scholarly journals Flutter of long flexible cylinders in axial flow

2007 ◽  
Vol 571 ◽  
pp. 371-389 ◽  
Author(s):  
E. DE LANGRE ◽  
M. P. PAÏDOUSSIS ◽  
O. DOARÉ ◽  
Y. MODARRES-SADEGHI
Keyword(s):  
Axial Flow ◽  
Equation Of Motion ◽  
External Flow ◽  
Transverse Motion ◽  
Control Parameters ◽  
Limit Case ◽  
Finite Region ◽  
Flexible Cylinder ◽  
Linear And Nonlinear ◽  
The Stability

We consider the stability of a thin flexible cylinder considered as a beam, when subjected to axial flow and fixed at the upstream end only. A linear stability analysis of transverse motion aims at determining the risk of flutter as a function of the governing control parameters such as the flow velocity or the length of the cylinder. Stability is analysed applying a finite-difference scheme in space to the equation of motion expressed in the frequency domain. It is found that, contrary to previous predictions based on simplified theories, flutter may exist for very long cylinders, provided that the free downstream end of the cylinder is well-streamlined. More generally, a limit regime is found where the length of the cylinder does not affect the characteristics of the instability, and the deformation is confined to a finite region close to the downstream end. These results are found complementary to solutions derived for shorter cylinders and are confirmed by linear and nonlinear computations using a Galerkin method. A link is established to similar results on long hanging cantilevered systems with internal or external flow. The limit case of vanishing bending stiffness, where the cylinder is modelled as a string, is analysed and related to previous results. Comparison is also made to existing experimental data, and a simple model for the behaviour of long cylinders is proposed.

scholarly journals Flutter of Long Flexible Cylinders in Axial Flow

2006 ◽  
Author(s):  
E. de Langre ◽  
M. P. Paidoussis ◽  
Y. Modarres-Sadeghi ◽  
O. Doare´
Keyword(s):  
Stability Analysis ◽  
Axial Flow ◽  
Equation Of Motion ◽  
External Flow ◽  
Transverse Motion ◽  
Control Parameters ◽  
Limit Case ◽  
Finite Region ◽  
Flexible Cylinder ◽  
The Stability

We consider the stability of a thin flexible cylinder considered as a beam, when subjected to axial flow and fixed at the up-stream end only. A linear stability analysis of transverse motion aims at determining the risk of flutter as a function of the governing control parameters such as the flow velocity or the length of the cylinder. Stability is analysed applying a finite difference scheme in space to the equation of motion expressed in the frequency domain. It is found that, contrary to previous predictions based on simplified theories, flutter may exist for very long cylinders, provided that the free downstream end of the cylinder is well-streamlined. More generally, a limit regime is found where the length of the cylinder does not affect the characteristics of the instability, and the deformation is confined to a finite region close to the downstream end. These results are found complementary to solutions derived for shorter cylinders and are confirmed by linear computations using a Galerkin method. A link is established to similar results on long hanging cantilevered systems with internal or external flow. The limit case of vanishing bending stiffness, where the cylinder is modelled as a string, is analysed and related to previous results. A simple model for the behaviour of long cylinders is proposed.

Nonlinear Dynamics of Supported Cylinder Subjected to Axial Flow

2011 ◽  
Vol 243-249 ◽  
pp. 4712-4717
Author(s):  
Ji Duo Jin ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Flow Velocity ◽  
Nonlinear Model ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Equation Of Motion ◽  
Flexible Cylinder ◽  
Chaotic Motions ◽  
Flutter Instability ◽  
The Stability

In this paper, the stability and nonlinear dynamics are studied for a slender flexible cylinder subjected to axial flow. A nonlinear model is presented, based on the corresponding linear equation of motion, for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are only the additional axial force induced by the lateral motions of the cylinder. Using six-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain, with this relatively simple nonlinear model, the flutter instability found in experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. As the flow velocity increases further, the quasiperiodic motion around the buckled position occurs, and this evolves into chaotic motions at higher flow.

Stability of a String in Axial Flow

1985 ◽  
Vol 107 (4) ◽  
pp. 421-425 ◽  
Author(s):  
G. S. Triantafyllou ◽  
C. Chryssostomidis
Keyword(s):  
Stability Analysis ◽  
Frictional Coefficient ◽  
Axial Flow ◽  
Added Mass ◽  
Equation Of Motion ◽  
Bending Stiffness ◽  
Diameter Ratio ◽  
Constant Speed ◽  
Hamilton’S Principle ◽  
The Stability

The equation of motion of a long slender beam submerged in an infinite fluid moving with constant speed is derived using Hamilton’s principle. The upstream end of the beam is pinned and the downstream end is free to move. The resulting equation of motion is then used to perform the stability analysis of a string, i.e., a beam with negligible bending stiffness. It is found that the string is stable if (a) the external tension at the free end exceeds the value of a U2, where a is the “added mass” of the string and U the fluid speed; or (b) the length-over-diameter ratio exceeds the value 2Cf/π, where Cf is the frictional coefficient of the string.

Linear and Nonlinear Dynamics of Cantilevered Cylinders in Axial Flow

2014 ◽  
Author(s):  
Ahmad Jamal ◽  
Michael P. Païdoussis ◽  
Luc G. Mongeau
Keyword(s):  
Equations Of Motion ◽  
Axial Flow ◽  
Experimental System ◽  
Vital Role ◽  
Viscous Force ◽  
Flexible Cylinder ◽  
Force Coefficients ◽  
Precise Calculation ◽  
Linear And Nonlinear ◽  
Nonlinear Equations Of Motion

Understanding and prediction of the dynamics of slender flexible cylinders in axial flow is of interest for the design and safe operation of heat exchangers and nuclear reactors, specifically that of heat exchanger tubes, nuclear fuel elements, control rods, and monitoring tubes. In such fluid-structure interaction problems, the fluid forces acting on the flexible structure play a vital role in defining its dynamics. Therefore, a precise calculation of the coefficients associated to these forces, such as the longitudinal and normal viscous force coefficients, and base drag coefficient in the equation of motion is imperative. The present work is aimed at (i) calculating these force coefficients for a cantilevered slender flexible cylinder, fitted with an ogival end-piece, in axial flow and (ii) conducting experiments on the same system. In the calculation of these force coefficients, the parameters of the experimental system are used, so that the theoretically predicted dynamics would be representative of the actual physical system. These calculated force coefficients are then incorporated in the linear and nonlinear equations of motion and the predicted dynamics are compared with those of the experiments. The comparison shows good agreement between the theoretical and experimental results.

A Numerical Investigation on the Dynamics of Two-Dimensional Cantilevered Flexible Plates in Axial Flow

2006 ◽  
Author(s):  
Liaosha Tang ◽  
Michael P. Pai¨doussis
Keyword(s):  
Flow Velocity ◽  
Pressure Difference ◽  
Axial Flow ◽  
Equation Of Motion ◽  
Current Theory ◽  
Vortex Model ◽  
Flexible Plates ◽  
Flutter Boundary ◽  
The Stability ◽  
The Time Domain

A cantilevered plate immersed in an otherwise uniform flow may lose stability at a high enough flow velocity; flutter takes place when the flow velocity exceeds a critical value. In the current research, a nonlinear equation of motion of the plate is developed using the inextensibility condition. Also, an unsteady lumped vortex model is used to calculate the pressure difference across the plate. The pressure difference is then decomposed into a lift force and an inviscid drag force. The fluid loads are coupled with the plate equation of motion and a numerical model of the fluid-structure system is developed. Analysis of the system dynamics is carried out in the time-domain. Both the stability and the post-critical behaviour of the system are studied. The flutter boundary and the vibration modes predicted by the current theory are found to be in good agreement with published experimental data.

Nonlinear Dynamics of a Slender Flexible Cylinder in Axial Flow

2011 ◽  
Vol 130-134 ◽  
pp. 761-765
Author(s):  
Ji Duo Jin ◽  
N. Li ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Flow Velocity ◽  
Nonlinear Model ◽  
Dynamic Instability ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Viscous Force ◽  
Flexible Cylinder ◽  
Flutter Instability ◽  
The Stability

The stability and nonlinear dynamics are studied for a slender flexible cylinder subjected to axial flow. A nonlinear model is presented, based on the corresponding linear equation of motion, for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are the quadratic viscous force and the additional axial force induced by the lateral motions of the cylinder. Using two-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain, with this relatively simple nonlinear model, the flutter instability found in experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the buckled configuration becomes unstable at higher flow leading to post-divergence flutter. As the flow velocity increases further, the system is restabilized in the buckled configuration prior to another dynamic instability at higher flow.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

scholarly journals Delayed Trilateral Teleoperation of a Mobile Robot

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
D. Santiago ◽  
E. Slawiñski ◽  
V. Mut
Keyword(s):  
Stability Analysis ◽  
Mobile Robot ◽  
Shared Environment ◽  
Time Varying ◽  
Control Parameters ◽  
Simple Test ◽  
Control Loop ◽  
Teleoperation System ◽  
Human Operators ◽  
The Stability

This paper analyzes the stability of a trilateral teleoperation system of a mobile robot. This type of system is nonlinear, time-varying, and delayed and includes a master-slave kinematic dissimilarity. To close the control loop, three P+d controllers are used under a position master/slave velocity strategy. The stability analysis is based on Lyapunov-Krasovskii theory where a functional is proposed and analyzed to get conditions for the control parameters that assure a stable behavior, keeping the synchronism errors bounded. Finally, the theoretical result is verified in practice by means of a simple test, where two human operators both collaboratively and simultaneously drive a 3D simulator of a mobile robot to achieve an established task on a remote shared environment.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

The Stability-Limiting Flow Mechanisms in a Subsonic Axial-Flow Compressor and Its Passive Control With Casing Treatment

2008 ◽  
Author(s):  
Xingen Lu ◽  
Junqiang Zhu ◽  
Chaoqun Nie ◽  
Weiguang Huang
Keyword(s):  
Flow Instability ◽  
State Of The Art ◽  
Axial Flow ◽  
Flow Mechanism ◽  
Blade Passage ◽  
Casing Treatment ◽  
Compressor Rotor ◽  
Flow Compressor ◽  
The Stability ◽  
End Wall

The phenomenon of flow instability in the compression system such as fan and compressor has been a long-standing “bottle-neck” problem for gas turbines/aircraft engines. With a vision of providing a state-of-the-art understanding of the flow field in axial-flow compressor in the perspective of enhancing their stability using passive means. Two topics are covered in this paper. The first topic is the stability-limiting flow mechanism close to stall, which is the basic knowledge needed to manipulate end-wall flow behavior for the stability improvement. The physical process occurring when approaching stall and the role of complex tip flow mechanism on flow instability in current high subsonic axial compressor rotor has been assessed using single blade passage computations. The second topic is flow instability manipulation with casing treatment. In order to advance the understanding of the fundamental mechanisms of casing treatment and determine the change in the flow field by which casing treatment improve compressor stability, systematic studies of the coupled flow through a subsonic compressor rotor and various end-wall treatments were carried out using a state-of-the-art multi-block flow solver. The numerically obtained flow fields were interrogated to identify complicated flow phenomenon around and within the end-wall treatments and describe the interaction between the rotor tip flow and end-wall treatments. Detailed analyses of the flow visualization at the rotor tip have exposed the different tip flow topologies between the cases with treatment casing and with untreated smooth wall. It was found that the primary stall margin enhancement afforded by end-wall treatments is a result of the tip flow manipulation. Compared to the smooth wall case, the treated casing significantly dampen or absorb the blockage near the upstream part of the blade passage caused by the upstream movement of tip clearance flow and weakens the roll-up of the core vortex. These mechanisms prevent an early spillage of low momentum fluid into the adjacent blade passage and delay the onset of flow instability.

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