Coupled Surge-Heave-Pitch Dynamic Modeling of Spar-Moonpool-Riser Interaction

2009 ◽  
Author(s):  
Pol D. Spanos ◽  
Vincenzo Nava ◽  
Felice Arena
Keyword(s):  
Nonlinear Differential Equations ◽  
Wave Spectrum ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Parameter Study ◽  
Mooring Lines ◽  
Study Results ◽  
Highly Nonlinear

Due to the ongoing rather intense development of deep water gas and oil fields, the technical community has been increasingly focusing its attention to the dynamic behavior of Spar floating structures. Spar dynamics exhibits a highly nonlinear behavior due to the presence of various components such as mooring lines, moonpool, and risers (Spanos et al., 2005). In this regard Gupta et al, 2008a, have studied the reduction of the heave response in a single degree-of-freedom spar model due to the oscillations of water entrapped in the moonpool through the partially closed bottom plates. In this paper a novel coupled six-degree-of-freedom analytical model of a Spar system tensioned by TTR risers is proposed. The model accounts for the interactions among spar hull motions (heave, surge and pitch), the riser motion (heave and surge), and the moonpool. This model involves six coupled nonlinear differential equations comprising nonlinearity terms associated not only with stiffness and damping but also with inertia terms. A dynamic analysis is performed by subjecting the model to JONSWAP ocean wave spectrum compatible extreme forces (corresponding to the 100 yr wave); and to moments applied to the center of gravity computed by means of standard motion program. Both numerical and semi-analytical techniques (equivalent linearization including inertial terms) are used for the determination of the response of the proposed dynamic model both in the time and frequency domains. Some parameter study results are reported, including ones pertaining to the dependence of the spar motion on the open guide plates.

Coupled Surge-Heave-Pitch Dynamic Modeling of Spar-Moonpool-Riser Interaction

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Pol D. Spanos ◽  
Vincenzo Nava ◽  
Felice Arena
Keyword(s):  
Wave Spectrum ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Degree Of Freedom ◽  
Statistical Linearization ◽  
Parameter Study ◽  
Mooring Lines ◽  
Study Results ◽  
Highly Nonlinear ◽  
Ocean Wave Spectrum

Due to the rather intense ongoing development of deep water gas and oil fields, the technical community has devoted considerable attention to the dynamic behavior of Spar floating systems. Spar dynamics exhibits a highly nonlinear behavior due to the presence of various components such as mooring lines, moonpool, and risers. Certain studies have focused on the reduction of the heave response of single-degree-of-freedom Spar models due to the oscillations of water entrapped in the moonpool through the partially closed bottom plates. In this paper, a novel coupled six-degree-of-freedom analytical model of a Spar system comprising top tensioned risers is proposed. The model accounts for the interactions among the Spar hull kinematics (heave, surge, and pitch), the riser kinematics (heave and surge), and the moonpool. This model involves six coupled differential equations comprising nonlinearities associated not only with stiffness and damping but also with inertia terms. A dynamic analysis is performed by subjecting the model to JONSWAP ocean wave spectrum compatible extreme forces (corresponding to the 100 year wave) and to moments applied to the center of gravity computed by means of a standard motion simulation program. Both numerical and analytical techniques (statistical linearization including inertia terms) are used for the determination of the response of the proposed dynamic model, both in the time and the frequency domains. Related parameter study results are reported, including ones pertaining to the dependence of the Spar system motion on the degree of opening of the bottom plates.

Predictive Capability of a 2D FNPF Fluid-Structure Interaction Model

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Solomon C. Yim ◽  
Huan Lin ◽  
David C. Robinson ◽  
Katsuji Tanizawa
Keyword(s):  
Free Surface ◽  
Numerical Models ◽  
Fluid Structure Interaction ◽  
Nonlinear Behavior ◽  
Degree Of Freedom ◽  
Surface Boundary ◽  
Predictive Capability ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Highly Nonlinear

The predictive capability of two-dimensional (2D) fully-nonlinear-potential-flow (FNPF) models of an experimental submerged moored sphere system subjected to waves is examined in this study. The experimental system considered includes both single-degree-of-freedom (SDOF) surge-only and two-degree-of-freedom (2DOF) surge-heave coupled motions, with main sources of nonlinearity from free surface boundary, large geometry, and coupled fluid-structure interaction. The FNPF models that track the nonlinear free-surface boundary exactly hence can accurately model highly nonlinear (nonbreaking) waves. To examine the predictive capability of the approximate 2D models and keep the computational effort manageable, the structural sphere is converted to an equivalent 2D cylinder. Fluid-structure interaction is coupled through an implicit boundary condition enforcing the instantaneous dynamic equilibrium between the fluid and the structure. The numerical models are first calibrated using free-vibration test results and then employed to investigate the wave-excited experimental responses via comparisons of time history and frequency response diagrams. Under monochromatic wave excitations, both SDOF and 2DOF models exhibit complex nonlinear experimental responses including coexistence, harmonics, subharmonics, and superharmonics. It is found that the numerical models can predict the general qualitative nonlinear behavior, harmonic and subharmonic responses as well as bifurcation structure. However, the predictive capability of the models deteriorates for superharmonic resonance possibly due to three-dimensional (3D) effects including diffraction and reflection. To accurately predict the nonlinear behavior of moored sphere motions in the highly sensitive response region, it is recommended that the more computationally intensive 3D numerical models be employed.

Route to Chaos of an Articulated Offshore Loading Platform

2004 ◽  
Author(s):  
A. P. Shashikala
Keyword(s):  
Wind Waves ◽  
Nonlinear Behavior ◽  
Mooring Line ◽  
Response Analysis ◽  
Mooring Lines ◽  
Restoring Force ◽  
Highly Nonlinear ◽  
Waves And Currents ◽  
Time Domain Response ◽  
The Time Domain

Articulated Loading Platforms are compliant structures which undergo excessive displacements due to large hydrodynamic loads produced by wind, waves and currents. Prediction of nonlinear behavior of these complex structures in the nonlinear environment is extremely difficult. The discontinuity in the mooring line stiffness at the equilibrium position due to slackening of the mooring line between tower and tanker introduces nonlinearity in the equation of motion. An attempt to study the effect of the highly nonlinear restoring force and hydrodynamic forces on the system was performed. The time domain response analysis was done on the basis of approximate analytical investigations. The solution of the nonlinear simultaneous equations was performed and the results were interpreted by means of phase plots and poincare mapping. The effect of forcing amplitude on the behavior of the system was studied by varying the frequency ratio. Possible occurrence of sub harmonic and chaotic responses and hence different routes to chaos were also identified. These results can be made use of in the design of mooring lines to avoid structural instabilities in the evolving offshore environment.

Performance analysis of global local mean square error criterion of stochastic linearization for nonlinear oscillator

2019 ◽  
Author(s):  
Nguyen Cao Thang ◽  
Luu Xuan Hung
Keyword(s):  
Performance Analysis ◽  
Mean Square Error ◽  
Nonlinear Oscillators ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Stochastic Linearization ◽  
Local Mean ◽  
Mean Square Error Criterion

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

Optimization Design of Trusses Based on Covariance Matrix Adaptation Evolution Strategy Algorithm

2012 ◽  
Vol 215-216 ◽  
pp. 133-137
Author(s):  
Guo Shao Su ◽  
Yan Zhang ◽  
Zhen Xing Wu ◽  
Liu Bin Yan
Keyword(s):  
Stochastic Optimization ◽  
Covariance Matrix ◽  
Optimization Problems ◽  
Fitness Function ◽  
Optimization Methods ◽  
Evolution Strategy ◽  
Covariance Matrix Adaptation ◽  
Study Results ◽  
Highly Nonlinear ◽  
Adaptation Evolution

Covariance matrix adaptation evolution strategy algorithm (CMA-ES) is a newly evolution algorithm. It has become a powerful tool for solving highly nonlinear multi-peak optimization problems. In many real-world optimization problems, the location of multiple optima is often required in a search space. In order to evaluate the solution, thousands of fitness function evaluations are involved that is a time consuming or expensive processes. Therefore, conventional stochastic optimization methods meet a special challenge for a very large number of problem function evaluations. Aiming to overcome the shortcoming of stochastic optimization methods in the high calculation cost, a truss optimal method based on CMA-ES algorithm is proposed and applied to solve the section and shape optimization problems of trusses. The study results show that the method is feasible and has the advantages of high accuracy, high efficiency and easy implementation.

How to measure the radial load of radial lip seals

2021 ◽  
Vol 68 (3-4) ◽  
pp. 5-12
Author(s):  
Simon Feldmeth ◽  
Mario Stoll ◽  
Frank Bauer
Keyword(s):  
Practice Guideline ◽  
Best Practice ◽  
Parameter Study ◽  
Radial Load ◽  
Measurement Device ◽  
Lip Seal ◽  
Study Results ◽  
Lip Seals ◽  
German Standard ◽  
The University

The radial load of a radial lip seal indicates how strongly the sealing lip is pressed on the shaft. The radial load significantly affects the function of the seal. The German standard DIN 3761-9 describes the measurement of the radial load according to the split-shaft method but leaves room for interpretation. During the revision of the standard, a parameter study was conducted at the University of Stuttgart. This study analyses the influence of the measurement device, the mandrels and the measuring procedure on the results. Based on the study results, recommendations are derived and summarized in a best-practice guideline, which should enable an appropriate and reproducible measurement of the radial load.

scholarly journals Homotopy Analysis of Carreau Fluid Flow Over a Stretching Cylinder

2021 ◽  
Vol 88 (2) ◽  
pp. 80-92
Author(s):  
Lim Yeou Jiann ◽  
Sharidan Shafie ◽  
Ahmad Qushairi Mohamad ◽  
Noraihan Afiqah Rawi
Keyword(s):  
Nonlinear Differential Equations ◽  
Velocity Profiles ◽  
Weissenberg Number ◽  
Stretching Cylinder ◽  
Series Solutions ◽  
Carreau Fluid ◽  
Keller Box Method ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Curvature Parameter

Carreau fluid flows past a stretching cylinder is elucidated in the present study. The transformed self-similarity and dimensionless boundary layer equations are solved by using the Homotopy analysis method. A convergence study of the method is illustrated explicitly. Series solutions of the highly nonlinear differential equations are computed and it is very efficient in demonstrating the characteristic of the Carreau fluid. Validation of the series solutions is achieved via comparing with earlier published results. Those results are obtained by using the Keller-Box method. The effects of the Weissenberg number and curvature parameter on the velocity profiles are discussed by graphs and tabular. The velocity curves have shown different behavior in and for an increase of the Weissenberg number. Further, the curvature parameter K does increase the velocity profiles.

Detection of Damages in Mooring Lines of Spar Type Floating Offshore Wind Turbines Using Fuzzy Classification and Arma Parametric Modeling

2021 ◽  
pp. 2150111
Author(s):  
Mousa Rezaee ◽  
Reza Fathi ◽  
Vahid Jahangiri ◽  
Mir Mohammad Ettefagh ◽  
Aysan Jamalkia ◽  
...  
Keyword(s):  
Damage Detection ◽  
Success Rate ◽  
Wind Turbines ◽  
Parametric Modeling ◽  
Degree Of Freedom ◽  
Fuzzy Classification ◽  
Detection Methods ◽  
Measured Signal ◽  
Mooring Lines ◽  
Floating Offshore Wind Turbines

Floating wind turbines may encounter severe situations because of harsh environments. Higher cost of repair and maintenance of floating wind turbines have led researches to focus on damage detection methods that can prevent sudden failures. This paper presents an applicable method of damage detection and structural health monitoring for floating wind turbines based on the autoregressive moving average (ARMA) model and fuzzy classification. First, the dynamic model of a spar type floating wind turbine is constructed, by which the time responses of each degree of freedom of the system are acquired. With the system’s nonlinearity included, the intrinsic mode functions are obtained for the response signal. The Hilbert–Huang transform is applied and the appropriate measured signal for each degree of freedom is chosen for the ARMA modeling. In order to evaluate the proposed method, the ARMA parameters are first estimated for the undamaged condition then assumed damages are injected to the model and the ARMA parameters are once again estimated for the damaged condition. These parameters are considered as inputs for the fuzzy classification method. After training the system using the assumed damaged and undamaged conditions, the proposed method is simulated. Furthermore, the effect of measurement noise on the success rate is investigated. The results show that, in the presence of noise, the proposed method is able to identify the damage location and severity of mooring lines with acceptable success rate.

Stable and Unstable Quasiperiodic Oscillations in Robot Dynamics

1993 ◽  
Author(s):  
G. Stépán ◽  
G. Haller
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Time Lag ◽  
Nonlinear Behavior ◽  
Degree Of Freedom ◽  
Robot Dynamics ◽  
Robot Arm ◽  
Delayed Systems ◽  
Nonlinear Dynamical ◽  
Quasiperiodic Oscillations

Abstract Delays in robot control may result in unexpectedly sophisticated nonlinear dynamical behavior. Experiments on force controlled robots frequently show periodic and quasiperiodic oscillations which cannot be explained without including the time lag and/or the sampling time of the system in our models. Delayed systems, even of low degree of freedom, can produce phenomena which are already well understood in the theory of nonlinear dynamical systems but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm. The analytical results show typical nonlinear behavior in the system which may go through a codimension two Hopf bifurcation for an infinite set of parameter values, leading to the creation of two-tori in the phase space. These results give a qualitative explanation for the existence of self-excited quasiperiodic oscillations in the dynamics of force controlled robots.

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