Fluid-loaded elastic plate with mean flow: point forcing and three-dimensional effects

2001 ◽  
Vol 428 ◽  
pp. 305-331
Author(s):  
M. R. GREEN ◽  
D. G. CRIGHTON
Keyword(s):  
Elastic Plate ◽  
Critical Angle ◽  
Single Frequency ◽  
Absolute Instability ◽  
Frequency Range ◽  
Mean Flow ◽  
Curvature Effects ◽  
Flow Speeds ◽  
Neutral Mode ◽  
Asymptotic Forms

The unsteady behaviour of an infinitely long fluid-loaded elastic plate subject to a single-frequency line forcing in the presence of a uniform mean flow is known to exhibit a number of interesting phenomena. These include the onset of absolute instability for non-dimensional flow speeds U in excess of some critical speed Uc, and various interesting propagation effects when U < Uc. In the latter respect Crighton & Oswell (1991) have shown that over a particular frequency range there exists an anomalous neutral mode with group velocity directed towards the driver, in violation of the usual Lighthill outgoing radiation condition. Similar results have been found by Peake (1997) when transverse curvature effects are included. In this paper we seek to extend these results and consider the substantially harder problem of a fluid-loaded elastic plate with uniform mean flow which is subject to a point forcing, thereby resulting in a two-dimensional structural problem. A systematic method for determining the absolute instability threshold is developed, and it is shown that the flow is absolutely unstable for flow speeds U > Uc, where Uc is the one-dimensional value found by Crighton & Oswell. At flow speeds U < Uc the flow is marginally stable and convective growth is found to occur downstream of the driver, over a particular frequency range depending on the transverse Fourier wavenumber ky, within a wedge-shaped region. Outside this wedge-shaped region there is only neutral mode behaviour. Asymptotic forms are found for the dominant large-distance causal flexion response downstream of the driver inside and outside the wedge region, and the appropriate critical angle for the wedge region is identified. Within the convective instability wedge the flexion and critical angle take two different forms depending on whether the frequency ω is greater or less than U2/√5. In addition to this interesting behaviour, the flow also exhibits the usual anomalous neutral mode behaviour and, as with Peake's problem, we also find an extra stability (hoop) resulting in neutral mode behaviour over a small frequency range. Asymptotic forms are also found for the threshold frequencies which divide up the various regions of stability of the system (neutral, neutral anomalous, convectively unstable), as a function of ky, and are compared with the results of both Crighton & Oswell and Peake.

On the behaviour of a fluid-loaded cylindrical shell with mean flow

1997 ◽  
Vol 338 ◽  
pp. 387-410 ◽  
Author(s):  
N. PEAKE
Keyword(s):  
Flat Plate ◽  
Critical Radius ◽  
Radiation Condition ◽  
Negative Energy ◽  
Flow Speed ◽  
Single Frequency ◽  
Engineering Practice ◽  
Absolute Instability ◽  
Mean Flow ◽  
Flow Speeds

The unsteady behaviour of an infinitely long fluid-loaded elastic plate which is driven by a single-frequency point-force excitation in the presence of mean flow is known to exhibit a number of unexpected features, including absolute instability when the normalized flow speed, U, lies above some critical speed U0, and certain unusual propagation effects for U<U0. In the latter respect Crighton & Oswell (1991) have demonstrated most significantly that for a particular frequency range there exists an anomalous neutral (negative energy) mode which has group velocity pointing towards the driver, in violation of the usual radiation condition of outgoing waves at infinity. They show that the rate of working of the driver can be negative, due to the presence of other negative-energy waves, and can also become infinite at a critical frequency corresponding to a real modal coalescence. In this paper we attempt to extend these results by including, as is usually the case in a practical situation, plate curvature in the transverse direction, by considering a fluid-loaded cylinder with axial mean flow. In the limit of infinite normalized cylinder radius, a, Crighton & Oswell's results are regained, but for finite a very significant modifications are found. In particular, we demonstrate that the additional stiffness introduced by the curvature typically moves the absolute-instability boundary to a much higher flow speed than for the flat-plate case. Below this boundary we show that Crighton & Oswell's anomalous neutral mode can only occur for a>a1(U), but in practical situations it turns out that a1(U) is exceedingly large, and indeed seems much larger than radii of curvature achievable in engineering practice. Other negative-energy waves are seen to exist down to a smaller, but still very large, critical radius a2(U), while the existence of a real modal coalescence point, leading to a divergence in the driver admittance, occurs down to a slightly smaller critical radius a3(U). The transition through these various flow regimes as U and a vary is fully described by numerical investigation of the dispersion relation and by asymptotic analysis in the (realistic) limit of small U. The inclusion of plate dissipation is also considered, and, in common with Abrahams & Wickham (1994) for the flat plate, we show how the flow then becomes absolutely unstable at all flow speeds provided that a>a2(U).

ABSOLUTE INSTABILITY OR CHAOS? — A TRIBUTE TO DR. DAVID G. CRIGHTON

2002 ◽  
Vol 10 (04) ◽  
pp. 407-419
Author(s):  
SEAN F. WU
Keyword(s):  
Elastic Plate ◽  
Equilibrium Position ◽  
Flexural Vibration ◽  
Critical Value ◽  
Flow Speed ◽  
Multiple Equilibrium ◽  
Absolute Instability ◽  
Mean Flow ◽  
Structural Nonlinearities ◽  
The Mean

The stabilities of an elastic plate clamped on an infinite, rigid baffle subject to any time dependent force excitation in the presence of mean flow are examined. The mechanisms that can cause plate flexural vibrations to be absolute unstable when the mean flow speed exceeds a critical value are revealed. Results show that the instabilities of an elastic plate are mainly caused by an added stiffness due to acoustic radiation in mean flow, but controlled by the structural nonlinearities. This added stiffness is shown to be negative and increase quadratically with the mean flow speed. Hence, as the mean flow speed approaches a critical value, the added stiffness may null the overall stiffness of the plate, leading to an unstable condition. Note that without the inclusion of the structural nonlinearities, the plate has only one equilibrium position, namely, its undeformed flat position. Under this condition, the amplitude of plate flexural vibration would grow exponentially in time everywhere, known as absolute instability. With the inclusion of structural nonlinearities, the plate may possess multiple equilibrium positions. When the mean flow speed exceeds the critical values, the plate may be unstable and jump from one equilibrium position to another. Since this jumping is random, the plate flexural vibration may seem chaotic.

Fluid loading with mean flow. I. Response of an elastic plate localized excitation

1991 ◽  
Vol 335 (1639) ◽  
pp. 557-592 ◽  
Keyword(s):  
Group Velocity ◽  
Elastic Plate ◽  
Energy Equation ◽  
Excitation Frequency ◽  
Negative Energy ◽  
Significant Feature ◽  
Frequency Range ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Waves

The response to localized forcing of a fluid-loaded elastic plate is studied in the case when there is uniform incompressible flow over the plate. Absolute instability of the fluid-plate system is found when the dimensionless mean velocity U exceeds a threshold U c which is found exactly. For U < U c the system is convectively unstable for 0 < ω <ω s ( U ), neutrally stable, with anomalous features, for ω s ( U ) < ω < ω p ( U ) and stable, with conventional features, for ω > ω p (U), ω being the excitation frequency: here asymptotic expressions are found for the frequencies and for the wavenumbers and amplitudes of the waves found upstream and downstream of the excitation. A significant feature is that Re A 0 < 0 throughout 0 < ω < ω p , A 0 being the drive admittance (velocity at the point of application of the force); this means that throughout the convectively unstable and the anomalous neutral frequency ranges, the exciting force must absorb energy. An exact energy equation is derived, and shown to require the introduction of a new fluid-plate interaction flux UnO t , where O is the fluid potential and n the plate deflexion. The energy equation is used to illuminate properties of the convectively unstable and neutral waves, to verify the property Re A 0 < 0 and to trace the waves responsible for this. Anomalous features in the frequency range ω s (U) < ω < ω p ( U ) are investigated further from the viewpoint of the theory of negative energy waves, and it is found that not only can some wave modes in this frequency range have negative energy, but also group velocity in an inward direction (towards the excitation). It is argued that this does not contradict the outward group velocity ‘radiation condition’ of M. J. Lighthill, because that condition refers expressly to circumstances in which the excitation is the sole source of all the wave energy, whereas here the excitation acts also as a scatterer, transferring energy from the mean flow to the wave field.

scholarly journals The stability and transition of the boundary layer on a rotating sphere

2002 ◽  
Vol 456 ◽  
pp. 199-218 ◽  
Author(s):  
S. J. GARRETT ◽  
N. PEAKE
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Convective Instability ◽  
Reverse Flow ◽  
Experimental Studies ◽  
Rotating Disk ◽  
Absolute Instability ◽  
Mean Flow ◽  
Streamline Curvature ◽  
Curvature Effects

This paper is concerned with convective and absolute instabilities in the boundary-layer flow over the outer surface of a sphere rotating in an otherwise still fluid. Viscous and streamline-curvature effects are included and the analysis is conducted between latitudes of 10° and 80° from the axis of rotation. Both convective and absolute instabilities are found at each latitude within specific parameter spaces. The results of the convective instability analysis show that a crossflow instability mode is the most dangerous below θ = 66°. Above this latitude a streamline-curvature mode is found to be the most dangerous, which coincides with the appearance of reverse flow in the radial component of the mean flow. At low latitudes the disturbances are considered to be stationary, but at higher latitudes they are taken to rotate at 76% of the sphere surface speed, as observed in experimental studies. Our predictions of the Reynolds number and vortex angle at the onset of convective instability are consistent with existing experimental measurements. Results are also presented that suggest that the occurrence of the slowly rotating vortices is associated with the dominance of the streamline-curvature mode at θ = 66°. The local Reynolds number at the predicted onset of absolute instability matches experimental data well for the onset of turbulence at θ = 30°; beyond this latitude the discrepancy increases but remains relatively small below θ = 70°. It is suggested that this absolute instability may cause the onset of transition below θ = 70°. Close to the pole the predictions of each stability analysis are seen to approach those of existing rotating disk investigations.

Fluctuating boundary layer on a magnetized plate

1967 ◽  
Vol 63 (2) ◽  
pp. 513-525 ◽  
Author(s):  
Sahib Singh Chawla
Keyword(s):  
Boundary Layer ◽  
Low Frequency ◽  
Surface Current ◽  
Frequency Range ◽  
Mean Flow ◽  
Wave Type ◽  
High Frequencies ◽  
Phase Lead ◽  
The Mean ◽  
The Magnetic Field

The laminar boundary layer on a magnetized plate, when the magnetic field oscillates in magnitude about a constant non-zero mean, is analysed. For low-frequency fluctuations the solution is obtained by a series expansion in terms of a frequency parameter, while for high frequencies the flow pattern is of the ‘skin-wave’ type unaffected by the mean flow. In the low-frequency range, the phase lead and the amplitude of the skin-friction oscillations increase at first and then decrease to their respective ‘skin-wave’ values. On the other hand the phase angle of the surface current decreases from 90° to 45° and its amplitude increases with frequency.

scholarly journals Coupling between the ocean and an ice shelf

1991 ◽  
Vol 15 ◽  
pp. 101-108 ◽  
Author(s):  
Colin Fox ◽  
Vernon A. Squire
Keyword(s):  
Elastic Plate ◽  
Velocity Potential ◽  
Open Water ◽  
Ocean Waves ◽  
Ocean Wave ◽  
Single Frequency ◽  
Plate Model ◽  
Ice Shelf ◽  
Long Period ◽  
Set Up

The possibility of long-period ocean waves coupling to an ice shelf is investigated. A thick elastic plate model is used for the ice shelf with comparisons made to the simpler thin-plate model. The strain set up on the ice shelf by a normally incident single frequency ocean wave is calculated by completely solving the equations governing the velocity potential for such a system. In the absence of measurements on an ice shelf, existing measurements of long-period strain on an ice tongue are used to estimate the required incident amplitude in the open water to induce the observed oscillations. It is found that the height of seas required indicates that ocean wave driving is a plausible forcing mechanism for observed oscillations.

scholarly journals Measurements of acoustic scattering from zooplankton and oceanic microstructure using a broadband echosounder

2009 ◽  
Vol 67 (2) ◽  
pp. 379-394 ◽  
Author(s):  
Andone C. Lavery ◽  
Dezhang Chu ◽  
James N. Moum
Keyword(s):  
High Frequency ◽  
System Performance ◽  
Pulse Compression ◽  
Acoustic Scattering ◽  
Single Frequency ◽  
Frequency Range ◽  
Range Resolution ◽  
Continuous Frequency ◽  
Processing Techniques ◽  
Signal Processing Techniques

Abstract Lavery, A. C., Chu, D., and Moum, J. N. 2010. Measurements of acoustic scattering from zooplankton and oceanic microstructure using a broadband echosounder. – ICES Journal of Marine Science, 67: 379–394. In principle, measurements of high-frequency acoustic scattering from oceanic microstructure and zooplankton across a broad range of frequencies can reduce the ambiguities typically associated with the interpretation of acoustic scattering at a single frequency or a limited number of discrete narrowband frequencies. With this motivation, a high-frequency broadband scattering system has been developed for investigating zooplankton and microstructure, involving custom modifications of a commercially available system, with almost complete acoustic coverage spanning the frequency range 150–600 kHz. This frequency range spans the Rayleigh-to-geometric scattering transition for some zooplankton, as well as the diffusive roll-off in the spectrum for scattering from turbulent temperature microstructure. The system has been used to measure scattering from zooplankton and microstructure in regions of non-linear internal waves. The broadband capabilities of the system provide a continuous frequency response of the scattering over a wide frequency band, and improved range resolution and signal-to-noise ratios through pulse-compression signal-processing techniques. System specifications and calibration procedures are outlined and the system performance is assessed. The results point to the utility of high-frequency broadband scattering techniques in the detection, classification, and under certain circumstances, quantification of zooplankton and microstructure.

Influence of camber on sound generation by airfoils interacting with high-frequency gusts

1997 ◽  
Vol 353 ◽  
pp. 221-259 ◽  
Author(s):  
MATTHEW R. MYERS ◽  
E. J. KERSCHEN
Keyword(s):  
Flat Plate ◽  
High Frequency ◽  
Incidence Angle ◽  
Outer Region ◽  
Asymptotic Region ◽  
Mean Flow ◽  
Previous Theory ◽  
Airfoil Surface ◽  
Curvature Effects ◽  
Flow Past

A theoretical model is developed for the sound generated when a convected disturbance encounters a cambered airfoil at non-zero angle of attack. The model is a generalization of a previous theory for a flat-plate airfoil, and is based on a linearization of the Euler equations about the steady, subsonic flow past the airfoil. High-frequency gusts, whose wavelengths are short compared to the airfoil chord, are considered. The airfoil camber and incidence angle are restricted so that the mean flow past the airfoil is a small perturbation to a uniform flow. The singular perturbation analysis retains the asymptotic regions present in the case of a flat-plate airfoil: local regions, which scale on the gust wavelength, at the airfoil leading and trailing edges; a ‘transition’ region behind the airfoil which is similar to the transition zone between illuminated and shadow regions in optical problems; and an outer region, far away from the airfoil edges and wake, in which the solution has a geometric-acoustics form. For the cambered airfoil, an additional asymptotic region in the form of an acoustic boundary layer adjacent to the airfoil surface is required in order to account for surface curvature effects. Parametric calculations are presented which illustrate that, like incidence angle, moderate amounts of airfoil camber can significantly affect the sound field produced by airfoil–gust interactions. Most importantly, the amount of radiated sound power is found to correlate very well with a single aerodynamic loading parameter, αeff, which is an effective mean-flow incidence angle for the airfoil leading edge.

scholarly journals Conductivity tomography at two frequencies

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 516-522 ◽  
Author(s):  
Junxing Cao ◽  
Zhenhua He ◽  
Jieshou Zhu ◽  
Peter K. Fullagar
Keyword(s):  
Single Frequency ◽  
Dual Frequency ◽  
Frequency Range ◽  
Frequency Method ◽  
New Approach ◽  
Electromagnetic Absorption ◽  
Universal Approach ◽  
Approximate Frequency ◽  
Transmitting Antenna

We present a new approach for crosshole radio tomography. Conductivity images of the investigated area are reconstructed from the ratio of the electric field intensities measured at two similar frequencies. The method largely avoids assumptions about the radiation pattern and in‐situ intensity of the transmitting antenna, which introduce errors in conventional single‐frequency crosshole electromagnetic‐absorption tomography. Application of the method to field data achieved an improvement in resolution of anomalies over traditional single‐frequency absorption tomography. The dual‐frequency method is not a universal approach; it is suitable for moderately conductive media (<0.01 S/m) over the approximate frequency range 1–100 MHz.

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