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.

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.

scholarly journals Analysis of Displacement of Vibrating of Mass Spring Due to Opposition Force

2020 ◽  
Vol 35 (1) ◽  
pp. 21-32
Author(s):  
Puskar R. Pokhrel ◽  
Bhabani Lamsal ◽  
Jeevan Kafle ◽  
Parameshwari Kattel
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
External Force ◽  
Model Equation ◽  
Order Differential Equation ◽  
Second Order ◽  
Second Order Differential Equation ◽  
Spring System ◽  
Mass Spring

Employing the model equation for mass spring system, which is of second order differential equation, we analyze the displacement with various opposition forces applied on the mass of the spring. We observe that if there is no external force on the mass of the spring, the opposition force causes the displacements of mass of spring. We also analyze the system by finding its analytic and numerical solution, and compare their results.

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.

Second Order Model for Wave Crests Used in Prediction of Green Water Load and Volume on Ships in Random Waves

2004 ◽  
Author(s):  
Hanne Therese Wist ◽  
Dag Myrhaug ◽  
Ha˚vard Rue
Keyword(s):  
Wave Theory ◽  
Rayleigh Distribution ◽  
Second Order ◽  
Green Water ◽  
Wave Crest ◽  
Random Waves ◽  
Sea State ◽  
Water Load ◽  
Height Model ◽  
Crest Height

The probability that a wave crest in a random sea will exceed a specified height has long been recognized as important statistics in practical work, e.g., in predicting green water load and volume on a ship. Nonlinear probability density functions for predicting green water load and volume are presented. The models are based on the linear model of [1] in combination with transformation of a second order wave crest height model. The wave crest height model is obtained from second order wave theory for a narrow-banded sea state in combination with transformation of the Rayleigh distribution. Results from the models are compared with model tests of a cargo ship presented in [1].

Characteristics of Steep Second-Order Random Waves in Finite and Shallow Water

2011 ◽  
Author(s):  
Carl Trygve Stansberg
Keyword(s):  
Time Series ◽  
Shallow Water ◽  
Frequency Component ◽  
Second Order ◽  
Difference Frequency ◽  
Nonlinear Interactions ◽  
Random Waves ◽  
Theoretical Formulation ◽  
Sum Frequency ◽  
The Difference

The theoretical formulation of second-order random waves in deep and finite water is reviewed. In particular, the increased nonlinear interactions with decreasing depth are addressed, including both the sum-frequency as well as the slowly varying difference-frequency components. Depth-defined limitations in the valid range for random waves are suggested based on the Ursell number. Numerical time series realizations at various depths and for two sea states are obtained by an efficient bifrequency summation procedure. Resulting time series show moderate average second-order energy contents, except for the steep sea state Hs = 15m, Tp = 14s in depths of 30m and 20m which are outside the suggested valid second-order range. The two largest wave events from the simulations are studied in particular for the different depths. Nonlinear interactions increase significantly with decreasing depth. Still, within the valid range, extreme second-order crests and peak particle velocities are only moderately increased with decreasing depth, while the negative peaks increase significantly. This is because the difference-frequency component almost compensates for the sum-frequency part at crests, while it is opposite at troughs. Maximum slopes, however, are clearly increased in shallow water, eventually leading to increased breaking (which is beyond second order of course). Velocity profiles under the crests are also shown, confirming the findings from the elevation.

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.

Graphene-Based Resonant Sensors for Detection of Ultra-Fine Nanoparticles: Molecular Dynamics and Nonlocal Elasticity Investigations

NANO ◽  
2015 ◽  
Vol 10 (02) ◽  
pp. 1550024 ◽  
Author(s):  
S. Kamal Jalali ◽  
M. Hassan Naei ◽  
Nicola Maria Pugno
Keyword(s):  
Molecular Dynamics ◽  
Nonlocal Elasticity ◽  
Md Simulations ◽  
Small Scale ◽  
Frequency Shifts ◽  
Resonant Sensors ◽  
Embedded Atom ◽  
Metal Metal ◽  
Spring System ◽  
Mass Spring

Application of single layered graphene sheets (SLGSs) as resonant sensors in detection of ultra-fine nanoparticles (NPs) is investigated via molecular dynamics (MD) and nonlocal elasticity approaches. To take into consideration the effect of geometric nonlinearity, nonlocality and atomic interactions between SLGSs and NPs, a nonlinear nonlocal plate model carrying an attached mass-spring system is introduced and a combination of pseudo-spectral (PS) and integral quadrature (IQ) methods is proposed to numerically determine the frequency shifts caused by the attached metal NPs. In MD simulations, interactions between carbon–carbon, metal–metal and metal–carbon atoms are described by adaptive intermolecular reactive empirical bond order (AIREBO) potential, embedded atom method (EAM), and Lennard–Jones (L–J) potential, respectively. Nonlocal small-scale parameter is calibrated by matching frequency shifts obtained by nonlocal and MD simulation approaches with same vibration amplitude. The influence of nonlinearity, nonlocality and distribution of attached NPs on frequency shifts and sensitivity of the SLGS sensors are discussed in detail.

Non‐Gaussian Properties of Second‐Order Random Waves

1993 ◽  
Vol 119 (2) ◽  
pp. 344-364 ◽  
Author(s):  
Sau‐Lon James Hu ◽  
Dongsheng Zhao
Keyword(s):  
Second Order ◽  
Random Waves ◽  
Non Gaussian

scholarly journals Reduced Mass-Weighted Proper Decomposition for Modal Analysis

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Venkata K. Yadalam ◽  
B. F. Feeny
Keyword(s):  
Modal Analysis ◽  
Mass Distribution ◽  
Mass Matrix ◽  
Linear Interpolation ◽  
Modal Identification ◽  
Distributed Parameter ◽  
Arbitrary Mass ◽  
Spring System ◽  
Mass Spring ◽  
Proper Orthogonal

A method of modal analysis by a mass-weighted proper orthogonal decomposition for multi-degree-of-freedom and distributed-parameter systems of arbitrary mass distribution is outlined. The method involves reduced-order modeling of the system mass distribution so that the discretized mass matrix dimension matches the number of sensed quantities, and hence the dimension of the response ensemble and correlation matrix. In this case, the linear interpolation of unsensed displacements is used to reduce the size of the mass matrix. The idea is applied to the modal identification of a mass-spring system and an exponential rod.

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