An Investigation of Riser Fairing Instability

2015 ◽  
Author(s):  
Trygve Kristiansen ◽  
Henning Braaten ◽  
Halvor Lie ◽  
Rolf Baarholm ◽  
Kjetil Skaugset
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Diameter Ratio ◽  
Instability Region ◽  
The Other ◽  
Two Degrees Of Freedom ◽  
Linearized Equations ◽  
Different Types ◽  
Instability Regions ◽  
Damping Model

An analysis of galloping of two different types of riser fairings is presented. The first is named “long fairing” (LF) and the other “Short Crab Claw” (Short CC). The first one has a traditionally winged formed shape with a cord-to-diameter ratio of 2.43. The other one is more truncated in shape, and has cord-to-diameter ratio of only 1.4. Results from two related experimental set-ups are included in the work; one 2D experiment with towing tests of fairings that are free to translate and rotate to investigate instability regions, and one 2D experiment with fixed fairings to obtain drag, moment and lift curves. The present analysis is based on two-degrees of freedom, linearized equations of motion, and predicts a range of velocities where instability occurs. Below and above this region, the fairing is stable. Damping complicates the analysis. An empirical damping model is included and discussed. The two fairing types inhibit appreciably different instability characteristics. In particular, the Short CC fairing has a narrower instability region than the long fairing, and is therefore less prone to instabilities.

The Conceptual Design of Differential Mechanisms

2013 ◽  
Vol 284-287 ◽  
pp. 973-978
Author(s):  
Chia Chun Chu
Keyword(s):  
Conceptual Design ◽  
Design Process ◽  
Degrees Of Freedom ◽  
Geometric Constraints ◽  
The Other ◽  
Design Approach ◽  
Process Step ◽  
Two Degrees Of Freedom ◽  
Number Synthesis

The purpose of this paper is to present a design approach based on the geometric constraints of joints for synthesizing differential mechanisms with two degrees-of-freedom, including some mechanisms with the same functions but distinct structures. The concept of virtual axes is presented. And, there are five steps in the design process. Step 1 is to decide fundamental entities by the properties of existing mechanisms and the technique of number synthesis, and 10 suitable fundamental entities of differential mechanisms are available. Step 2 is to compose geometric constraints, and 14 items are obtained. Step 3 is to compose links, and 15 items are derived. Step 4 is to assign fixed constraints for inputs or outputs, and 15 results are found. The final step is to particularize the obtained events by the properties of existing mechanisms and the structures of fundamental entities. As a result, 8 feasible results for differential mechanisms with two degrees-of-freedom and two basic loops are obtained in which 2 are existing designs and the other 6 are novel.

Synthesis of Seven-Link Mechanisms

1973 ◽  
Vol 95 (2) ◽  
pp. 533-540 ◽  
Author(s):  
D. Kohli ◽  
A. H. Soni
Keyword(s):  
Closed Form ◽  
Nonlinear Equations ◽  
Degrees Of Freedom ◽  
The Other ◽  
Linear Superposition ◽  
Two Degrees Of Freedom ◽  
Closed Form Solutions ◽  
Highly Nonlinear ◽  
Principle Of Linear Superposition

The mechanisms derived from the seven-link chains with five links in their two loops and having two degrees of freedom are examined for six synthesis problems. Using displacement matrices, closed form synthesis equations are derived. It is shown that three synthesis problems may be solved using the principle of linear superposition, and closed form solutions may be obtained. The other three synthesis problems involve highly nonlinear equations and must be solved numerically.

Helicopter Ground Resonance Phenomenon With Blade Stiffness Dissimilarities: Experimental and Theoretical Developments

2012 ◽  
Author(s):  
Leonardo Sanches ◽  
Guilhem Michon ◽  
Alain Berlioz ◽  
Daniel Alazard
Keyword(s):  
Equations Of Motion ◽  
Resonance Phenomenon ◽  
Aging Effects ◽  
Ground Resonance ◽  
Different Types ◽  
Stability Chart ◽  
Instability Regions ◽  
The Stability ◽  
Theoretical Results ◽  
Theoretical Developments

Recent works study the ground resonance in helicopters under the aging effects. Indeed, the blades lead-lag stiffness may vary randomly with time and be different from each other (i.e.: anisotropic rotor). The influence of stiffness dissimilarities between blades on the stability of the ground resonance phenomenon is determined through numerical investigations on the periodical equations of motion, treated by using Floquet’s theory. Stability chart highlights the appearance of new instability zones as function of the perturbation introduced on the lead-lag stiffness of one blade. In order to validate the theoretical results, a new experimental setup is designed and developed. The ground resonance instabilities are investigated for different types of rotor configurations (i.e.: isotropic and anisotropic rotors) and the boundaries of stability are determined. A good correlation between both theoretical and experimental results is obtained and the new instability zones, found in asymmetric rotors, are verified experimentally. The temporal responses of the measured signals highlight the exponential divergence at the instability regions.

Trajectories Generated by a Novel Cam Driven Five-Bar Mechanism

2015 ◽  
Vol 799-800 ◽  
pp. 685-692
Author(s):  
Shinn Liang Chang ◽  
Dai Jia Juan ◽  
You Huang Syu
Keyword(s):  
Degrees Of Freedom ◽  
Trajectory Generation ◽  
Special Kind ◽  
Degree Of Freedom ◽  
Two Degrees Of Freedom ◽  
Different Types

In industry, the special kind of trajectory is often designed to fit the desired motion required. In literature, four-bar mechanism is popularly applied and well studied in the trajectory generation. Different types of trajectories are generated by the choose of the ratio of links. The five-bar mechanism is another popular one to generate the desired trajectory and it is more flexible due to it has two degrees of freedom. The geared five-bar mechanism is then commonly used by reducing the degree of freedom of the mechanism into one by implied one pair of gear. In this study, the trajectories generated by a novel cam driven five-bar mechanism proposed by the authors are investigated. It could supply more choices in the application of trajectory generation.

Investigation of manipulator dynamics with a viscous damping model

2007 ◽  
Vol 221 (5) ◽  
pp. 513-517
Author(s):  
P Herman
Keyword(s):  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Viscous Damping ◽  
First Order ◽  
Manipulator Dynamics ◽  
Interesting Insight ◽  
Damping Model ◽  
Insight Into

In this article, some remarks concerning dynamics investigation of a manipulator described using first-order equations of motion with a viscous damping model is conducted. The viscous damping model arises from the Rayleigh dissipation potential and decomposition of the manipulator mass matrix. As a result, it takes into account both kinematic and mechanical parameters of the system. Moreover, the use of first-order equations of motion leads to obtaining some interesting insight into the manipulator dynamics. The proposed approach was tested on a three-degrees-of-freedom, three-dimensional Yasukawa-like robot.

Two-Degree-of-Freedom Decoupled Nonredundant Cable-Loop-Driven Parallel Mechanism

2013 ◽  
Vol 6 (1) ◽  
Author(s):  
Hanwei Liu ◽  
Clément Gosselin ◽  
Thierry Laliberté
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
The Other ◽  
End Effector ◽  
Two Degrees Of Freedom ◽  
Actuation Redundancy ◽  
Rigid Link ◽  
Force Closure ◽  
Two Degree Of Freedom

A novel two-degree-of-freedom (DOF) cable-loop slider-driven parallel mechanism is introduced in this paper. The novelty of the mechanism lies in the fact that no passive rigid-link mechanism or springs are needed to support the end-effector (only cables are connected to the end-effector) while at the same time there is no actuation redundancy in the mechanism. Sliders located on the edges of the workspace are used and actuation redundancy is eliminated while providing force closure everywhere in the workspace. It is shown that the two degrees of freedom of the mechanism are decoupled and only two actuators are needed to control the motion. There are two cable loops for each direction of motion: one acts as the actuating loop while the other is the constraint loop. Due to the simple geometric design, the kinematic and static equations of the mechanism are very compact. The stiffness of the mechanism is also analyzed in the paper. It can be observed that the mechanism's stiffness is much higher than the stiffness of the cables. The proposed mechanism's workspace is essentially equal to its footprint and there are no singularities.

Lyapunov Functions and Sliding Mode Control for Two Degrees-of-Freedom and Multidegrees-of-Freedom Fractional Oscillators

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Youan Zhang ◽  
Jian Yuan ◽  
Jingmao Liu ◽  
Bao Shi
Keyword(s):  
Differential Equations ◽  
Sliding Mode Control ◽  
Lyapunov Functions ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Control Design ◽  
State Equations ◽  
Two Degrees Of Freedom ◽  
Mode Control

This paper addresses the Lyapunov functions and sliding mode control design for two degrees-of-freedom (2DOF) and multidegrees-of-freedom (MDOF) fractional oscillators. First, differential equations of motion for 2DOF fractional oscillators are established by adopting the fractional Kelvin–Voigt constitute relation for viscoelastic materials. Second, a Lyapunov function candidate for 2DOF fractional oscillators is suggested, which includes the potential energy stored in fractional derivatives. Third, the differential equations of motion for 2DOF fractional oscillators are transformed into noncommensurate fractional state equations with six dimensions by introducing state variables with physical significance. Sliding mode control design and adaptive sliding mode control design are proposed based on the noncommensurate fractional state equations. Furthermore, the above results are generalized to MDOF fractional oscillators. Finally, numerical simulations are carried out to validate the above control designs.

A New Method for Modeling of Fully Flexible Aircrafts

2011 ◽  
Vol 383-390 ◽  
pp. 2350-2355
Author(s):  
Dong Guo ◽  
Min Xu ◽  
Shi Lu Chen ◽  
Yu Qian
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Structural Model ◽  
Equations Of Motion ◽  
Flight Mechanics ◽  
Lagrangian Mechanics ◽  
Seamless Integration ◽  
Different Types ◽  
New Formulation ◽  
Nonlinear Rigid

The purpose of this study is to produce a modeling capability for integrated flight dynamics of flexible aircraft that can better predict some of the complex behaviors in flight due to multi-physics coupling. Based on the studying of the exiting modeling approaches, the author put forward a new modeling method, and developed a new formulation integrating nonlinear rigid-body flight mechanics and linear aeroelastic dynamics for fully elastic aircrafts using Lagrangian mechanics. The new equations of motion overcome the disadvantages of the exiting methods, and include automatically all six rigid-body degrees of freedom and elastic information, the seamless integration is achieved by using the same reference frame and the same variables to describe the aircraft motions and the forces acting on it, including the aerodynamic forces. The formulation is modular in nature, in the sense that the structural model, the aerodynamic theory, and the controls method can be replaced by any other ones to better suit different types of aircraft.

Stability of the Vibrations of a Parameter-Excited System

1982 ◽  
Vol 49 (4) ◽  
pp. 920-921
Author(s):  
M. Gu¨rgo¨ze
Keyword(s):  
Differential Equation ◽  
Degrees Of Freedom ◽  
Instability Region ◽  
Horizontal Plate ◽  
Two Degrees Of Freedom ◽  
Excited System ◽  
The Subject ◽  
Excitation Frequencies ◽  
The Stability ◽  
Special Parameter

The subject of this Brief Note is to introduce a special parameter-excited system with two degrees of freedom, which has its principal instability region at ω ≈ ω0 instead at ω ≈ 2ω0. It consists of a horizontal plate with a fixed pin and a slotted rigid bar on it, in which the bar can rotate and translate with respect to the plate. The stability of its vibrations is investigated for the case in which the plate is harmonicaly excited in its own plane. Starting with the Mathieu differential equation, which governs the rotational vibrations, it is possible to predict the excitation frequencies, which must be avoided, to ensure the stability.

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