scholarly journals Resonance of a tension leg platform exited by third-harmonic force in nonlinear regular waves

2015 ◽  
Vol 373 (2033) ◽  
pp. 20140105 ◽  
Author(s):  
B. Z. Zhou ◽  
G. X. Wu
Keyword(s):  
Harmonic Wave ◽  
The Body ◽  
Initial Time ◽  
Wave Forces ◽  
Regular Waves ◽  
Harmonic Force ◽  
Tension Leg Platform ◽  
Incoming Wave ◽  
Third Harmonic ◽  
The Third

The resonance of a floating tension leg platform (TLP) excited by the third-harmonic force of a regular wave is investigated based on fully nonlinear theory with a higher order boundary element method (BEM). The total wave elevation and the total velocity potential are separated into two parts, based on the incoming wave from infinity and the disturbed potential by the body. A numerical radiation condition is then applied at the far field to absorb the disturbed potential without affecting the incident potential. The BEM mesh on the free surface is generated only once at the initial time and the element nodes are rearranged subsequently without changing their connectivity by using a spring analysis method. Through some auxiliary functions, the mutual dependence of fluid/structure motions is decoupled, which allows the body acceleration to be obtained without the knowledge of the pressure distribution. Numerical simulation is carried out for the interaction of a floating TLP with waves. The focus is on the motion principally excited by higher harmonic wave forces. In particular, the resonance of the ISSC TLP generated by the third-order force at the triple wave frequency in regular waves is investigated, together with the tensions of the tendons.

Wave Forcing and Wave Scattering From a Vertical Surface-Piercing Cylinder

2005 ◽  
Author(s):  
Chris Swan ◽  
Stephen Masterton ◽  
Rizwan Sheikh ◽  
Alessandra Cavalletti
Keyword(s):  
High Frequency ◽  
Harmonic Wave ◽  
Laboratory Data ◽  
Perturbation Expansion ◽  
Vertical Cylinder ◽  
Scattered Wave ◽  
Vertical Surface ◽  
The Body ◽  
Wave Forces ◽  
High Frequency Waves

This paper concerns the nonlinear, higher-harmonic, wave-forces acting on a vertical surface-piercing cylinder. New laboratory data is presented which confirms that in the case a vertical cylinder, the diameter of which is large but not sufficiently large that the body lies within the linear diffraction regime, the second- and third-harmonic forces are not well described by existing models. This is particularly apparent when the incident waves are steep and have a relatively small wave period. Indeed, under these conditions the second-, third- and fourth-harmonic forces are shown to be comparable in size. This is clearly at odds with the results of a traditional perturbation expansion. An explanation for this lies in the nature of the scattered wave field, particularly the high-frequency waves identified by Sheikh & Swan [1]. The phasing of these scattered waves are, at least in part, dependent upon the motion of the fluid around the circumference of the cylinder and will not therefore be captured by a series solution based solely on the harmonics of the incident wave motion. The paper considers several test cases, fully exploring the correlation between the nonlinear forcing and the high-frequency scattering. The practical implications of these results are also addressed.

An experimental investigation of higher-harmonic wave forces on a vertical cylinder

2000 ◽  
Vol 414 ◽  
pp. 75-103 ◽  
Author(s):  
MORTEN HUSEBY ◽  
JOHN GRUE
Keyword(s):  
Wave Amplitude ◽  
Harmonic Wave ◽  
Small Scale ◽  
Large Set ◽  
Harmonic Force ◽  
Incoming Wave ◽  
Wave Tank ◽  
Fully Nonlinear ◽  
Cylinder Radius ◽  
Higher Harmonic

First- and higher-harmonic wave loads on a vertical circular cylinder are investigated experimentally in a wave tank of small scale. The incoming waves are (periodic) Stokes waves with wave slope up to 0.24. A large set of waves which are long compared to the cylinder radius is calibrated. The first seven harmonic components of the measured horizontal force on the cylinder are analysed. The higher-harmonic forces are significantly smaller than the first-harmonic force for all wave parameters. The measurements are continued until the wave amplitude is comparable to the cylinder radius, where the second-, third- and fourth-harmonic forces become of comparable size. Comparison with existing perturbation and fully nonlinear models shows, with a few exceptions, an overall good agreement for small and moderate wave amplitude. A fully nonlinear model agrees with the experiments even up to the seventh-harmonic force for part of the amplitude range. For the large amplitudes the models mostly give conservative predictions. It is important that the distance from the wave maker to the cylinder is large in order to avoid parasitic effects in the incoming wave field. The limited width of the wave tank is not important to the results except when close to resonance.

Forcing of a bottom-mounted circular cylinder by steep regular water waves at finite depth

2014 ◽  
Vol 755 ◽  
pp. 1-34 ◽  
Author(s):  
Bo T. Paulsen ◽  
H. Bredmose ◽  
H. B. Bingham ◽  
N. G. Jacobsen
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Water Waves ◽  
Finite Depth ◽  
Load Cycle ◽  
Harmonic Force ◽  
Third Harmonic ◽  
The Third ◽  
Nonlinear Motion ◽  
Secondary Load

AbstractForcing by steep regular water waves on a vertical circular cylinder at finite depth was investigated numerically by solving the two-phase incompressible Navier–Stokes equations. Consistently with potential flow theory, boundary layer effects were neglected at the sea bed and at the cylinder surface, but the strong nonlinear motion of the free surface was included. The numerical model was verified and validated by grid convergence and by comparison to relevant experimental measurements. First-order convergence towards an analytical solution was demonstrated and an excellent agreement with the experimental data was found. Time-domain computations of the normalized inline force history on the cylinder were analysed as a function of dimensionless wave height, water depth and wavelength. Here the dependence on depth was weak, while an increase in wavelength or wave height both lead to the formation of secondary load cycles. Special attention was paid to this secondary load cycle and the flow features that cause it. By visual observation and a simplified analytical model it was shown that the secondary load cycle was caused by the strong nonlinear motion of the free surface which drives a return flow at the back of the cylinder following the passage of the wave crest. The numerical computations were further analysed in the frequency domain. For a representative example, the secondary load cycle was found to be associated with frequencies above the fifth- and sixth-harmonic force component. For the third-harmonic force, a good agreement with the perturbation theories of Faltinsen, Newman & Vinje (J. Fluid Mech., vol. 289, 1995, pp. 179–198) and Malenica & Molin (J. Fluid Mech., vol. 302, 1995, pp. 203–229) was found. It was shown that the third-harmonic forces were estimated well by a Morison force formulation in deep water but start to deviate at decreasing depth.

Generation and radiation of third harmonics by an electrostatic wave in a narrow inhomogeneous layer of a warm plasma

1991 ◽  
Vol 45 (2) ◽  
pp. 153-157 ◽  
Author(s):  
A. M. Hussein
Keyword(s):  
Nonlinear Interaction ◽  
Wave Process ◽  
Harmonic Wave ◽  
Higher Order ◽  
Inhomogeneous Layer ◽  
Electrostatic Wave ◽  
Third Harmonic ◽  
The Third ◽  
Initial Wave ◽  
Warm Plasma

An investigation is made of wave generation and the radiation of third harmonics by an electrostatic wave in a narrow inhomogeneous layer of a warm plasma. The amplitudes of the third-harmonic wave are calculated. It is found that they depend both on the nonlinear interaction of the initial waves and on the interaction of second harmonics with the initial wave. The generation of third harmonics by interaction of the initial waves is a four-wave process, i.e. a higher-order nonlinearity.

scholarly journals Resonant third harmonic generation in clusters with density ripple: Effect of pulse slippage

2016 ◽  
Vol 34 (1) ◽  
pp. 171-177 ◽  
Author(s):  
Shivani Vij ◽  
Niti Kant ◽  
Munish Aggarwal
Keyword(s):  
Harmonic Generation ◽  
Short Pulse ◽  
Harmonic Wave ◽  
Matching Condition ◽  
Third Harmonic Generation ◽  
Fundamental Wave ◽  
Ripple Effect ◽  
Third Harmonic ◽  
The Third ◽  
The Impact

AbstractA model is presented for the resonant third harmonic generation of short pulse lasers in cluster plasma in the presence of density ripple. Because of ripple in cluster density and plasma electron density outside the cluster, the phase-matching condition for the third harmonic process is satisfied, leading to resonant enhancement of harmonic generation. We explore the impact of laser intensity, cluster size, and collisional frequency of electrons on the efficiency of third harmonic generation. Moreover, since the group velocity of the third harmonic wave is greater than that of the fundamental wave, it causes the slippage of the generated harmonic pulse out of the fundamental laser pulse and its amplitude increases with time.

Impact of spatial modulation on the third harmonic wave propagation and far-field focal spot in frequency conversion system

Optik ◽  
2014 ◽  
Vol 125 (14) ◽  
pp. 3628-3632
Author(s):  
M.Z. Sun ◽  
J.Y. Zhang ◽  
Y.L. Zhang ◽  
Q.Y. Bi ◽  
X.L. Xie ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Frequency Conversion ◽  
Focal Spot ◽  
Harmonic Wave ◽  
Spatial Modulation ◽  
Far Field ◽  
Third Harmonic ◽  
The Third ◽  
Conversion System

scholarly journals Resonant third harmonic generation of an infrared laser in a semiconductor wave guide

2010 ◽  
Vol 28 (2) ◽  
pp. 327-332 ◽  
Author(s):  
Vijay Garg ◽  
V.K. Tripathi
Keyword(s):  
Harmonic Generation ◽  
Electron Concentration ◽  
Harmonic Wave ◽  
Third Harmonic Generation ◽  
Infrared Laser ◽  
Wave Number ◽  
Phase Matching ◽  
Third Harmonic ◽  
The Third ◽  
Harmonic Radiation

AbstractAn infrared laser propagating through a semiconductor waveguide, embedded with a density ripple of wave number q, resonantly excites third harmonic radiation. The phase matching is achieved when q equals difference between third harmonic wave number and three times the wave number of the laser. The excited third harmonic is in higher order radial Eigen mode than the pump laser. The third harmonic efficiency increases with electron concentration and decreases with the frequency of the laser.

The Concept of treaty in Islamic Jurisprudence: A comparative view of the classical jurists

2010 ◽  
Vol 7 (1) ◽  
pp. 55
Author(s):  
Labeeb Bsoul
Keyword(s):  
International Law ◽  
The Body ◽  
Mutual Understanding ◽  
Contemporary World ◽  
The Third ◽  
Islamic Jurisprudence ◽  
Shed Light

This article aims to shed light on a particular area in the field of Islamic International law (siyar) treaty in Islamic jurisprudence. It addresses a comparative view of classical jurists of treaties both theoretically and historically and highlights their continued relevance to the contemporary world. Since the concept of treaty a lacuna in scholarship as well as the familiar of international legal theorists to study and integrate the Islamic treaty system into the body of modern international law in order to have a mutual understanding and respect and honor for treaties among nations. I would like to present a series of three parts the first one addresses the concept of treaty in Islamic jurisprudence the second addresses the process of drafting treaties and their conclusion and the third addresses selected treaties, including the treaty of H{udaybiya that took place between Muslims and non-Muslims..

The Concept of the Optimum Alignment of Discharge Pipelines Due to the Minimization of the Wave Forces

1992 ◽  
Vol 25 (9) ◽  
pp. 211-216
Author(s):  
A. Akyarli ◽  
Y. Arisoy
Keyword(s):  
Wave Height ◽  
Wave Force ◽  
Wave Forces ◽  
Wave Direction ◽  
Incoming Wave ◽  
Pipeline Route ◽  
Optimum Alignment ◽  
The Cost ◽  
Resultant Wave

As the wave forces are the function of the wave height, period and the angle between the incoming wave direction and the axis of the discharge pipeline, the resultant wave force is directly related to the alignment of the pipeline. In this paper, a method is explained to determine an optimum pipeline route for which the resultant wave force becomes minimum and hence, the cost of the constructive measures may decrease. Also, the application of this method is submitted through a case study.

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