scholarly journals Non-linear time domain analysis of cross-flow vortex-induced vibrations

2017 ◽  
Vol 51 ◽  
pp. 134-151 ◽  
Author(s):  
M.J. Thorsen ◽  
S. Sævik ◽  
C.M. Larsen
Keyword(s):  
Time Domain ◽  
Linear Time ◽  
Cross Flow ◽  
Time Domain Analysis ◽  
Domain Analysis ◽  
Vortex Induced Vibrations ◽  
Non Linear ◽  
Flow Vortex

Concrete Modeling for Extreme Wave Slam Events

2017 ◽  
Author(s):  
Kasper Wåsjø ◽  
Terje P. Stavang ◽  
Tore H. Søreide
Keyword(s):  
Time Domain ◽  
Linear Time ◽  
Limit State ◽  
Material Model ◽  
Time Domain Analysis ◽  
Domain Analysis ◽  
Capacity Control ◽  
Extreme Wave ◽  
Conventional Design ◽  
Non Linear

Experience from model tests has initiated a growing attention towards extreme wave slam as a critical load situation for offshore large volume structures. Most of the problem is related to the local slam pressure, which may go up to several MPa’s for 100-year and 10 000-year waves. The paper deals with modeling techniques for marine concrete structures under extreme slam loading from waves where dynamic effects together with material softening play a major role for the response. Different analysis approaches for ultimate limit state (ULS) and accidental limit state (ALS) controls are discussed in view of reliability philosophy as basis for conventional design approach. The present paper is devoted to the local impact scenario and the alternative approaches for response and capacity control involving non-linear time domain analyses. Conventional design schemes as based on linear elastic models for response calculation together with code specified capacity control often come out more conservative than non-linear approach. The paper demonstrates by case studies how softening of the structure in general reduces the response in terms of section forces. A key issue when going from conventional linear approaches into non-linear techniques is to still keep an acceptable reliability level on the capacity control. Load and material factors are normally based on structures with limited non-linearity where linear response modeling is representative. Implementing non-linear material model in time domain analysis has a major challenge in limiting the sensitivity in response and capacity calculation. The paper demonstrates the way material model of concrete affects the section forces to go into local capacity control, and concludes on needed sensitivity analyses. Practical approaches on the concrete slam problem together with resulting utilizations from the control are demonstrated. The full non-linear technique by response and capacity control in one analysis is also handled, using average material parameters and justifying safety factors for the effect of implementing characteristic lower strength of concrete in the capacity. The paper ends up in a recommendation on non-linear time domain analysis procedure for typically slam problems. A discussion is also given on applicable design codes with attention to non-linear analysis.

Frequency and Time Domain Analysis of Vortex Induced Vibrations for Free Span Pipelines

2002 ◽  
Author(s):  
Carl M. Larsen ◽  
Kamran Koushan ◽  
Elizabeth Passano
Keyword(s):  
Time Domain ◽  
Structural Model ◽  
Linear Time ◽  
Time Domain Analysis ◽  
Linear Response Theory ◽  
Domain Model ◽  
Vortex Induced Vibrations ◽  
Non Linear ◽  
New Strategy ◽  
Stress Prediction

The present paper will discuss various models for calculation of vortex induced vibrations (VIV) of free span pipelines, and present a new strategy for such analyses. Applications of traditional models are presented and their limitations discussed. The new approach is based on the combination of an empirical linear frequency domain model, and a non-linear time domain structural model. The first step is to carry out the VIV analysis according to linear response theory, and next introduce the calculated hydrodynamic forces to the non-linear structural model. The benefit from using the non-linear model is to describe stresses at the shoulders more accurately, which is important since fatigue damage in many cases will be largest in this area. The conclusion is that the interaction between pipe and seafloor is crucial for accurate stress prediction, and that a non-linear time domain model will give the most accurate result.

Time and Frequency Domain Analysis of Catenary Risers Subjected to Vortex Induced Vibrations

2006 ◽  
Author(s):  
Carl M. Larsen ◽  
Elizabeth Passano
Keyword(s):  
Frequency Domain ◽  
Linear Model ◽  
Time Domain ◽  
Structural Model ◽  
Linear Time ◽  
Domain Analysis ◽  
Domain Model ◽  
Vortex Induced Vibrations ◽  
Non Linear ◽  
Bending Stresses

Catenary risers in deep waters will experience conditions with insignificant wave forces in combination with strong current. The response will in such cases be dominated by vortex induced vibrations (VIV). Dynamic bending stresses will vary along the riser, but a large peak will almost always be seen near the touch down point. This peak is caused by the restrictions on riser displacements from the presence of the seafloor, and the local bending stresses will be influenced by stiffness and damping propertoes of the bottom. Analysis models based on finite elements will represent the interaction between riser and seafloor by discrete springs, which for the linear case will remain constant independent of the displacements. This type of model may give a significant over-prediction of bending stresses at the touch down point since a linear spring will give tensile forces instead of being released and allowing the pipe to lift off from the bottom. A non-linear time domain model will, however, account for changes by releasing springs if tension occurs and adding in new springs if free nodes obtain temporary contact with the bottom. The results will hence become far more realistic. Traditional empirical models for VIV prediction are based on a frequency domain dynamic analysis with constant stiffness. There is hence an obvious need for improvements when dealing with catenary risers. This paper will describe a new approach that is based on combined use of an empirical linear frequency domain model for VIV, and a non-linear model for time domain analysis. The first step is to carry out the VIV analysis according to linear response theory, and next introduce the calculated hydrodynamic forces to the non-linear structural model. The benefit from using the non-linear model is that stresses in the touch down area are described more accurately. A case study is also reported. Bottom stiffness and friction are varied, and results are compared to a simple model with a hinge at the touch down point. The conclusion is that the interaction between riser and seafloor is crucial for accurate stress prediction, and that a non-linear time domain model will give the most accurate result.

A Frequency Domain Analysis of Learning Control

1994 ◽  
Vol 116 (4) ◽  
pp. 781-786 ◽  
Author(s):  
C. J. Goh
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Linear Time ◽  
Planning Horizon ◽  
Time Domain Analysis ◽  
Learning Control ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Convergence Criterion ◽  
The Time Domain

The convergence of learning control is traditionally analyzed in the time domain. This is because a finite planning horizon is often assumed and the analysis in time domain can be extended to time-varying and nonlinear systems. For linear time-invariant (LTI) systems with infinite planning horizon, however, we show that simple frequency domain techniques can be used to quickly derive several interesting results not amenable to time-domain analysis, such as predicting the rate of convergence or the design of optimum learning control law. We explain a paradox arising from applying the finite time convergence criterion to the infinite time learning control problem, and propose the use of current error feedback for controlling possibly unstable systems.

Modelling and simulation of a compliant tilting pad air bearing

2015 ◽  
Vol 230 (1) ◽  
pp. 69-87 ◽  
Author(s):  
Frans Duijnhouwer ◽  
Henk Nijmeijer
Keyword(s):  
Dynamic Simulation ◽  
Time Domain ◽  
Linear Time ◽  
Simulation Models ◽  
Time Domain Analysis ◽  
Air Bearing ◽  
Rotor Systems ◽  
Tilting Pad ◽  
Non Linear ◽  
Dynamic Simulation Model

The compliant tilting pad air bearing concept, a tilting pad bearing with the pivot of the pads placed on radial springs, is a promising aerodynamic bearing solution. Nevertheless, its non-linear dynamics make a time domain dynamic simulation model an essential tool for the design of rotor systems with these bearings. Development of these dynamic simulation models is the subject of this paper that provides a detailed description of an extendible model of the compliant tilting pad air bearing concept suitable for non-linear time domain analysis. 2D and 3D time domain simulations implementing the model are discussed in detail and some of their capabilities to model the non-linear behaviour of the bearing concept are demonstrated with examples.

Non-Linear Time Domain Analysis of Vortex Induced Vibrations for Free Spanning Pipelines

2004 ◽  
Author(s):  
Carl M. Larsen ◽  
Elizabeth Passano ◽  
Gro Sagli Baarholm ◽  
Kamran Koushan
Keyword(s):  
Fatigue Damage ◽  
Time Domain ◽  
Linear Time ◽  
Linear Method ◽  
Empirical Models ◽  
Nonlinear Behaviour ◽  
Hydrodynamic Coefficients ◽  
New Approach ◽  
Vortex Induced Vibrations ◽  
Non Linear

Pipelines from offshore petroleum fields must frequently pass over areas with uneven seafloor. In such cases the pipeline may have free spans when crossing depressions. Hence, if dynamic loads can occur, the free span may oscillate and time varying stresses may give unacceptable fatigue damage. A major source for dynamic stresses in deep water free span pipelines is vortex induced vibrations (VIV) caused by current. Two alternative strategies for calculation of VIV are seen today. Practical engineering is still based on empirical models, while use of computational fluid dynamics (CFD) is considered immature mainly because of the needed computing resources. Most empirical models are based on frequency domain dynamic solutions and linear structural models, cf. Larsen (2000). The reason for this is simply that hydrodynamic coefficients as needed in a VIV analysis are available as functions of frequency, and therefore not directly applicable in a transient time domain simulation. A free span pipeline has, however, important nonlinearities that should be taken into consideration. Both tension variation and pipe-seafloor interaction at the span shoulders will contribute to nonlinear behaviour, which means that most empirical models will have significant limitations when dealing with the free span case. The need for non-linear time domain methods is therefore obvious. This paper describes a new approach for VIV analysis of free span pipelines where both linear frequency and non-linear time domain analyses are employed. The first step is to carry out a conventional VIV analysis that will determine response frequency and hydrodynamic coefficients by use of a linear response model. This result is then used in a time domain model that can handle non-linear boundary conditions at the span shoulders. This approach is valid as long as the response amplitudes at the main part of the span are the same for both analysis methods. The significance of the new method is that displacements, and hence also stresses, in the pipe at the shoulders will be far better described by the non-linear method than what is possible from linear theory. Since fatigue damage in most cases is larger at the shoulder than within the mid section of the span, the new approach represents an important step forward for free span pipeline analysis.

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