Multi-Wave Flutter Vibrations in Mistuned Cascades with Tip-Shroud Friction

2020 ◽  
Author(s):  
Johann Gross ◽  
Malte Krack
Keyword(s):  
Single Mode ◽  
Wave Form ◽  
Modal Interaction ◽  
Modal Interactions ◽  
Multiple Wave ◽  
Aero Engine ◽  
Wave Forms ◽  
Nonlinear Modal Interaction ◽  
The Rich ◽  
Tip Shroud

Abstract Measurements taken during aero engine tests and in the field showed that flutter vibrations of shrouded blades can feature rich wave content (multi-wave flutter vibrations). In a previous work, we demonstrated that this behavior can be explained by the nonlinear interaction of aeroelastically unstable traveling wave modes. The resulting vibrations are quasi-periodic. In the present work, we show that the nonlinear modal interaction is not strictly needed, but actually mistuning alone can explain the multi-wave form of flutter vibrations. The resulting vibrations are periodic and dominated by only a single mode shape of the mistuned system. However, unrealistically high mistuning intensities are needed to obtain significant contributions of multiple wave forms under the considered strong inter-blade coupling. Thus, we conclude that mistuning cannot explain the rich wave content observed in the measurements. Moreover, mistuning tends to hamper the nonlinear modal interactions and, thus, the occurrence of quasi-periodic multi-wave flutter vibrations. This implies that intentional mistuning is not only useful to stabilize flutter, but might also play an important role in developing flutter-tolerant blade designs.

scholarly journals Fundamental Study of Oscillations in the Nigerian Power System

2021 ◽  
Author(s):  
Nnaemeka Sunday UGWUANYI ◽  
Uma Uzubi Uma ◽  
Arthur Obiora Ekwue
Keyword(s):  
Power Systems ◽  
Power System ◽  
Low Frequency ◽  
Modal Interaction ◽  
Modal Interactions ◽  
Fundamental Study ◽  
Power Stations ◽  
Nonlinear Modal Interaction ◽  
Stability Limits ◽  
Comprehensive Study

The power systems in developing countries are usually stressed and operated near their stability limits. Consequently, accurate sources of oscillations and their controls can present a challenge. This paper reports a comprehensive study of the oscillations in the Nigerian 48-bus power system. The dominant modes, sensitive locations for faults, and the most responsible generators were identified by modal analysis. Uniquely, the potential for nonlinear modal interaction of these modes was carefully investigated. The low-frequency modes identified are 1 Hz, 1.14 Hz, and 1.37 Hz, and they are associated mainly with the generators at Kainji, Afam, and Delta power stations. The results indicate the existence of inter-area phenomena and nonlinear modal interactions among these modes. Also, the analysis revealed that the generator at the Kainji power station is most affected by the nonlinear interactions.<br>

scholarly journals Fundamental Study of Oscillations in the Nigerian Power System

2021 ◽  
Author(s):  
Nnaemeka Sunday UGWUANYI ◽  
Uma Uzubi Uma ◽  
Arthur Obiora Ekwue
Keyword(s):  
Power Systems ◽  
Power System ◽  
Low Frequency ◽  
Modal Interaction ◽  
Modal Interactions ◽  
Fundamental Study ◽  
Power Stations ◽  
Nonlinear Modal Interaction ◽  
Stability Limits ◽  
Comprehensive Study

The power systems in developing countries are usually stressed and operated near their stability limits. Consequently, accurate sources of oscillations and their controls can present a challenge. This paper reports a comprehensive study of the oscillations in the Nigerian 48-bus power system. The dominant modes, sensitive locations for faults, and the most responsible generators were identified by modal analysis. Uniquely, the potential for nonlinear modal interaction of these modes was carefully investigated. The low-frequency modes identified are 1 Hz, 1.14 Hz, and 1.37 Hz, and they are associated mainly with the generators at Kainji, Afam, and Delta power stations. The results indicate the existence of inter-area phenomena and nonlinear modal interactions among these modes. Also, the analysis revealed that the generator at the Kainji power station is most affected by the nonlinear interactions.<br>

Elastic displacements in the near-field of a propagating fault

1969 ◽  
Vol 59 (2) ◽  
pp. 865-908
Author(s):  
N. A. Haskell
Keyword(s):  
Fault Plane ◽  
Near Field ◽  
Strong Motion ◽  
Dislocation Motion ◽  
Displacement Discontinuity ◽  
Wave Form ◽  
Strong Motion Station ◽  
Ramp Function ◽  
Wave Forms ◽  
Parkfield Earthquake

abstract Displacement, particle velocity, and acceleration wave forms in the near field of a propagating fault have been computed by numerical integration of the Green's function integrals for an infinite medium. The displacement discontinuity (dislocation) on the fault plane is assumed to have the form of a unilaterally propagating finite ramp function in time. The calculated wave forms in the vicinity of the fault plane are quite similar to those observed at the strong motion station nearest the fault plane at the Parkfield earthquake. The comparison suggests that the propagating ramp time function is roughly representative of the main features of the dislocation motion on the fault plane, but that the actual motion has somewhat more high frequency complexity. Calculated amplitudes indicate that the average final dislocation on the fault at the Parkfield earthquake was more than an order of magnitude greater than the offsets observed on the visible surface trace. Computer generated wave form plots are presented for a variety of locations with respect to the fault plane and for two different assumptions on the relation between fault length and ramp function duration.

Some numerical solutions for Lamb's problem

1974 ◽  
Vol 64 (2) ◽  
pp. 473-491
Author(s):  
Harold M. Mooney
Keyword(s):  
Rayleigh Wave ◽  
Poisson’S Ratio ◽  
Pulse Width ◽  
Numerical Solutions ◽  
Pulse Height ◽  
P Wave ◽  
Poisson's Ratio ◽  
Wave Form ◽  
Lamb’S Problem ◽  
Wave Forms

abstract We consider a version of Lamb's Problem in which a vertical time-dependent point force acts on the surface of a uniform half-space. The resulting surface disturbance is computed as vertical and horizontal components of displacement, particle velocity, acceleration, and strain. The goal is to provide numerical solutions appropriate to a comparison with observed wave forms produced by impacts onto granite and onto soil. Solutions for step- and delta-function sources are not physically realistic but represent limiting cases. They show a clear P arrival (larger on horizontal than vertical components) and an obscure S arrival. The Rayleigh pulse includes a singularity at the theoretical arrival time. All of the energy buildup appears on the vertical components and all of the energy decay, on the horizontal components. The effects of Poisson's ratio upon vertical displacements for a step-function source are shown. For fixed shear velocity, an increase of Poisson's ratio produces a P pulse which is larger, faster, and more gradually emergent, an S pulse with more clear-cut beginning, and a much narrower Rayleigh pulse. For a source-time function given by cos2(πt/T), −T/2 ≦ T/2, a × 10 reduction in pulse width at fixed pulse height yields an increase in P and Rayleigh-wave amplitudes by factors of 1, 10, and 100 for displacement, velocity and strain, and acceleration, respectively. The observed wave forms appear somewhat oscillatory, with widths proportional to the source pulse width. The Rayleigh pulse appears as emergent positive on vertical components and as sharp negative on horizontal components. We show a theoretical seismic profile for granite, with source pulse width of 10 µsec and detectors at 10, 20, 30, 40, and 50 cm. Pulse amplitude decays as r−1 for P wave and r−12 for Rayleigh wave. Pulse width broadens slightly with distance but the wave form character remains essentially unchanged.

STUDIES OF DISTAL COLONIC MOTILITY IN CHILDREN

PEDIATRICS ◽  
1956 ◽  
Vol 17 (6) ◽  
pp. 820-833
Author(s):  
Murray Davidson ◽  
Marvin H. Sleisenger ◽  
Thomas P. Almy ◽  
Samuel Z. Levine
Keyword(s):  
Ulcerative Colitis ◽  
Bowel Movement ◽  
Colonic Motility ◽  
Distal Colon ◽  
Wave Form ◽  
Spontaneous Bowel Movement ◽  
Normal Individuals ◽  
Iced Water ◽  
Wave Forms

A characteristic propulsive wave, previously reported in adults with ulcerative colitis, has been found in infants with acute diarrhea but not in children with ulcerative colitis. The reasons for this are discussed. The induction of propulsive wave forms in normal individuals by administration of magnesium sulfate orally is described and attention is called to its application to therapeutic studies. The relation of this wave form to propulsion of fecal contents and defecation and its role in the production of abdominal discomfort are considered. Observed variations in the responses of individual children to subcutaneous injection of Mecholyl®, to oral administration of iced water, and to rectal distention may explain innate differences in susceptibility to the development of colonic symptoms in different children. A classification of wave forms from the distal colon based on current concepts of their probable physiologic significance is offered. A tracing from the distal colon in a child having a spontaneous bowel movement is presented and commented on.

Bioelectric Regulation of Tentacle Movement in a Dinoflagellate

1967 ◽  
Vol 47 (3) ◽  
pp. 433-446
Author(s):  
ROGER ECKERT ◽  
TAKAO SIBAOKA
Keyword(s):  
Temporal Relationship ◽  
Sea Water ◽  
Outward Current ◽  
Wave Form ◽  
Applied Current ◽  
Inward Current ◽  
Wave Forms ◽  
Noctiluca Miliaris ◽  
Spike Wave ◽  
Peripheral Cytoplasm

1. Recurring extensions and flexions of the food-gathering tentacle of Noctiluca miliaris occur spontaneously. Identical movements can be evoked by appropriate electrical stimulation. 2. Spontaneous recurring potential wave forms (TRPs) were recorded from the vacuole of the luminescent form of Noctiluca during movements of the tentacle. The basic TRP wave form consists of a characteristic negative-going spike which arises at -20 to -30 mV. from the slowly redeveloping negativity of a pre-spike depolarization, and is followed by a quasi-stable post-spike d.c. level of relative vacuolar negativity (-45 to -60 mV.). 3. The TRP complex, similar in shape to that which occurs spontaneously, follows an intracellularly applied current pulse of either polarity if the vacuolar potential is at the post-spike level. The duration of the evoked pre-spike wave is related to the current intensity and duration. During the pre-spike state outward current is ineffective, although a TR spike occurs in response to inward current. 4. The TRP is distinct in its behaviour and wave form from the flash-triggering potential, which can be evoked in the same cell, even though both exhibit all-or-none spikes. 5. Simultaneous recordings of intracellular potentials and movements of the tentacle showed a consistent temporal relationship between potential changes and subsequent movement. Extension of the tentacle begins 1-2 sec. after the spike and flexion begins within 1 sec. after beginning of the pre-spike wave. 6. Tentacle movement ceased in Ca-free sea water even though the cyclic potential changes continued normally. 7. Electron micrographs of the tentacle showed longitudinal aggregations of microtubules near the outer surface of the peripheral cytoplasm. It is proposed that contraction of these microtubules is the immediate cause of tentacle movements.

Effect of Forcing Terms and General Characteristics of Torsional Vibrations of Marine Engine Systems with Variable Inertia

1974 ◽  
Vol 18 (02) ◽  
pp. 131-138
Author(s):  
W. D. Carnegie ◽  
M. S. Pasricha
Keyword(s):  
Equations Of Motion ◽  
Mean Value ◽  
Wave Form ◽  
Actual System ◽  
Computer Methods ◽  
Reciprocating Engine ◽  
Complex Wave ◽  
Wave Forms ◽  
Crankshaft Rotation ◽  
Engine Systems

The torsional vibration phenomenon in the running gear of reciprocating engine systems is usually dealt with by considering a series of constant inertias connected by sections of massless shafting. Such a simplified model does not reproduce the exact dynamic characteristics of the actual system. In recent years several cases of marine crankshaft failures have been attributed to the phenomenon of secondary resonance, which is explained by the fact that the effective inertia of each slider crankmechanism varies about a mean value in relation to the position of the crank. When the variableinertia effect is allowed for, the equations of motion taking into account the effect are nonlinear. Assuming small displacements, the equations can be linearized to predict important characteristics of the motion. The motions in the form of complex wave forms are studied at different speeds of engine rotation and some of the wave form solutions are analyzed in the range of present investigations. Computer methods making use of numerical analysis processes, namely, the modifiedEuler's equations and the Runge-Kutta constants, have been applied in the investigations. A study of the effect on the motion of the system due to variation of inertia ratio is carried out at a particular speed of the crankshaft rotation; also investigated are the variations in the motions due to the action of external excitations with respect to changes in phase angle and inertia ratio. General comments on Draminsky's work in the light of the present investigations are included.

Uterine work in parturition

1976 ◽  
Vol 41 (3) ◽  
pp. 316-322 ◽  
Author(s):  
T. J. Kriewall
Keyword(s):  
Viscoelastic Model ◽  
Geometrical Model ◽  
Clinical Findings ◽  
Cervical Dilatation ◽  
Wave Form ◽  
Intrauterine Pressure ◽  
Wave Forms ◽  
Internal Volume ◽  
Synergistic Relationship ◽  
Incremental Volume

This paper presents a theoretical analysis relating work expended by the uterus to the synergistic relationship between intrauterine pressure (IUP) and cervical dilatation (CD). By utilizing a geometrical model for the fetal presenting part which is assumed to be in contact with the cervix, the changes in internal volume of the uterus with each contraction can be shown to be functionally related to cervical dilatation. Thus work, expressed in terms of foot-pounds, can be calculated using the integral of pressure times incremental volume. By simulating intrauterine pressure and cervical dilatation with continuous analytical wave forms, the alterations required in uterine work to dilate the cervix are calculated for various wave-form aberrations which are seen in clinical situations. The wave-form aberrations are applied to an elastic cervical model as well as a viscoelastic model. Using the principles of thermodynamics the areas of the fetouterine complex which absorb the work generated by the contractions are defined. It is shown that the efficiency of the contractions to dilate the cervix can be calculated by evaluating the work expended in these various areas of energy absorption. The purpose of this paper is to present the theory upon which clinical findings in obstetrics can be based so that conclusions drawn will be technically sound.

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