Instability of an Elastic Strip Hanging in an Airstream

1975 ◽  
Vol 42 (1) ◽  
pp. 195-198 ◽  
Author(s):  
S. K. Datta ◽  
W. G. Gottenberg
Keyword(s):  
Small Amplitude ◽  
Critical Speed ◽  
Bending Stiffness ◽  
Elastic Strip ◽  
Approximate Analysis ◽  
Rectangular Strip ◽  
Length Width ◽  
Air Speed ◽  
The Stability

The stability of a long, thin elastic strip hanging vertically in a downward flowing airstream was considered. Experimentally it was observed that the strip remained essentially motionless or at most developed a small amplitude bounded oscillation as the air speed was increased until a critical speed was attained beyond which violent oscillations of the free-ended strip occurred. A linear approximate analysis was performed for this problem which accounted for shape-induced lift and bending stiffness of the strip and which closely predicted critical air speeds for this instability. The critical air speed was studied as a function of the length, width, and thickness of the rectangular strip.

On The Lateral Stability of a Flexible Truck

1983 ◽  
Vol 105 (2) ◽  
pp. 120-125 ◽  
Author(s):  
A. M. Whitman
Keyword(s):  
Asymptotic Expansion ◽  
Geometric Parameter ◽  
Symmetric Function ◽  
Critical Speed ◽  
Numerical Solutions ◽  
Bending Stiffness ◽  
Lateral Stability ◽  
Expansion Parameter ◽  
Entire Structure ◽  
The Stability

Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets based on an asymptotic expansion in a truck geometric parameter are derived. No restriction is placed on the values of either the shear or bending stiffness; consequently, the entire structure of the stability surface is obtained. The surface is a symmetric function of the two dimensionless stiffnesses and it depends predominantly on their series combination. Expressions are obtained for the local and global extrema and their locations. The frequency varies monotonically from the wheelset kinematic frequency to the rigid truck frequency as a function of stiffness. The results are compared with numerical solutions and found to be accurate in the region of physically obtainable values of the expansion parameter.

Torsional Oscillations in Moving Bands

1988 ◽  
Vol 110 (3) ◽  
pp. 350-355 ◽  
Author(s):  
S. T. Ariaratnam ◽  
S. F. Asokanthan
Keyword(s):  
Small Amplitude ◽  
Equation Of Motion ◽  
System Of Equations ◽  
Torsional Motion ◽  
Method Of Averaging ◽  
Gyroscopic System ◽  
Excitation Parameter ◽  
Simply Supported ◽  
Rectangular Strip ◽  
The Stability

The torsional vibration of moving bands subject to harmonic tension fluctuation is investigated. A thin rectangular strip translating longitudinally with a constant speed and simply supported at its end is considered. The linearized equation of motion, when suitably discretized, represents a linear gyroscopic system with periodically varying stiffness. The stability of the trivial solution of this system of equations, for tension fluctuations of small amplitude, is examined using the method of averaging. Analytic conditions for stability of torsional motion are obtained explicitly and shown graphically in the frequency vs excitation parameter space.

scholarly journals Steady-state $$\dot{V}{\text{O}}_{2}$$ above MLSS: evidence that critical speed better represents maximal metabolic steady state in well-trained runners

2021 ◽  
Author(s):  
Rebekah J. Nixon ◽  
Sascha H. Kranen ◽  
Anni Vanhatalo ◽  
Andrew M. Jones
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Lactate Concentration ◽  
Practical Interest ◽  
Blood Lactate Concentration ◽  
Distance Runners ◽  
Severe Intensity ◽  
The Stability ◽  
Trained Runners ◽  
Over Time

AbstractThe metabolic boundary separating the heavy-intensity and severe-intensity exercise domains is of scientific and practical interest but there is controversy concerning whether the maximal lactate steady state (MLSS) or critical power (synonymous with critical speed, CS) better represents this boundary. We measured the running speeds at MLSS and CS and investigated their ability to discriminate speeds at which $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 was stable over time from speeds at which a steady-state $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 could not be established. Ten well-trained male distance runners completed 9–12 constant-speed treadmill tests, including 3–5 runs of up to 30-min duration for the assessment of MLSS and at least 4 runs performed to the limit of tolerance for assessment of CS. The running speeds at CS and MLSS were significantly different (16.4 ± 1.3 vs. 15.2 ± 0.9 km/h, respectively; P < 0.001). Blood lactate concentration was higher and increased with time at a speed 0.5 km/h higher than MLSS compared to MLSS (P < 0.01); however, pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 did not change significantly between 10 and 30 min at either MLSS or MLSS + 0.5 km/h. In contrast, $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 increased significantly over time and reached $$\dot{V}{\text{O}}_{2\,\,\max }$$ V ˙ O 2 max at end-exercise at a speed ~ 0.4 km/h above CS (P < 0.05) but remained stable at a speed ~ 0.5 km/h below CS. The stability of $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 at a speed exceeding MLSS suggests that MLSS underestimates the maximal metabolic steady state. These results indicate that CS more closely represents the maximal metabolic steady state when the latter is appropriately defined according to the ability to stabilise pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 .

scholarly journals On the linear stability of compressible plane Couette flow

1994 ◽  
Vol 258 ◽  
pp. 131-165 ◽  
Author(s):  
Peter W. Duck ◽  
Gordon Erlebacher ◽  
M. Yousuff Hussaini
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Small Amplitude ◽  
Reynolds Numbers ◽  
Inviscid Limit ◽  
Plane Couette Flow ◽  
Moving Wall ◽  
Type Boundary ◽  
The Stability ◽  
Radiation Type

The linear stability of compressible plane Couette flow is investigated. The appropriate basic velocity and temperature distributions are perturbed by a small-amplitude normal-mode disturbance. The full small-amplitude disturbance equations are solved numerically at finite Reynolds numbers, and the inviscid limit of these equations is then investigated in some detail. It is found that instabilities can occur, although the corresponding growth rates are often quite small; the stability characteristics of the flow are quite different from unbounded flows. The effects of viscosity are also calculated, asymptotically, and shown to have a stabilizing role in all the cases investigated. Exceptional regimes to the problem occur when the wave speed of the disturbances approaches the velocity of either of the walls, and these regimes are also analysed in some detail. Finally, the effect of imposing radiation-type boundary conditions on the upper (moving) wall (in place of impermeability) is investigated, and shown to yield results common to both bounded and unbounded flows.

Influence of Interaction Between Torsion and Bending on Long-Term Nonlinear Rotor Dynamics

1999 ◽  
Author(s):  
Jiazhong Zhang ◽  
Bram de Kraker ◽  
Dick H. van Campen
Keyword(s):  
Critical Speed ◽  
Floquet Theory ◽  
Rotor Dynamics ◽  
Steady State Response ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
State Response ◽  
Stability And Bifurcation ◽  
The Stability

Abstract An elementary system with gears and excited by unbalance mass has been constructed for analyzing the interaction between torsion and bending vibration in rotor dynamics. For this system, only the interaction caused primarily by unbalance mass has been investigated. The stability and bifurcation characteristics of the system have been studied by numerical computation based on Hopf bifurcation and Floquet theory. The results show that the interaction between torsion and bending vibrations can affect the stability and bifurcation of the unbalance response, in particular the onset speed of instability. In addition to the above, the interaction also affects the steady-state response. To investigate the influence of unbalance mass, the periodic solution and its stability have been studied near the first bending critical speed of the decoupled system. All the results show that the coupling of torsion and bending vibrations can have a significant influence on the nonlinear dynamics of the whole system.

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.

scholarly journals Road train motion stability in BRT system

2019 ◽  
Vol 254 ◽  
pp. 03007 ◽  
Author(s):  
Vladimir Sakhno ◽  
Juraj Gerlici ◽  
Viktor Poliakov ◽  
Alexandr Kravchenko ◽  
Oleg Omelnitcky ◽  
...  
Keyword(s):  
Critical Speed ◽  
Motor Vehicles ◽  
Mass Center ◽  
Passenger Transportation ◽  
Wheel Drive ◽  
Main Index ◽  
Rapid Transport ◽  
The Stability ◽  
The City ◽  
Potential Stability

The peculiarities of organization and perspectives of mass passenger transportation in the city and beyond are considered with the use of "Bus Rapid Transport" (BRT) or Metrobus. Different aspects of study of motor vehicles (MV) controllability and stability are analyzed. It is substantiated that it is sufficient to consider the potential stability of the MV itself, in order to guarantee the stability of the "driver MV" system with a large reserve. A mathematical model of a three-axle bus train consisting of a bus and two trains (metrobus) is developed and the factors influencing the critical speed as the main index of the stability of its movement are determined. It is established that the increase of the critical speed of the metrobus can be achieved by increasing the base of the bus, the first and the second trailer, as well as the mass of the bus and the coefficients of resistance of the drive wheels of the bus driving axle and the trailers axles. At the same time, increasing the distance from the mass center to the bus rear axle, increasing the distance from the mass center to the point of the coupling of the bus with the first trailer, increasing the mass of trailers and the resistance of the resistance of the wheel drive of the bus axis lead to a decrease in the critical speed of the metrobus. This must be taken into account both when designing metrobuses, and when operating them.

scholarly journals Dynamic Characteristics and Experimental Research of a Two-Span Rotor-Bearing System with Rub-Impact Fault

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Rui Zhu ◽  
Guang-chao Wang ◽  
Qing-peng Han ◽  
An-lei Zhao ◽  
Jian-xing Ren ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Critical Speed ◽  
Great Influence ◽  
Experimental Platform ◽  
Rotating Machine ◽  
Rotor Bearing ◽  
Before And After ◽  
Analysis System ◽  
The Stability ◽  
Bearing System

Rotor rub-impact has a great influence on the stability and safety of a rotating machine. This study develops a dynamic model of a two-span rotor-bearing system with rubbing faults, and numerical simulation is carried out. Moreover, frictional screws are used to simulate a rubbing state by establishing a set of experimental devices that can simulate rotor-stator friction in the rotor system. Through the experimental platform and its analysis system, the rubbing experiment was conducted, and the vibration of the rotor-bearing system before and after the critical speed is observed. Rotors running under normal condition, local slight rubbing, and severe rubbing throughout the entire cycle are simulated. Dynamic trajectories, frequency spectrum diagrams, chart of axis track, and Poincare maps are used to analyze the features of the rotor-bearing system with rub-impact faults under various parameters. The vibration characteristics of rub impact are obtained. Results show that the dynamic characteristics of the rotor-bearing system are affected by the change in velocity and degree of impact friction. The findings are helpful in further understanding the dynamic characteristics of the rub-impact fault of the two-span rotor-bearing system and provide reference for fault diagnosis.

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