On the coupled time-harmonic motion of water and a body freely floating in it

2011 ◽  
Vol 679 ◽  
pp. 616-627 ◽  
Author(s):  
NIKOLAY KUZNETSOV ◽  
OLEG MOTYGIN
Keyword(s):  
Boundary Value Problem ◽  
Small Amplitude ◽  
Three Dimensional ◽  
Water Layer ◽  
The Body ◽  
Body Motion ◽  
Constant Depth ◽  
Harmonic Motion ◽  
Time Harmonic ◽  
Equipartition Of Energy

We consider a spectral problem that describes the time-harmonic small-amplitude motion of the mechanical system that consists of a three-dimensional water layer of constant depth and a body (either surface-piercing or totally submerged), freely floating in it. This coupled boundary-value problem contains a spectral parameter – the frequency of oscillations – in the boundary conditions as well as in the equations governing the body motion. It is proved that the total energy of the water motion is finite and the equipartition of energy of the whole system is established. Under certain restrictions on body's geometry the problem is proved to have only a trivial solution for sufficiently large values of the frequency. The uniqueness frequencies are estimated from below.

Two-dimensional water waves in the presence of a freely floating body: trapped modes and conditions for their absence

2015 ◽  
Vol 779 ◽  
pp. 684-700 ◽  
Author(s):  
Nikolay Kuznetsov
Keyword(s):  
Water Waves ◽  
Small Amplitude ◽  
Floating Body ◽  
Two Dimensional ◽  
Trapped Modes ◽  
Constant Depth ◽  
Time Harmonic ◽  
Equipartition Of Energy ◽  
Linear Setting ◽  
Inverse Procedure

The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes. Under the assumption that the motion is of small amplitude near equilibrium, a linear setting is applicable, and for the time-harmonic oscillations it reduces to a spectral problem with the frequency of oscillations as the spectral parameter. Within this framework, it is shown that the total energy of the water motion is finite and the equipartition of energy holds for the whole system. On this basis two results are obtained. First, the so-called semi-inverse procedure is applied for the construction of a family of two-dimensional bodies trapping the heave mode. Second, it is proved that no wave modes can be trapped provided that their frequencies exceed a bound depending on the cylinder properties, whereas its geometry is subject to some restrictions and, in some cases, certain restrictions are imposed on the type of mode.

On the coupled time-harmonic motion of deep water and a freely floating body: trapped modes and uniqueness theorems

2012 ◽  
Vol 703 ◽  
pp. 142-162 ◽  
Author(s):  
Nikolay Kuznetsov ◽  
Oleg Motygin
Keyword(s):  
Small Amplitude ◽  
Velocity Potential ◽  
The Body ◽  
Floating Body ◽  
Trapped Modes ◽  
Dimensionless Quantity ◽  
Time Harmonic ◽  
Equipartition Of Energy ◽  
Zero Vector ◽  
Inverse Procedure

AbstractWe investigate the time-harmonic small-amplitude motion of the mechanical system that consists of water and a body freely floating in it; water occupies a half-space, whereas the body is either surface-piercing or totally submerged. As a mathematical model of this coupled motion, we consider a spectral problem (the spectral parameter is the frequency of oscillations), for which the following results are obtained. The total energy of the water motion is finite and the equipartition of energy holds for the whole system. For any value of frequency, infinitely many eigensolutions are constructed and each of them consists of a non-trivial velocity potential and the zero vector describing the motion of the body; the latter means that trapping bodies (infinitely many of them are found) are motionless although they float freely. They are surface-piercing, have axisymmetric submerged parts and are obtained by virtue of the so-called semi-inverse procedure. We also prove that certain restrictions on the body geometry (which are violated for the constructed trapping bodies) guarantee that the problem has only a trivial solution for frequencies that are sufficiently large being measured in terms of a certain dimensionless quantity.

ENVELOPING SURFACES AND ADMISSIBLE VELOCITIES OF HEAVY RIGID BODIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2525-2553 ◽  
Author(s):  
IGOR N. GASHENENKO ◽  
PETER H. RICHTER
Keyword(s):  
Three Dimensional ◽  
Rigid Bodies ◽  
First Integrals ◽  
The Body ◽  
Heegaard Splitting ◽  
Body Motion ◽  
Invariant Sets ◽  
Poisson Problem ◽  
Integral Manifolds ◽  
Angular Velocities

The general Euler-Poisson problem of rigid body motion is investigated. We study the three-dimensional algebraic level surfaces of the first integrals, and their topological bifurcations. The main result of this article is an analytical and qualitatively complete description of the projections of these integral manifolds to the body-fixed space of angular velocities. We classify the possible types of these invariant sets and analyze the dependence of their topology on the parameters of the body and the constants of the first integrals. Particular emphasis is given to the enveloping surfaces of the sets of admissible angular velocities. Their pre-images in the reduced phase space induce a Heegaard splitting which lends itself for a general choice of complete Poincaré surfaces of section, irrespective of whether or not the system is integrable.

scholarly journals Skimming impacts and rebounds of smoothly shaped bodies on shallow liquid layers

2020 ◽  
Vol 124 (1) ◽  
pp. 41-73
Author(s):  
Ryan A. Palmer ◽  
Frank T. Smith
Keyword(s):  
Shallow Water ◽  
Liquid Layer ◽  
Contact Point ◽  
Water Layer ◽  
Small Time ◽  
The Body ◽  
Body Motion ◽  
Water Model ◽  
Initial Contact ◽  
Trailing Edge

Abstract Investigated in this paper is the coupled fluid–body motion of a thin solid body undergoing a skimming impact on a shallow-water layer. The underbody shape (the region that makes contact with the liquid layer) is described by a smooth polynomic curve for which the magnitude of underbody thickness is represented by the scale parameter C. The body undergoes an oblique impact (where the horizontal speed of the body is much greater than its vertical speed) onto a liquid layer with the underbody’s trailing edge making the initial contact. This downstream contact point of the wetted region is modelled as fixed (relative to the body) throughout the skimming motion with the liquid layer assumed to detach smoothly from this sharp trailing edge. There are two geometrical scenarios of interest: the concave case ($$C<0$$ C < 0 producing a hooked underbody) and the convex case ($$C > 0$$ C > 0 producing a rounded underbody). As C is varied the rebound dynamics of the motion are predicted. Analyses of small-time water entry and of water exit are presented and are shown to be broadly in agreement with the computational results of the shallow-water model. Reduced analysis and physical insights are also presented in each case alongside numerical investigations and comparisons as C is varied, indicating qualitative analytical/numerical agreement. Increased body thickness substantially changes the interaction structure and accentuates inertial forces in the fluid flow.

Hydrodynamics of larval fish quick turning: A computational study

2017 ◽  
Vol 232 (14) ◽  
pp. 2515-2523 ◽  
Author(s):  
Jialei Song ◽  
Yong Zhong ◽  
Haoxiang Luo ◽  
Yang Ding ◽  
Ruxu Du
Keyword(s):  
Larval Fish ◽  
Computational Study ◽  
Three Dimensional ◽  
Interaction Model ◽  
The Body ◽  
Body Motion ◽  
Body Interaction ◽  
Fluid Body ◽  
Preparatory Stage ◽  
Tangential Acceleration

A three-dimensional fluid–body interaction model was established to study the hydrodynamics of larval fish at a quick start with a turning angle of approximately 80°. The bending curves of the larval fish were attained by extracting the middle line of fish snapshots from a previously published paper. The fluid–body interaction was implemented to empower the self-propelling function of the larval fish. In this study, the swimmer’s kinematics of the body as well as hydrodynamics at preparatory and propulsive stages of the larval fish were extensively analysed. It shows that during the preparatory stage, the larval fish produces a significant force against the escaping direction. Nevertheless, this force leads to a large turning torque, helping to accomplish a quick turning. During the propulsive stage, the force increases quickly in the escape direction, resulting in a large velocity for the escape. The characteristics of body motion and the flow field are consistent with the previous observation on adult fish: the bimodal mode on velocity and tangential acceleration and three jets of fluids. In addition, the research also reveals that the forces generated at anterior and posterior parts of the larval fish generally point to the opposite directions at both preparatory and propulsive strokes of C-start.

On the coupled time-harmonic motion of a freely floating body and water covered by brash ice

2016 ◽  
Vol 795 ◽  
pp. 174-186 ◽  
Author(s):  
Nikolay Kuznetsov ◽  
Oleg Motygin
Keyword(s):  
Small Amplitude ◽  
Finite Interval ◽  
Finite Energy ◽  
Floating Body ◽  
Coupled Motion ◽  
Time Harmonic ◽  
All Solutions ◽  
Equipartition Of Energy ◽  
Linear Setting ◽  
Inverse Procedure

A mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium is considered. The water occupies a half-space into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes of the coupled motion, which is assumed to be of small amplitude. The corresponding linear setting for time-harmonic oscillations reduces to a spectral problem whose parameter is the frequency. A constant that characterises the brash ice divides the set of frequencies into two subsets and the results obtained for each of these subsets are essentially different. For frequencies belonging to a finite interval adjacent to zero, the total energy of motion is finite and the equipartition of energy holds for the whole system. For every frequency from this interval, a family of motionless bodies trapping waves is constructed by virtue of the semi-inverse procedure. For sufficiently large frequencies outside of this interval, all solutions of finite energy are trivial.

scholarly journals Water entry of a body which moves in more than six degrees of freedom

2015 ◽  
Vol 471 (2177) ◽  
pp. 20150058 ◽  
Author(s):  
Y.-M. Scolan ◽  
A. A. Korobkin
Keyword(s):  
Degrees Of Freedom ◽  
Early Stage ◽  
Three Dimensional ◽  
Vertical Displacement ◽  
Oblique Impact ◽  
Water Entry ◽  
The Body ◽  
Body Motion ◽  
Elliptic Paraboloid ◽  
Over Time

The water entry of a three-dimensional smooth body into initially calm water is examined. The body can move freely in its 6 d.f. and may also change its shape over time. During the early stage of penetration, the shape of the body is approximated by a surface of double curvature and the radii of curvature may vary over time. Hydrodynamic loads are calculated by the Wagner theory. It is shown that the water entry problem with arbitrary kinematics of the body motion, can be reduced to the vertical entry problem with a modified vertical displacement of the body and an elliptic region of contact between the liquid and the body surface. Low pressure occurrence is determined; this occurrence can precede the appearance of cavitation effects. Hydrodynamic forces are analysed for a rigid ellipsoid entering the water with 3 d.f. Experimental results with an oblique impact of elliptic paraboloid confirm the theoretical findings. The theoretical developments are detailed in this paper, while an application of the model is described in electronic supplementary materials.

Matrix Solution of Digitized Planar Human Body Dynamics for Biomechanics Laboratory Instruction

1992 ◽  
Author(s):  
David G. Alciatore ◽  
Lawrence D. Abraham ◽  
Ronald E. Barr
Keyword(s):  
Human Body ◽  
Body Position ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Iterative Solution ◽  
The Body ◽  
Body Motion ◽  
Laboratory Instruction ◽  
Matrix Formulation ◽  
Body Dynamics

Abstract The dynamics of planar human body motion, solved with a non-iterative matrix formulation, is presented. The approach is based on applying Newton-Euler equations of motion to an assumed 15 body segment model resulting in a system of 48 equations. The system of equations was carefully ordered to result in a banded system (bandwidth = 10) which is solved efficiently. The method is more favorable than a traditional iterative solution because it is more easily coded, reaction forces are more easily dealt with, and multiple solutions for a given body position can be readily obtained. The results described are limited to planar body motion but the method is easily extendible to general three-dimensional motion. A computer program was developed to process digitized body point coordinate data and calculate resultant joint forces and moments for each frame of data. This method of human body dynamics analysis was developed to support laboratory instruction for an Engineering Biomechanics course. Athletic activities are captured with a three-dimensional video digitizing system and the data is processed resulting in time histories of force and moment distributions throughout the body during the captured event. Computer software performs the analyses and provides real-time graphical illustrations of the kinematics and dynamics results. The dynamics results for the leg of a runner are presented here as an example of the application of the method.

Instantaneous center/axis of rotation for planar and three-dimensional motion

2021 ◽  
pp. 030641902110511
Author(s):  
Donald L Kunz
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Three Dimensional ◽  
The Body ◽  
Body Motion ◽  
Planar Motion ◽  
Instantaneous Axis Of Rotation ◽  
Axis Of Rotation ◽  
Instantaneous Center ◽  
Instantaneous Axis

This article discusses a direct analytical method for calculating the instantaneous center of rotation and the instantaneous axis of rotation for the two-dimensional and three-dimensional motion, respectively, of rigid bodies. In the case of planar motion, this method produces a closed-form expression for the instantaneous center of rotation based on a single point located on the rigid body. It can also be used to derive closed-form expressions for the body and space centrodes. For three-dimensional, rigid body motion, an extension of the technique used for planar motion locates a point on the instantaneous axis of rotation, which is parallel to the body angular velocity vector. In addition, methods are demonstrated that can be used to map the body and space cones for general rigid body motion, and locate the fixed point for the body.

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