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.

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.

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.

scholarly journals Global Dynamics Behaviors of Viral Infection Model for Pest Management

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Chunjin Wei ◽  
Lansun Chen
Keyword(s):  
Small Amplitude ◽  
Critical Value ◽  
Infection Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Virus Particles ◽  
All Solutions ◽  
Pest Eradication ◽  
Viral Infection Model

According to biological strategy for pest control, a mathematical model with periodic releasing virus particles for insect viruses attacking pests is considered. By using Floquet's theorem, small-amplitude perturbation skills and comparison theorem, we prove that all solutions of the system are uniformly ultimately bounded and there exists a globally asymptotically stable pest-eradication periodic solution when the amount of virus particles released is larger than some critical value. When the amount of virus particles released is less than some critical value, the system is shown to be permanent, which implies that the trivial pest-eradication solution loses its stability. Further, the mathematical results are also confirmed by means of numerical simulation.

Classification of U(1)-vortices with target ℂN

2015 ◽  
Vol 26 (13) ◽  
pp. 1550109 ◽  
Author(s):  
Guangbo Xu
Keyword(s):  
Complex Plane ◽  
Moduli Spaces ◽  
Finite Energy ◽  
Adiabatic Limit ◽  
Target Space ◽  
Vortex Equation ◽  
All Solutions

We study the symplectic vortex equation over the complex plane, for the target space [Formula: see text] ([Formula: see text]) with diagonal [Formula: see text]-action. Using adiabatic limit argument, we classify all solutions with finite energy and identify their moduli spaces, which generalizes Taubes’ result for [Formula: see text].

Nonlinear analysis of sloshing and floating body coupled motion in the time-domain

2018 ◽  
Vol 164 ◽  
pp. 350-366 ◽  
Author(s):  
Shuo Huang ◽  
Wenyang Duan ◽  
Xuliang Han ◽  
Ryan Nicoll ◽  
Yage You ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Time Domain ◽  
Floating Body ◽  
Coupled Motion ◽  
The Time Domain

Parametric subharmonic instability of internal waves: locally confined beams versus monochromatic wavetrains

2014 ◽  
Vol 757 ◽  
pp. 381-402 ◽  
Author(s):  
Hussain H. Karimi ◽  
T. R. Akylas
Keyword(s):  
Small Amplitude ◽  
Evolution Equations ◽  
Plane Waves ◽  
Inviscid Limit ◽  
Short Scale ◽  
Time Harmonic ◽  
Minimum Number ◽  
Boussinesq Fluid ◽  
Parametric Subharmonic Instability ◽  
Triad Interactions

AbstractInternal gravity wavetrains in continuously stratified fluids are generally unstable as a result of resonant triad interactions which, in the inviscid limit, amplify short-scale perturbations with frequency equal to one half of that of the underlying wave. This so-called parametric subharmonic instability (PSI) has been studied extensively for spatially and temporally monochromatic waves. Here, an asymptotic analysis of PSI for time-harmonic plane waves with locally confined spatial profile is made, in an effort to understand how such wave beams differ, in regard to PSI, from monochromatic plane waves. The discussion centres upon a system of coupled evolution equations that govern the interaction of a small-amplitude wave beam with short-scale subharmonic wavepackets in a nearly inviscid uniformly stratified Boussinesq fluid. For beams with general localized profile, it is found that triad interactions are not strong enough to bring about instability in the limited time that subharmonic perturbations overlap with the beam. On the other hand, for quasi-monochromatic wave beams whose profile comprises a sinusoidal carrier modulated by a locally confined envelope, PSI is possible if the beam is wide enough. In this instance, a stability criterion is proposed which, under given flow conditions, provides the minimum number of carrier wavelengths a beam of small amplitude must comprise for instability to arise.

scholarly journals Abnormal stresses in underground pipeline due to static and dynamic reversal of several foundation blocks

2020 ◽  
pp. 53-60
Author(s):  
M.I. Vaskovskyi ◽  
A. B. Struk ◽  
M. V. Makoviichuk ◽  
I. P. Shatskyi
Keyword(s):  
Equivalent Stress ◽  
Normal Pressure ◽  
Forced Oscillations ◽  
Underground Pipeline ◽  
Harmonic Oscillations ◽  
Time Harmonic ◽  
Block Foundation ◽  
Solid Foundation ◽  
Ultimate Equilibrium ◽  
Linear Setting

The article discusses the issues of forecasting the strength of underground pipelines laid in seismically active areas through sections composed of relatively rigid moving blocks. In such dangerous areas, in addition to the normal pressure load of the transported product, the pipe is subjected to additional effects from the movements of the fragments of the block foundation. As the literature data show, the problems of the influence of the interaction of faults on the stress state of the pipeline have not yet been studied. The aim of the study is to develop a model for the analysis of abnormal stresses in the underground pipeline on a damaged foundation caused by static or time-harmonic reciprocal turns of the blocks around the axis of the pipe on both sides of several faults. Static equilibrium and harmonic oscillations of the pipeline are investigated in a linear setting, modelling it with a rod with an annular cross section. The inertia of the transported product is not taken into account. To consider the issues of the ultimate equilibrium of the pipe, the momentless theory of shells and the energy theory of strength are used. The soil backfill is considered as Winkler’s elastic layer. Multiple damages to the solid foundation are presented in the form of several faults on which there is a rupture of the angle of rotation around the axis of the pipe. We formulated boundary value problems for differential equations of static torsion and torsional harmonic oscillations with discontinuous right-hand sides. Based on the analytical solutions of these problems for the cases of antisymmetric and symmetrical reversal of the foundation blocks, the distributions of the torsion angle and equivalent stress in the pipe, depending on the distance between faults and the frequency of forced oscillations of the system, are investigated.

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