Peak Response Statistics of Vertical Cylinders in Two-Dimensional Irregular Waves

1996 ◽  
Vol 118 (4) ◽  
pp. 276-283
Author(s):  
N. Haritos
Keyword(s):  
Wave Structure ◽  
Irregular Waves ◽  
Force Model ◽  
Offshore Structure ◽  
Gaussian Form ◽  
Peak Response ◽  
Response Characteristics ◽  
Straight Line ◽  
Non Gaussian ◽  
Vertical Cylinders

When dealing with the probabilistic estimation of the peak response of an offshore structure dynamically responding under excitation by unidirectional irregular waves, it becomes apparent that nonlinearities introduced by the wave-structure interaction, and principally associated with the drag contribution of the Morison force model that has been traditionally used to describe this forcing, leads to non-Gaussian statistical properties of not only the forcing, but also the response. However, it is also apparent that for lightly damped structures, the response under certain circumstances can be very “narrow-banded,” and hence its statistical description would then approach the Gaussian form irrespective of whether the forcing associated with the response is itself highly non-Gaussian or otherwise. This paper treats both a numerical and experimental investigation of the peak response characteristics of compliant bottom-pivoted surface-piercing cylinders subjected to hydrodynamic excitation by unidirectional Pierson-Moskowitz (P-M) irregular waves and modeled as single-degree-of-freedom (SDOF) oscillators with a fixed “straight line” mode shape (the result of the bottom-pivoted support condition). Conditions under which the response can reasonably be approximated as Gaussian are identified via an upcrossing investigation for the likely peak response in a storm of a nominated period of duration.

Nonlinear Effects on Fatigue Analysis for Fixed Offshore Structures

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Oleg Gaidai ◽  
Arvid Naess
Keyword(s):  
Dynamic Analysis ◽  
Direct Method ◽  
Nonlinear Effects ◽  
Offshore Structures ◽  
Fatigue Analysis ◽  
Irregular Waves ◽  
Problem Solution ◽  
Offshore Structure ◽  
Drag Forces ◽  
Non Gaussian

Fatigue analysis for fixed offshore structures is an important practical issue. These structures are often drag dominated, which makes the deck response a non-Gaussian process when it is assumed that the irregular waves are Gaussian. Incorporating nonlinear and non-Gaussian modeling in the fatigue analysis can be a complicated issue, cf. work of Madhavan Pillai and Meher Prasad [2000, “Fatigue Reliability Analysis in Time Domain for Inspection Strategy of Fixed Offshore Structures,” Ocean Eng., 27(2), pp. 167–186]. The goal of this paper is to provide evidence that for drag dominated offshore structures it is, in fact, sufficient to perform linearization in order to obtain accurate estimates of fatigue damage. The latter fact brings fatigue analysis back into the Gaussian domain, which facilitates the problem solution. Beyond straightforward linearization of the exciting wave forces, this paper employs two different approaches accounting for nonlinear effects in fatigue analysis. One is an application of the quadratic approximation approach described in the work of Naess and co-workers [1997, “Frequency Domain Analysis of Dynamic Response of Drag Dominated Offshore Structures,” Appl. Ocean. Res., 19(3), pp. 251–262;1996, “Stochastic Response of Offshore Structures Excited by Drag Forces,” J. Eng. Mech., ASCE, 122, pp. 155–160]. to the stochastic fatigue estimation of jacket type offshore structures. An alternative method proposed is based on a spectral approximation, and this approximation turns out to be accurate and computationally simple. The stress cycles causing structural fatigue are considered to be directly related to the horizontal excursions of the fixed offshore structure in random seas. Besides inertia forces, it is important to study the effect of the nonlinear Morison type drag forces. Since no direct method for dynamic analysis with Morison type forces is available, it is a goal to find an accurate approximation, allowing efficient dynamic analysis. This has implications for long term fatigue analysis, which is an important issue for design of offshore structures.

scholarly journals WAVE LOADS ON HORIZONTAL CYLINDERS

1978 ◽  
Vol 1 (16) ◽  
pp. 147
Author(s):  
P. Holmes ◽  
J.R. Chaplin
Keyword(s):  
Oscillatory Flow ◽  
Vertical Plane ◽  
Vertical Cylinder ◽  
Irregular Waves ◽  
Wave Loads ◽  
Incident Flow ◽  
Cylinder Axis ◽  
Straight Line ◽  
Horizontal Cylinders ◽  
Wave Induced

The problem of predicting wave induced loads on cylinders is an enormously complex one. It is clear from the scatter present in most experimental determinations of force coefficients that there are many individual factors which influence the mechanisms of flow induced loading. Among these are some, for instance Reynolds number, separation and periodic vortex shedding, which are inter-related and whose influences cannot be studied in isolation. Others, such as shear flow, irregular waves and free surface effects, can at least be eliminated in the laboratory, in order to approach an understanding of the more fundamental characteristics of the flow. A vertical cylinder in uniform waves experiences an incident flow field which can be described in terms of rotating velocity and acceleration vectors, always in the same vertical plane, containing also the cylinder axis, whose magnitudes are functions of time and of position along the length of the cylinder. Some of the essential features of this flow can be studied under two-dimensional oscillatory conditions, in which either the cylinder or the fluid is oscillated relative to the other along a straight line (planar oscillatory flow). The incident velocity and acceleration vectors are then always concurrent, normal to the cylinder axis, and oscillating in magnitude with time.

scholarly journals Energy-efficient non-linear k-barrier coverage in mobile sensor network

2020 ◽  
Vol 17 (3) ◽  
pp. 737-758
Author(s):  
Zijing Ma ◽  
Shuangjuan Li ◽  
Longkun Guo ◽  
Guohua Wang
Keyword(s):  
Sensor Network ◽  
Mobile Sensors ◽  
Barrier Coverage ◽  
Force Model ◽  
Mobile Sensor ◽  
Mobile Sensor Network ◽  
Virtual Force ◽  
Straight Line ◽  
Non Linear ◽  
Single Sensor

K-barrier coverage is an important coverage model for achieving robust barrier coverage in wireless sensor networks. After initial random sensor deployment, k-barrier coverage can be achieved by moving mobile sensors to form k barriers consisting of k sensor chains crossing the region. In mobile sensor network, it is challenging to reduce the moving distances of mobile sensors to prolong the network lifetime. Existing work mostly focused on forming linear barriers, that is the final positions of sensors are on a straight line, which resulted in large redundant movements. However, the moving cost of sensors can be further reduced if nonlinear barriers are allowed, which means that sensors? final positions need not be on a straight line. In this paper, we propose two algorithms of forming non-linear k barriers energy-efficiently. The algorithms use a novel model, called horizontal virtual force model, which considers both the euclidean distance and horizontal angle between two sensors. Then we propose two barrier forming algorithms. To construct a barrier, one algorithm always chooses the mobile sensor chain with the largest horizontal virtual force and then flattens it, called sensor chain algorithm. The other chooses the mobile sensor with the largest horizontal virtual force to construct the barrier, other than the mobile sensor chain, called single sensor algorithm. Simulation results show that the algorithms significantly reduce the movements of mobile sensors compared to a linear k-barrier coverage algorithm. Besides, the sensor chain algorithm outperforms the single sensor algorithm when the sensor density becomes higher.

Unstable Motion of a Floating Structure in Surface Waves

2011 ◽  
Author(s):  
Hongmei Yan ◽  
Yuming Liu ◽  
Yile Li
Keyword(s):  
Natural Frequencies ◽  
Wave Structure ◽  
The Body ◽  
Body Motion ◽  
Irregular Waves ◽  
Nonlinear Instability ◽  
Physical Factors ◽  
Floating Structure ◽  
Practical Applications ◽  
Sum Frequency

Unstable resonant heave and pitch motions of a floating deep draft platform, under the action of a regular wave with the frequency equal to the sum of the heave and pitch natural frequencies, can be developed by nonlinear instability (Liu, Yan & Yung 2010). The instability is associated with difference-frequency interactions between the body motion and the ambient wave. In this work, we study the effect of the nonlinear instability upon floating platforms with relatively shallow drafts whose wave damping at heave/pitch natural frequencies may not be small. Direct time-domain numerical simulations of wave-structure interactions, which can take into account different levels of nonlinearity effects, are applied to understand the characteristics of the unstable coupled heave/pitch (or heave/roll) resonant motion and its dependence on the key physical factors. In particular, it is found that such a nonlinear instability at other wave conditions involving sum-frequency interactions between the body motion and the ambient wave can also occur. For practical applications, long-time nonlinear simulations with irregular waves are also performed. The results show that depending on the sea conditions and damping in the system, the unstable resonant motion associated with the nonlinear instability can be significant for platforms with shallow drafts.

Planning and Design of Floating Offshore Architecture

2020 ◽  
Author(s):  
Akane Takahashi ◽  
Ikuo Yoshida
Keyword(s):  
Offshore Structures ◽  
Tokyo Bay ◽  
Offshore Structure ◽  
Floating Structure ◽  
Sea Levels ◽  
Motion Response ◽  
Response Characteristics ◽  
Planning And Design ◽  
Movement Characteristics ◽  
Rising Sea Levels

Abstract Floating offshore structures are attracting increasing attention as a method for addressing problems such as rising sea levels due to global warming and the increasing global populations. However, unlike ground structures, floating offshore structures must consider the effects of waves. The movement characteristics of the floating offshore structure have been reported. However, no studies have compared variations in motion response characteristics according to the scale of floating structures or buildings atop them, so it is currently difficult during the initial planning and design stages to estimate the size of superstructures that can be designed for a given marine area. Therefore, with the aim of obtaining basic data for planning floating offshore structures, in this study we developed floating structure modules (a square 36m on a side) according to their superstructure and investigated the basic motion response characteristics for each. We furthermore derived tendencies for horizontal acceleration and inclination occurring in individual modules according to design waves for Tokyo Bay.

scholarly journals Modeling Traveling Waves Using Mode Superposition

2010 ◽  
Author(s):  
Vivek Jaiswal ◽  
Aditi Sheshadri ◽  
J. Kim Vandiver
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Force Model ◽  
Superposition Method ◽  
Mode Superposition ◽  
Response Characteristics ◽  
Excitation Region ◽  
Mode Superposition Method ◽  
Excitation Force ◽  
Measured Response

Analysis of the data from two Vortex-Induced Vibration (VIV) experiments conducted in the Gulf Stream on a 500-foot-long, 1.43 inches diameter, flexible, tension dominated riser model revealed that the response is predominantly characterized by the presence of traveling waves. It was also observed that the location of the VIV excitation region (power-in) affects the characteristics of the response. The conventional method of modeling the excitation force as a standing wave was found inadequate to predict the location of the peak measured response accurately, especially in the cases where the excitation region is close to a boundary (the ends of the riser model). A modified excitation force model consisting of a combination of standing and traveling wave excitation regions is demonstrated to predict the location of the peak response more accurately. This work presents the idea of modifying the VIV excitation model to include traveling wave characteristics and using mode superposition method for computing the response to this modified force. Examples of the implementation of this method are shown for the two distinct cases of the location of the power-in region — the power-in region adjacent to the boundary and the power-in region away from the boundary. Depending on the location of the power-in region, different proportions of standing and traveling wave excitations are used to yield predicted responses that match the measured response characteristics.

Current Effects on a Moored Floating Platform in a Sea State

2008 ◽  
Author(s):  
Carl Trygve Stansberg
Keyword(s):  
Irregular Waves ◽  
Mooring Line ◽  
Viscous Effects ◽  
Floating Platform ◽  
Sea State ◽  
Scaled Model ◽  
Wave Drift ◽  
Wave Basin ◽  
Wave Drift Damping ◽  
Non Gaussian

The significance of current-induced forces and effects on a moored semisubmersible production platform in various sea state conditions is explored, with emphasis on surge motions. Experimental data from 1:55 scaled model tests in a 50m × 80m wave basin are investigated. A description of the current generation is given first. The current in the actual basin is modelled by use of a return current under a false bottom. The importance of modelling a “real” physical current for the proper reproduction of platform responses is pointed out. The semisubmersible tests are carried out with the platform in current only, in irregular waves only, and in combined waves and current conditions. The effects from the current on platform motions and mooring line tensions are investigated. Vortex-Induced motions (VIM) are observed in pure current, depending on the actual combination of current velocity and natural sway period. In combined waves and current the VIM seems to be more or less disappearing. A large effect is seen on the wave drift responses. Both drift forces, non-Gaussian properties and resulting extreme motions and line tensions are significantly increased, especially in high sea states. This is explained through a combination of wave drift damping and viscous effects. At the same time the damping is also increased, but this only partly compensates for the increased forces.

The Influence of Alternative Wave Loading and Support Modeling Assumptions on Jack-Up Rig Response Extremes

1996 ◽  
Vol 118 (2) ◽  
pp. 109-114 ◽  
Author(s):  
L. Manuel ◽  
C. A. Cornell
Keyword(s):  
Nonlinear Models ◽  
Random Wave ◽  
Force Model ◽  
Wave Loading ◽  
Force Modeling ◽  
Hydrodynamic Damping ◽  
Extreme Response ◽  
The Absolute ◽  
Non Gaussian ◽  
Jack Up

A study is conducted of the response of a jack-up rig to random wave loading. Steady current and wind load effects are also included. The effects of varying the relative motion assumption (in the Morison equation) and of varying the bottom fixity assumptions are investigated. One “fixity” model employs nonlinear soil springs. Time domain simulations are performed using linearized as well as fully nonlinear models for the jack-up rig. Comparisons of response statistics are made for two seastates. Hydrodynamic damping causes the rms response to be lower in the relative Morison case. The absence of this source of damping in the absolute Morison force model gives rise to larger resonance/dynamic effects—this tends to “Gaussianize” the response. Hence, the relative Morison model leads to stronger non-Gaussian behavior than the absolute Morison model. This is reflected in moments as well as extremes. The different support conditions studied are seen to significantly influence extreme response estimates. In general, stiffer models predict smaller rms response estimates, but also exhibit stronger non-Gaussian behavior. The choice of the Morison force modeling assumption (i.e., the relative versus the absolute motion formulation) is seen to have at least a secondary role in influencing response moments and extremes.

scholarly journals Climate Sensitivity via a Nonparametric Fluctuation–Dissipation Theorem

2011 ◽  
Vol 68 (5) ◽  
pp. 937-953 ◽  
Author(s):  
Fenwick C. Cooper ◽  
Peter H. Haynes
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Climate System ◽  
External Parameter ◽  
Gaussian Form ◽  
Stochastic Version ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Non Gaussian

Abstract The fluctuation–dissipation theorem (FDT) has been suggested as a method of calculating the response of the climate system to a small change in an external parameter. The simplest form of the FDT assumes that the probability density function of the unforced system is Gaussian and most applications of the FDT have made a quasi-Gaussian assumption. However, whether or not the climate system is close to Gaussian remains open to debate, and non-Gaussianity may limit the usefulness of predictions of quasi-Gaussian forms of the FDT. Here we describe an implementation of the full non-Gaussian form of the FDT. The principle of the quasi-Gaussian FDT is retained in that the response to forcing is predicted using only information available from observations of the unforced system, but in the non-Gaussian case this information must be used to estimate aspects of the probability density function of the unforced system. Since this estimate is implemented using the methods of nonparametric statistics, the new form is referred to herein as a “nonparametric FDT.” Application is demonstrated to a sequence of simple models including a stochastic version of the three-component Lorenz model. The authors show that the nonparametric FDT gives accurate predictions in cases where the quasi-Gaussian FDT fails. Practical application of the nonparametric FDT may require optimization of the method set out here for higher-dimensional systems.

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