2017 ◽  
Author(s):  
Sergei K. Buruchenko ◽  
Ricardo B. Canelas
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Stokes Equations ◽  
Offshore Structures ◽  
Water Entry ◽  
Surface Flow ◽  
Rigid Body Dynamics ◽  
Structural Safety ◽  
Entry And Exit ◽  
Momentum Exchange

Water entry and exit of a body is an important topic in naval hydrodynamics as these phenomena play relevant roles both for offshore structures and vessels. Water entry and exit events are intrinsically transient and represent intense topological changes in the system, with large amounts of momentum exchange between phases. At its onset, they can be characterized by highly localized, both in space and time, loads on the vessel, influencing both the local structural safety of the structure and the global loads acting on it. The DualSPHysics code is proposed as a numerical tool for the simulation of fluid and floating object interaction. The numerical model is based on a Smoothed Particle Hydrodynamics discretization of the Navier-Stokes equations and Newton’s equations for rigid body dynamics. This paper examines the water impact, fluid motions, and movement of objects in the conventional case studies of object entry and exit from still water. A two dimensional body drop analysis was carried out demonstrating acceptable agreement of the movement of the object with published experimental and numerical results. The velocity field of the fluid is also captured and analyzed. Simulations for water entry and exit of a buoyant and neutral density cylinder compares well with previous experimental, numerical, and empirical studies in penetration, free surface evolution and object kinematics. These results provide a good foundation to evaluate the accuracy and stability of the DualSPHysics implementation for modeling the interaction between free surface flow and free moving floating objects.

Centrifugal waves

1960 ◽  
Vol 7 (3) ◽  
pp. 340-352 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Free Surface ◽  
Angular Velocity ◽  
Circular Cylinder ◽  
Rigid Body ◽  
Water Depth ◽  
Frequency Equation ◽  
Rigid Rotation ◽  
Body Motion ◽  
Small Perturbations ◽  
The Stability

When a hollow circular cylinder with its axis horizontal is partially filled with water and rotated rapidly about its axis, an almost rigid-body motion results with an interior free surface. The emotion is analysed assuming small perturbations to a rigid rotation, and a criterion is found for the stability of the motion. This is confirmed experimentally under varying conditions of water depth and angular velocity of the cylinder. The modes of oscillation (centrifugal waves) of the free surface are examined and a frequency equation deduced. Two particular modes are considered in detail, and satisfactory agreement is found with the frequencies observed.

On the harmonic oscillations of a rigid body on a free surface

1965 ◽  
Vol 21 (3) ◽  
pp. 427-451 ◽  
Author(s):  
W. D. Kim
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Rigid Body ◽  
Potential Problem ◽  
Harmonic Oscillation ◽  
Added Mass ◽  
The Body ◽  
Rigorous Solution ◽  
Damping Coefficients

The present paper deals with the practical and rigorous solution of the potential problem associated with the harmonic oscillation of a rigid body on a free surface. The body is assumed to have the form of either an elliptical cylinder or an ellipsoid. The use of Green's function reduces the determination of the potential to the solution of an integral equation. The integral equation is solved numerically and the dependency of the hydrodynamic quantities such as added mass, added moment of inertia and damping coefficients of the rigid body on the frequency of the oscillation is established.

Some Plastic Deformation Modes for Indentation of Half Space by a Rigid Body With Serrated Surface as a Model of Roughness Transfer in Metal Forming

2002 ◽  
Vol 124 (2) ◽  
pp. 146-151 ◽  
Author(s):  
Jingyu Shi ◽  
D. L. S. McElwain ◽  
S. A. Domanti
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Free Surface ◽  
Rigid Body ◽  
Half Space ◽  
Metal Forming ◽  
Forming Process ◽  
Perfectly Plastic ◽  
Metal Forming Process ◽  
Deformation Modes

This paper is concerned with the plastic deformation modes of the free surface of the half space between the teeth on the serrated surface of a rigid body. The rigid body indents the half space perpendicularly and the material of the half space is assumed to be elastic/rigid perfectly plastic. Plane-strain conditions are assumed. The emphasis in this paper is on the profile left on the surfaces of the material when the indentation proceeds to some depth and then the indenter is removed. Based on the observations from finite element results, slip line fields for the plastic deformation regions at various stages of indentation are proposed and the corresponding hodographs for the velocity field are presented. This has application in roughness transfer of final metal forming process.

Lagrangian Expressions of the Hydrodynamic Forces Acting on a Rigid Body in the Presence of a Free Surface

1985 ◽  
Vol 29 (01) ◽  
pp. 12-22
Author(s):  
G. A. Athanassoulis ◽  
T. A. Loukakis
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Hydrodynamic Pressure ◽  
Hydrodynamic Forces ◽  
Ship Motions ◽  
Analytical Dynamics ◽  
Motion Equations ◽  
Hydromechanical System ◽  
Complete Set ◽  
Virtual Velocity

The formalism of classical analytical dynamics is used in conjunction with the principle of virtual velocity to derive Lagrangian expressions for the hydrodynamic forces acting on a rigid body moving through an in-viscid and incompressible liquid with a free surface. Simultaneously, a corresponding Lagrangian expression is derived for the hydrodynamic pressure acting on the free surface itself. The expressions for the hydrodynamic forces degenerate to the classical ones if the free surface is not present, and the expression for the pressure is reduced to that obtained by Milder if the rigid boundaries are all kept fixed. The derived Lagrangian expressions for the hydrodynamic reactions are used to obtain a complete set of motion equations for the examined hydromechanical system, and to discuss another Lagrangian approach to the ship-motions problem, presented by Wang.

Transformation of Arbitrary Elastic Mode Shapes Into Pseudo-Free-Surface and Rigid Body Modes for Multibody Dynamic Systems

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Karim Sherif ◽  
Hans Irschik ◽  
Wolfgang Witteveen
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Mode Shape ◽  
Frame Of Reference ◽  
Mode Shapes ◽  
Surface Mode ◽  
Elastic Mode ◽  
Surface Modes ◽  
Rigid Body Modes ◽  
Floating Frame

In multibody dynamics, the flexibility effects of each body are captured by using a linear combination of elastic mode shapes. If a co-rotational and co-translating frame of reference is used together with eigenvectors of the unconstraint body, which are free-surface modes, some spatial integrals in the floating frame of reference configuration do vanish. The corresponding coordinate system is the so-called Tisserand (or Buckens) reference frame. In the present contribution, a technique is developed for separating an arbitrary elastic mode shape into a pseudo-free-surface mode and rigid body modes. The generated pseudo-free-surface mode has most of the advantageous characteristics of a free-surface mode, and spans together with the rigid body modes the same solution space as it is spanned by the original mode shape. Due to the fact that, in the floating frame of reference configuration, the rigid body motions are already described by special generalized coordinates, only the resulting pseudo-free-surface modes are finally used to capture the flexibility effects of each body. A result of the generated pseudo-free-surface modes is that some of the spatial integrals do vanish and, thus, the equations of motion are significantly simplified. Two examples are presented in order to illustrate and to demonstrate the potential of the proposed method.

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