Theory of Short Wave Excitation

1986 ◽  
Vol 30 (03) ◽  
pp. 147-152
Author(s):  
Yong Kwun Chung
Keyword(s):  
Incident Wave ◽  
Characteristic Length ◽  
Finite Depth ◽  
Short Wave ◽  
The Body ◽  
Wave Number ◽  
Floating Body ◽  
Wave Excitation ◽  
Exciting Forces ◽  
Wave Exciting Forces

When the wavelength of the incident wave is short, the total surface potential on a floating body is found to be 2∅ i & O (m-l∅ i) on the lit surface and O (m-l∅ j) on the shadow surface where ~b i is the potential of the incident wave and m the wave number in water of finite depth. The present approximation for wave exciting forces and moments is reasonably good up to X/L ∅ 1 where h is the wavelength and L the characteristic length of the body.

Experimental Investigation of the First and Second Order Wave Exciting Forces on a Restrained Body in Long Crested Irregular Waves

2011 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
Suresh Rajendran ◽  
C. Guedes Soares
Keyword(s):  
Experimental Investigation ◽  
Transfer Functions ◽  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Irregular Waves ◽  
Numerical Predictions ◽  
Exciting Forces ◽  
Wave Exciting Forces

The paper presents an experimental investigation of the first order and second order wave exciting forces acting on a body of simple geometry subjected to long crested irregular waves. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is restrained from moving. Second order spectral analysis is applied to obtain the linear spectra, coherence spectra and cross bi-spectra of both the incident wave elevation and of the horizontal and vertical wave exciting forces. Then the linear and quadratic transfer functions (QTF) of the exciting forces are obtained. The QTF obtained from the analysis of irregular wave measurements are compared with results from experiments in bi-chromatic waves and with numerical predictions from a second order potential flow code.

scholarly journals The Exciting Forces on Fixed Bodies in Waves

1962 ◽  
Vol 6 (04) ◽  
pp. 10-17 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Wave Amplitude ◽  
Amplitude Ratio ◽  
Exciting Force ◽  
The Body ◽  
Forced Oscillations ◽  
Wave Number ◽  
Far Field ◽  
Two Dimensional ◽  
Calm Water ◽  
Exciting Forces

General expressions, originally given by Haskind, are derived for the exciting forces on an arbitrary fixed body in waves. These give the exciting forces and moments in terms of the far-field velocity potentials for forced oscillations in calm water and do not depend on the diffraction potential, or the disturbance of the incident wave by the body. These expressions are then used to compute the exciting forces on a submerged ellipsoid, and on floating two-dimensional ellipses. For the ellipsoid, the problem is solved using the far-field potentials, and detailed results and calculations are given for the roll moment. The other forces agree, for the special case of a spheroid, with earlier results obtained by Havelock. In the case of two-dimensional motion the exciting forces are related to the wave amplitude ratio A for forced oscillations in calm water, and this relation is used to compute the heave exciting force for several elliptic cylinders. Expressions are also given relating the damping coefficients and the exciting forces. A = wave amplitude A = wave-height ratio for forced oscillations(a1 a2 a3) = semi-axis of ellipsoidBij = damping coefficientsC4 = nondimensional roll exciting-force coefficientDj = virtual-mass coefficients, defined by equations (18) and (19)g = gravitational accelerationh = depth of submergencei = √ — 1j = index referring to direction of force or motionn(z) = spherical Bessel function, K = wave number, K = ω2/gPj = functions defined following equation (17)R = polar coordinateV, = velocity components (x, y, z) = Cartesian coordinatesαi = Green's integrals, defined by equation (20)β = angle of incidence of wave systemθ = polar coordinateρ= fluid densityφj = velocity potentialsω = circular frequency of encounter

scholarly journals Wave forces on three-dimensional floating bodies with small forward speed

1991 ◽  
Vol 227 ◽  
pp. 135-160 ◽  
Author(s):  
Jan Nossen ◽  
John Grue ◽  
Enok Palm
Keyword(s):  
Velocity Potential ◽  
The Body ◽  
Wave Forces ◽  
Forward Speed ◽  
Floating Bodies ◽  
Wave Drift ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Wave Drift Damping ◽  
The Mean

A boundary-integral method is developed for computing first-order and mean second-order wave forces on floating bodies with small forward speed in three dimensions. The method is based on applying Green's theorem and linearizing the Green function and velocity potential in the forward speed. The velocity potential on the wetted body surface is then given as the solution of two sets of integral equations with unknowns only on the body. The equations contain no water-line integral, and the free-surface integral decays rapidly. The Timman-Newman symmetry relations for the added mass and damping coefficients are extended to the case when the double-body flow around the body is included in the free-surface condition. The linear wave exciting forces are found both by pressure integration and by a generalized far-field form of the Haskind relations. The mean drift force is found by far-field analysis. All the derivations are made for an arbitrary wave heading. A boundary-element program utilizing the new method has been developed. Numerical results and convergence tests are presented for several body geometries. It is found that the wave exciting forces and the mean drift forces are most influenced by a small forward speed. Values of the wave drift damping coefficient are computed. It is found that interference phenomena may lead to negative wave drift damping for bodies of complicated shape.

An Analytical Solution of Wave Exciting Loads on CALM Buoy with Skirt

2013 ◽  
Vol 477-478 ◽  
pp. 254-258 ◽  
Author(s):  
Dong Jiao Wang ◽  
Shi Peng Sun
Keyword(s):  
Analytical Solution ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Wave Theory ◽  
Finite Depth ◽  
Validation Process ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
Matched Eigenfunction Expansions ◽  
Truncated Cylinder

Linearized potential wave theory is applied to calculate the wave exciting loads on a CALM buoy in water of finite depth. The solution is based on the domain decomposition method and the unknown constants in the velocity potentials are determined by matched eigenfunction expansions. A comparison of the analytical solution with published experimental results on a vertical truncated cylinder is performed as part of the validation process. The effects of the disk on the wave exciting forces are discussed.

Wave Drift Forces and Resonance Analysis on Two Ships Arranged Side by Side

2014 ◽  
Author(s):  
Yu Zhang ◽  
Dapeng Yu ◽  
Shixiao Fu ◽  
Fei Guo ◽  
Wei Wei
Keyword(s):  
Hydrodynamic Performance ◽  
Floating Body ◽  
Period Effects ◽  
Added Masses ◽  
Floating System ◽  
Exciting Forces ◽  
Wave Exciting Forces ◽  
The Difference ◽  
Wave Drift Forces ◽  
Multi Body

In recent years, with the development of new ships and further utilization of marine resources, multi-body floating systems are widely used in practice. Compared with the single floating body, the movement in multi-body floating system is not only affected by the external environment, but the interaction between the bodies cannot be neglected. So analysis of hydrodynamic performance of a multi-body floating system is of great importance. In this paper, a multi-body system consisting of two side-by-side ships is studied. The code AQWA® is used for its hydrodynamic performance analysis in frequency domain. Its hydrodynamic parameters are compared with those of the related single-ship system and the difference is obvious. The two-ship system shows a peak in motion different from single-ship system at some frequencies and its wave exciting forces have period effects. Also, negative values appear in added masses, which never occur for a single-body floating system. When the gap between the two ships is changed, there is a significant trend that the wave frequency of the peak value decreases with the gap size between the two ships. In addition, this paper also discussed the length of wave and distance of ships ratio that the motion resonance usually happens. Through the analysis of this dimensionless parameter, a conclusion about resonance between two parallel ships is deducted.

Radiation and diffraction by a submerged sphere advancing in water waves of finite depth

1995 ◽  
Vol 448 (1932) ◽  
pp. 29-54 ◽  
Keyword(s):  
Water Waves ◽  
Finite Depth ◽  
Multipole Expansion ◽  
The Body ◽  
Field Equations ◽  
Damping Coefficients ◽  
Submerged Sphere ◽  
Added Masses ◽  
Exciting Forces ◽  
Depth Water

A submerged sphere advancing in a regular finite depth water wave at constant forward speed is analysed by linearized velocity potential. The solution is ob­tained by the multipole expansion extended from that developed for zero speed. Numerical results are obtained for wave-making resistance and lift, added masses, damping coefficients and exciting forces. Far field equations are also derived for calculating damping coefficients and exciting forces. They are used to check the results obtained from integrating pressure over the body surface. Excellent agree­ment is found.

scholarly journals On the complete radiation-diffraction problem and wave-drift damping of marine bodies in the yaw mode of motion

1998 ◽  
Vol 357 ◽  
pp. 289-320 ◽  
Author(s):  
STYRK FINNE ◽  
JOHN GRUE
Keyword(s):  
Rotation Axis ◽  
Diffraction Problem ◽  
Slow Motion ◽  
Vertical Axis ◽  
The Body ◽  
Floating Body ◽  
Slow Rotation ◽  
Wave Drift ◽  
Exciting Forces ◽  
Wave Drift Damping

The coupled radiation-diffraction problem due to a floating body with slow (time-dependent) rotation about the vertical axis in incoming waves is studied by means of potential theory. The water depth may be finite. First, the radiation problem is described. It is shown how the various components of the velocity potential may be obtained by means of integral equations. The first-order forces in the coupled radiation-diffraction problem are then considered. Generalized Haskind relations for the exciting forces and generalized Timman–Newman relations for the added mass and damping forces are deduced for bodies of arbitrary shape with vertical walls at the water line. The equation of motion is obtained, and the frequencies of the linear body responses superposed on the slow rotation are identified. Formulae for the wave-drift damping coefficients in the yaw mode of motion are derived in explicit form, and the energy equation is discussed. Computations illustrating the various aspects of the method are performed for two ships. The wave-drift damping moment is found to become positive in the present examples. When the rotation axis is moved far away from the body, the slow motion becomes effectively unidirectional, and results of the translational case are recovered.

An approximate treatment of high-frequency scattering

1957 ◽  
Vol 53 (3) ◽  
pp. 691-701 ◽  
Author(s):  
D. S. Jones ◽  
G. B. Whitham
Keyword(s):  
Approximate Method ◽  
Energy Flux ◽  
Incident Wave ◽  
High Frequency ◽  
Harmonic Wave ◽  
Incident Beam ◽  
Scattered Wave ◽  
The Body ◽  
Scattering Coefficient ◽  
Wave Number

In some recent work Kodis* considers the scattering of a plane harmonic wave by a circular cylinder and uses variational methods to deduce an asymptotic formula for the scattering coefficient in the case of high-frequency waves. The scattering coefficient, σ, is denned as the total energy flux outward from the cylinder in the scattered wave divided by the energy flux in the beam of the incident wave which falls on the cylinder. In the limit, of geometrical optics, the scattered wave is made up of a wave reflected from the forward half of the cylinder with energy flux equal to that in the incident beam, and a wave behind the cylinder cancelling the incident wave there to form the shadow. Thus σ → 2 as ka → ∞, k being the wave number of the incident wave and a the radius of the cylinder. The next term in the asymptotic expansion for σ is proportional to . It has been determined already from the exact series expression for the field by White (6), Wu and Rubinow (7) and Kear (3). But Kodis gives an approximate method which also supplies this result and, since the coefficient is in good agreement with the values obtained from the exact solution, concludes that his approximate procedure could also be used for more general obstacles. In the present paper, we propose an alternative approximate method which is related to the one given by Kodis but is very much simpler. Also we go on to obtain the correction terms for general obstacles in detail. Various writers (see, for example, Keller (4) and van de Hulst(8)) have suggested previously that the correction is still proportional to , where a is some length defined by the body shape. However, the determination of a and of the numerical coefficient has been limited to two-dimensional obstacles.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

Drift Forces on a Floating Body of Simple Geometry Due to Second Order Interactions Between Pairs of Harmonics With Different Frequencies

2009 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Order Problem ◽  
Simple Geometry ◽  
The Mean ◽  
Order Quantities ◽  
Drift Forces

The paper presents an investigation of the slowly varying second order drift forces on a floating body of simple geometry. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom and a ratio of diameter to draft of 3.25. The hydrodynamic problem is solved with a second order boundary element method. The second order problem is due to interactions between pairs of incident harmonic waves with different frequencies, therefore the calculations are carried out for several difference frequencies with the mean frequency covering the whole frequency range of interest. Results include the surge drift force and pitch drift moment. The results are presented in several stages in order to assess the influence of different phenomena contributing to the global second order responses. Firstly the body is restrained and secondly it is free to move at the wave frequency. The second order results include the contribution associated with quadratic products of first order quantities, the total second order force, and the contribution associated to the free surface forcing.

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