Springing Analysis of Elastic Vessels in Head and Oblique Seas Including Nonlinear Effects Due to Second Order Diffraction Pressures

2004 ◽  
Author(s):  
Haiping He ◽  
Armin W. Troesch ◽  
Yung Sup Shin ◽  
Boo-Ki Kim
Keyword(s):  
Theoretical Calculations ◽  
Bending Moment ◽  
Nonlinear Effects ◽  
Diffraction Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Sea State ◽  
Zero Crossing ◽  
Sum Frequency ◽  
State Dependent

The wave-induced vibration of the ship hull, commonly called springing, may not produce extreme stresses, but it is likely to have a direct effect on fatigue-life estimates due to its high frequency content. This research investigates the second order contribution to the springing bending moment from the sum frequency of incident ocean waves in both head and oblique seas. The computer program developed here extends the ABS SSRS (Ship Spring Response System) program to oblique seas using Troesch’s oblique sea linear diffraction theory [1]. The theoretical calculations for forward speed are modified by an empirical factor to correlate more closely with experimental results. An example calculation on a Bulk Carrier was performed for different heading angles. For one such representative sea state, the overall increase to the total bending moment from the nonlinear, sum-frequency excitation is found to be less than 12%. However, the nonlinear springing (RMS) increases the total RMS springing over the linear springing by more than 5 times in some stations, which has significant implications for fatigue studies. A sea state sweep study (using ITTC spectrum) also shows the springing effects are highly sea state dependent. Overall, springing effects decrease as zero crossing periods increase, which indicates springing is important in sea states with short waves and becomes less significant in sea states with long waves.

Sum-Frequency Diffraction Loads on Tension-Leg Platforms in Bidirectional Waves

1997 ◽  
Vol 119 (1) ◽  
pp. 14-19
Author(s):  
J. H. Vazquez ◽  
A. N. Williams
Keyword(s):  
Numerical Technique ◽  
Diffraction Theory ◽  
Potential Method ◽  
Second Order ◽  
Surface Integral ◽  
Hydrodynamic Loads ◽  
Infinite Depth ◽  
Sum Frequency ◽  
Wave Directionality ◽  
Green Function Approach

Second-order diffraction theory is utilized to compute the sum-frequency diffraction loads on a deepwater tension-leg platform (TLP) in bidirectional waves. The linear diffraction solution is obtained utilizing a Green function approach using higher-order boundary elements. The second-order hydrodynamic loads explicitly due to the second-order potential are computed using the indirect, assisting radiation potential method. An efficient numerical technique is presented to treat the free-surface integral which appears in the second-order load formulation. Numerical results are presented for a stationary ISSC TLP in water of infinite depth. It is found that wave directionality may have a significant influence on the second-order hydrodynamic loads on a TLP and that the assumption of unidirectional waves does not always lead to conservative estimates of the sum-frequency loading.

Nonlinear Wave Disturbance Around a Vertical Circular Column

2002 ◽  
Author(s):  
C. T. Stansberg ◽  
H. Braaten
Keyword(s):  
Linear Prediction ◽  
Harmonic Component ◽  
Nonlinear Effects ◽  
Second Order ◽  
Wave Disturbance ◽  
Difference Frequency ◽  
Irregular Waves ◽  
Order Effects ◽  
Sum Frequency ◽  
Circular Column

The wave disturbance close to vertical columns is analysed. In particular, the deviations from linear predictions are investigated, by experimental as well as by numerical methods. Thus a second-order numerical diffraction model is established by means of a diffraction analysis code (WAMIT) and compared to model tests with a single, fixed column with diameter 16m. Tests in regular, bi-chromatic as well as irregular waves are run. Significant nonlinear effects are observed, especially in steep waves, with the maximum elevation in front of the column increasing from 11.5m in a linear prediction to around 19m, in a 12s regular wave with 22m wave height. The main nonlinear effects in front of the column are identified as second-order sum-frequency and difference-frequency terms, plus a significant nonlinear increase in the first harmonic component. The WAMIT prediction of the second-order effects agrees fairly well with the measurements, although with some overprediction and underprediction, respectively, of the sum-frequency and difference-frequency (LF and mean set-up) terms in the steepest waves. For the underprediction of the first harmonic, however, a theory beyond second order is required.

Air-Gap Analysis of a Semi-Submersible Considering Full Second Order Effects

2019 ◽  
Author(s):  
Zhiyuan Pan ◽  
Torgeir Kirkhorn Vada ◽  
Arne Nestegård
Keyword(s):  
Gap Analysis ◽  
Low Frequency ◽  
Vertical Motion ◽  
Second Order ◽  
Surface Elevation ◽  
Asymmetry Factor ◽  
Order Effects ◽  
Short Term ◽  
Sea State ◽  
Sum Frequency

Abstract In the present paper, a complete and consistent second-order computation of airgap for a semi-submersible is presented. The second-order sum and difference frequency upwell will be calculated and combined with the linear upwell statistically to find the short-term extremes. The phasing of the low frequency surface elevation with respect to the low frequency vertical motion will be considered. The asymmetric characteristics of the surface elevation will be taken care of by the sum frequency surface elevation. By comparing the maximum and minimum extremes of surface elevation in a given sea state at specified off-body points, the “asymmetry factor” up to the second order can be obtained.

Wave Statistics in Nonlinear Sea States

2011 ◽  
Author(s):  
Mohamed Latheef ◽  
Chris Swan
Keyword(s):  
Empirical Distribution ◽  
Nonlinear Effects ◽  
Rayleigh Distribution ◽  
Second Order ◽  
Wave Crest ◽  
Statistical Distributions ◽  
Sea State ◽  
Wave Statistics ◽  
Wave Basin ◽  
Wave Heights

This paper concerns the statistical distribution of both wave crest elevations and wave heights in deep water. A new set of laboratory observations undertaken in a directional wave basin located in the Hydrodynamics laboratory in the Department of Civil and Environmental Engineering at Imperial College London is presented. The resulting data were analysed and compared to a number of commonly applied statistical distributions. In respect of the wave crest elevations the measured data is compared to both linear and second-order order distributions, whilst the wave heights were compared to the Rayleigh distribution, the Forristall (1978) [1] empirical distribution and the modified Glukhovskiy distribution ([2] and [3]). Taken as a whole, the data confirms that the directionality of the sea state is critically important in determining the statistical distributions. For example, in terms of the wave crest statistics effects beyond second-order are most pronounced in uni-directional seas. However, if the sea state is sufficiently steep, nonlinear effects arising at third order and above can also be significant in directionally spread seas. Important departures from Forristall’s empirical distribution for the wave heights are also identified. In particular, the data highlights the limiting effect of wave breaking in the most severe seas suggesting that many of the commonly applied design solutions may be conservative in terms of crest height and wave height predictions corresponding to a small (10−4) probability of exceedance.

scholarly journals Second-order statistics and ‘designer’ waves for violent free-surface motion around multi-column structures

2015 ◽  
Vol 373 (2033) ◽  
pp. 20140113 ◽  
Author(s):  
J. R. Grice ◽  
P. H. Taylor ◽  
R. Eatock Taylor
Keyword(s):  
Return Period ◽  
Incident Wave ◽  
Wave Structure ◽  
Diffraction Theory ◽  
Second Order ◽  
Trapped Modes ◽  
Extreme Wave ◽  
Sea State ◽  
Second Order Statistics ◽  
Column Structure

Extreme wave–structure interactions are investigated using second-order diffraction theory. The statistics of surface elevation around a multi-column structure are collected using Monte Carlo-type simulations for severe sea states. Within the footprint of a realistic four-column structure, we find that the presence of the structure can give rise to extreme crest elevations greater than twice those at the same return period in the incident wave field. Much of this extra elevation is associated with the excitation of second-order near-trapped modes. A ‘designer’ incident wave can be defined at each point around the structure for a given sea state as the average input wave to produce extreme crest elevations at a given return period, and we show that this wave can be simply vertically scaled to estimate the response at other return periods.

Springing Response Statistics of Tethered Platforms in Random Waves

2006 ◽  
Author(s):  
P. S. Teigen ◽  
O. Gaidai ◽  
A. Naess
Keyword(s):  
Volterra Series ◽  
Series Representation ◽  
Power Spectra ◽  
Second Order ◽  
Random Waves ◽  
Sea State ◽  
Sum Frequency ◽  
Wave Forcing ◽  
Spring System ◽  
Mass Spring

The paper investigates the wave forcing and motion response of a small size TLP, with particular focus on sum frequency effects related to the restrained modes, heave, roll and pitch. The fluid loading is obtained from a second order diffraction code, and the stochastic response in a random sea state is estimated using a Volterra series representation of the response process. Although the wave loading is assumed to be a second order process, the dynamical system as such is a damped, linear mass-spring system. Numerical results are presented both in terms of power spectra and as extreme value predictions. In the latter case three different methods are compared and evaluated.

Relative Intensities in ED Patterns From Thin Gold Films

1972 ◽  
Vol 30 ◽  
pp. 636-637
Author(s):  
R. H. Morriss ◽  
J. D. C. Peng ◽  
C. D. Melvin
Keyword(s):  
Theoretical Calculations ◽  
Diffraction Theory ◽  
Gold Films ◽  
Reasonable Accuracy ◽  
Experimental Conditions ◽  
Crystal Perfection ◽  
Heavy Atoms ◽  
Fine Focus ◽  
Convergent Beam ◽  
Beam Diffraction

Although dynamical diffraction theory was modified for electrons by Bethe in 1928, relatively few calculations have been carried out because of computational difficulties. Even fewer attempts have been made to correlate experimental data with theoretical calculations. The experimental conditions are indeed stringent - not only is a knowledge of crystal perfection, morphology, and orientation necessary, but other factors such as specimen contamination are important and must be carefully controlled. The experimental method of fine-focus convergent-beam electron diffraction has been successfully applied by Goodman and Lehmpfuhl to single crystals of MgO containing light atoms and more recently by Lynch to single crystalline (111) gold films which contain heavy atoms. In both experiments intensity distributions were calculated using the multislice method of n-beam diffraction theory. In order to obtain reasonable accuracy Lynch found it necessary to include 139 beams in the calculations for gold with all but 43 corresponding to beams out of the [111] zone.

Bulk Contributions Modulate the Sum-Frequency Generation Spectra of Interfacial Water on Model Sea-Spray Aerosols

2018 ◽  
Author(s):  
Sandeep K. Reddy ◽  
Raphael Thiraux ◽  
Bethany A. Wellen Rudd ◽  
Lu Lin ◽  
Tehseen Adel ◽  
...  
Keyword(s):  
Single Layer ◽  
Sum Frequency Generation ◽  
Second Order ◽  
Interfacial Structure ◽  
Sea Spray ◽  
Third Order ◽  
Systematic Analysis ◽  
Sum Frequency ◽  
Structure Of Water ◽  
Frequency Generation

Vibrational sum-frequency generation (vSFG) spectroscopy is used to determine the molecular structure of water at the interface of palmitic acid monolayers. Both measured and calculated spectra display speci c features due to third-order contributions to the vSFG response which are associated with nite interfacial electric potentials. We demonstrate that theoretical modeling enables to separate the third-order contributions, thus allowing for a systematic analysis of the strictly surface-sensitive, second-order component of the vSFG response. This study provides fundamental, molecular-level insights into the interfacial structure of water in a neutral surfactant system with relevance to single layer bio-membranes and environmentally relevant sea-spray aerosols. These results emphasize the key role that computer simulations can play in interpreting vSFG spectra and revealing microscopic details of water at complex interfaces, which can be difficult to extract from experiments due to the mixing of second-order, surface-sensitive and third-order, bulk-dependent contributions to the vSFG response.

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