The three-dimensional problem of the coupled time-harmonic motion of a freely floating body and water covered by brash ice

2016 ◽  
Author(s):  
Nikolay G. Kuznetsov ◽  
Oleg V. Motygin
Keyword(s):  
Three Dimensional ◽  
Floating Body ◽  
Dimensional Problem ◽  
Harmonic Motion ◽  
Time Harmonic

Inverse scattering for geophysical problems. III. On the velocity-in version problems of acoustics

1985 ◽  
Vol 399 (1816) ◽  
pp. 153-166 ◽  
Keyword(s):  
Speed Of Sound ◽  
Three Dimensional ◽  
Acoustic Medium ◽  
Inversion Problem ◽  
Dimensional Problem ◽  
Velocity Inversion ◽  
One Dimensional ◽  
Time Harmonic ◽  
Acoustic Media ◽  
Unknown Region

A bounded inhomogeneity D is immersed in an acoustic medium; the speed of sound is a function of position in D , and is constant outside. A time-harmonic source is placed at a point y and the pressure at a point x is measured. Given such measurements at all for all x ∈ P , for all y ∈ P where P is a plane that does not intersect D , can the speed of sound (in the unknown region D ) be recovered? This is a velocity-inversion problem. The three-dimensional problem has been solved analytically by Ramm ( Phys. Lett . 99A, 258-260 (1983)). In the present paper, analogous one-dimensional and two-dimensional problems are solved, as well as the problem where the plane P is the interface between two different acoustic media.

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.

Resonant and non-resonant acoustic properties of elastic panels. I. The radiation problem

1986 ◽  
Vol 406 (1831) ◽  
pp. 139-171 ◽  
Keyword(s):  
Power Flow ◽  
Three Dimensional ◽  
Acoustic Properties ◽  
Dimensional Problem ◽  
Harmonic Force ◽  
Asymptotic Results ◽  
Previous Theory ◽  
Near Resonance ◽  
Time Harmonic ◽  
Transition Formula

An elastic panel is excited by a time harmonic force and the power flow is calculated, averaged over a frequency band and all source positions. The two-dimensional problem is investigated asymptotically, for frequencies that are sufficiently high to ensure that many panel modes are near resonance. The asymptotic results are different according as the frequency is above or below the coincidence value; in the latter case account has to be taken of both resonance and non-resonance contributions to the power flow. A transition formula is given for frequencies near coincidence and the results agree well with numerical calculations. Corresponding results are given for the three-dimensional problem of the rectangular panel and previous theory is justified and extended.

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

Three-dimensional time-harmonic elastodynamic Green ’ s functions for anisotropic solids

1995 ◽  
Vol 449 (1937) ◽  
pp. 441-458 ◽  
Keyword(s):  
Differential Equations ◽  
Radon Transform ◽  
Transverse Isotropy ◽  
Three Dimensional ◽  
Surface Integral ◽  
Line Integral ◽  
Surface Integration ◽  
Time Harmonic ◽  
Inverse Radon Transform ◽  
Eigenvectors And Eigenvalues

A method based on the Radon transform is presented to determine the displacement field in a general anisotropic solid due to the application of a time-harmonic point force. The Radon transform reduces the system of coupled partial differential equations for the displacement components to a system of coupled ordinary differential equations. This system is reduced to an uncoupled form by the use of properties of eigenvectors and eigenvalues. The resulting simplified system can be solved easily. A back transformation to the original coordinate system and a subsequent application of the inverse Radon transform yields the displacements as a summation of a regular elastodynamic term and a singular static term. Both terms are integrals over a unit sphere. For the regular dynamic term, the surface integration can be evaluated numerically without difficulty. For the singular static term, the surface integral has been reduced to a line integral over half a unit circle. Reductions to the cases of isotropy and transverse isotropy have been worked out in detail. Examples illustrate applications of the method.

Numerical Research on FPSOs With Green Water Occurrence

2009 ◽  
Vol 53 (01) ◽  
pp. 7-18
Author(s):  
Renchuan Zhu ◽  
Guoping Miao ◽  
Zhaowei Lin
Keyword(s):  
Three Dimensional ◽  
Green Water ◽  
Floating Body ◽  
Incoming Wave ◽  
Model Case ◽  
Floating Structures ◽  
Design And Optimization ◽  
Head Waves ◽  
Wave Heights ◽  
The Impact

Green water loads on sailing ships or floating structures occur when an incoming wave significantly exceeds freeboard and water runs onto the deck. In this paper, numerical programs developed based on the platform of the commercial software Fluent were used to numerically model green water occurrence on floating structures exposed to waves. The phenomena of the fixed floating production, storage, and offloading unit (FPSO) model and oscillating vessels in head waves have been simulated and analyzed. For the oscillating floating body case, a combination idea is presented in which the motions of the FPSO are calculated by the potential theory in advance and computional fluid dynamics (CFD) tools are used to investigate the details of green water. A technique of dynamic mesh is introduced in a numerical wave tank to simulate the green water occurrence on the oscillating vessels in waves. Numerical results agree well with the corresponding experimental results regarding the wave heights on deck and green water impact loads; the two-dimensional fixed FPSO model case conducted by Greco (2001), and the three-dimensional oscillating vessel cases by Buchner (2002), respectively. The research presented here indicates that the present numerical scheme and method can be used to actually simulate the phenomenon of green water on deck, and to predict and analyze the impact forces on floating structures due to green water. This can be of great significance in further guiding ship design and optimization, especially in the strength design of ship bows.

Some Remarks on the Behaviour of Surface Source Distributions near the Edge of a Body

1973 ◽  
Vol 24 (1) ◽  
pp. 25-33
Author(s):  
J W Craggs ◽  
K W Mangler ◽  
M Zamir
Keyword(s):  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Symmetric Case ◽  
The Body ◽  
Dimensional Problem ◽  
Surface Source ◽  
Asymmetric Case ◽  
Main Flow Direction ◽  
Flow Plane

SummaryWhen the incompressible potential flow past a three-dimensional body is represented by source distributions on the body surface, these source distributions have singularities near an edge or corner, for example á trailing edge of a wing or the (unfaired) intersection of a body and a wing. The nature of these singularities is discussed. When assuming slow variations of the geometry in the main flow direction we can consider a two-dimensional problem in the cross-flow plane. Here the tangential velocities and source distributions are proportional to certain powers of the distance from the corner. For example at a convex right-angled corner these powers are − ⅓ in the asymmetric case (the bisector is a potential line) and ⅓ in the symmetric case (the bisector is a streamline) for both sources and tangential velocities. At a concave right-angled corner the corresponding values for the source distributions are ⅓ (asymmetric case) and − ⅓ (symmetric case) whereas they are 1 and 3 respectively for the tangential velocities.

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