Theoretical and experimental investigations of the dynamics of cantilevered flexible plates subjected to axial flow

In this paper, the dynamics of cantilevered flexible plates subjected to axial flow is investigated theoretically and experimentally. A nonlinear equation of motion of the plate based on the inextensibility assumption, coupled with an unsteady lumped vortex model for the aerodynamic part is used to analyze the instability and post-critical dynamical behaviour of this fluid–structure system theoretically. Experiments have been conducted in a 3 ft×2 ft (914 mm×610 mm) cross-section wind tunnel, using polypropylene carbonate (PPC) films, thin brass plates, polyethylene terephthalate (PET) sheets, and type 304 stainless steel sheets, with maximum dimensions 224 mm×168 mm. In the experiments, time traces, power spectral densities (PSDs), phase-plane plots, Poincaré maps, probability density functions (PDFs) and autocorrelations are used to characterize the motions of the system.Periodic and chaotic oscillations have been observed in the experiments. It has also been observed that flutter arises via a subcritical bifurcation involving hysteresis for large aspect ratio plates; this hysteresis does not occur for low aspect ratio plates. The hysteresis phenomenon is considered to be due to spanwise deformation of the plates. The effect of aspect ratio on critical flow velocity is investigated. The experimental critical flow velocities for flutter onset are in good agreement with the theoretically predicted values.     

轴向流对Z箍缩等离子体稳定性的影响

利用理想磁流体力学(MHD)模型对有轴向流参与的Z箍缩等离子体不稳定性进行了分析.对可压缩平板等离子体模型的色散关系进行了推导,讨论了三种不同等离子体状态下的不稳定性增长率.结果显示,等离子体的可压缩性对磁瑞利-泰勒/开尔文-亥姆霍兹(MRT/KH)杂化不稳定性有抑制作用,改善了轴向剪切流对长波长扰动的影响.分析了不同轴向流速度分布对系统稳定性的影响.结果表明,对于峰值相同的不同轴向流,其对不稳定性的抑制效果只依赖于扰动集中区域内速度剪切的大小,与其他位置的速度剪切无关.     

The effect of trailing end geometry on the vibration of a circular cantilevered rod in nominally axial flow

The effect of “trailing end” geometry on the vibration of a circular cantilevered rod in nominally axial water flow is reported. Eleven different trailing end geometries were tested. For each end geometry, rms displacement response and damping were measured and are presented as functions of mean axial flow velocity. The various geometric end shapes are ordered according to their effectiveness in attenuating rod vibration. The results, which are in qualitative agreement with similar experimental results from tests on flat plates, provide the designer with empirical information that allows selecting a trailing end geometry that minimizes response to parallel flow excitation. The results have application in the design of nuclear reactor fuel pins and certain instrumentation probes.     

轴向流对Z箍缩等离子体稳定性的影响

利用理想磁流体力学(MHD)模型对有轴向流参与的Z箍缩等离子体不稳定性进行了分析.对可压缩平板等离子体模型的色散关系进行了推导，讨论了三种不同等离子体状态下的不稳定性增长率.结果显示，等离子体的可压缩性对磁瑞利-泰勒/开尔文-亥姆霍兹(MRT/KH)杂化不稳定性有抑制作用，改善了轴向剪切流对长波长扰动的影响.分析了不同轴向流速度分布对系统稳定性的影响.结果表明，对于峰值相同的不同轴向流，其对不稳定性的抑制效果只依赖于扰动集中区域内速度剪切的大小，与其他位置的速度剪切无关. 关键词： Z箍缩 磁瑞利-泰勒不稳定性 轴向剪切流 MHD方程     

Flutter analysis of cantilevered quadrilateral plates

In this paper, the title problem is solved by using a numerical method involving an integral equation technique and a normal mode method. Linear plate theory has been used for computing the strain energy and kinetic energy of the plate. Piston theory has been used to describe the aerodynamic pressure distribution. Numerical work has been done and convergence of the solution has been studied. Results have also been obtained for various cases and compared with those of other investigators.     

The dynamics of clusters of flexible cylinders in axial flow: Theory and experiments

This paper presents an outline of the theory for the dynamics of clusters of independently supported flexible cylinders in axial flow, and an extensive discussion of the behaviour of such systems with increasing flow velocity, with special emphasis placed on the modal forms of free coupled motions of the cylinders and on the onset of instabilities. Results of an experimental study of the problem are also presented, involving systems of two, three or four cylinders supported at both ends and positioned symmetrically in the cylindrical test section of a water tunnel; experiments were conducted with different inter-cylinder gaps and support conditions. Both theory and experiment show that with increasing flow the system loses stability by buckling in one of its coupled modes, commonly in a pattern where cylinders move towards one another symmetrically, maximum displacement occurring just downstream of their midpoints. With increasing flow, theory predicts that other buckling instabilities are superimposed on the first; in the experiments the system remains buckled, changing modal patterns constantly; some of them correspond to those predicted by theory. At sufficiently high flow, oscillatory motion is observed, corresponding to theoretical flutter. Theory and experiment agree qualitatively in most essential features of the dynamical behaviour of the system, and quantitative agreement in the critical flow velocities for the onset of the first buckling instability is remarkably good.     

Three-dimensional free vibrations of thick skewed cantilevered plates

The natural frequencies of skewed cantilevered thick plates are determined by using the Ritz method. The present work is the first known three-dimensional study of the problem. Assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete. Accurate natural frequencies are calculated for skewed thick plates having arbitrary degrees of skewness. Detailed numerical studies reveal interesting trends concerning the variation of frequencies with increasing skew angle. Results obtained by using the present method are compared with those obtained by using three-dimensional finite elements.     

An analytical model for vibration of clusters of flexible cylinders in turbulent axial flow

This paper describes an analytical model for the flow-induced vibration of clusters of cylinders in axial flow, in the sub-critical flow regime (i.e., at flow velocities below the threshold for fluid-elastic instabilities). The vibration is excited by the random pressure fluctuations in the turbulent flow acting on the cylinders. Correlation of the excitation field is assumed to exist, with appropriate length scales, not only on the same cylinder, but also on adjacent cylinders in the cluster. In the absence of measured correlation functions for the system at hand, numerical calculations were conducted with available pipe-flow correlation functions, due to Bakewell et al., assumed to be approximately valid. Power- and cross-spectral densities of the vibration are presented, as well as r.m.s. amplitudes, for simple systems of two, three and four cylinders, and the characteristics of the flow-induced vibration are then discussed. It is seen that there is remarkable qualitative agreement with measured characteristics of vibration.     

The influence of a stationary uniform axial flow on the propagation of acoustic modes of vibration in a cylindrical duct

The propagation, in a cylindrical duct, of acoustic modes of vibration whose wavelength is smaller than the damping length, is studied in the presence of a stationary uniform axial flow.     

The influence of the quarter wave plates in automated photoelasticity

During the last decades, several methods have been proposed to automate photoelastic analyses. Some procedures are based on the circularly polarised light by using quarter wave plates. However, quarter wave plates are typically matched for a specific wavelength, and an error is introduced at different wavelengths. The error of quarter wave plates affects the measurement of isochromatic and isoclinic data. In this paper, the influence of the errors of quarter wave plates in some of the most common automated photoelastic methods is reviewed. The errors in the photoelastic data are given and the procedures to reduce, or eliminate, them are also suggested.     

The acoustic spectrum of axial flow machines

Rotor spectra from a variety of axial flow machines have been compared and acoustic trends examined. Types of rotor considered in the investigation included aircraft propellers, helicopter rotors, jet engine compressor and by-pass fans and a range of domestic, automotive and industrial cooling fans. Rotor sizes varied from 15 in to 60 ft in diameter and tip speeds from 200 ft/s to transonic speeds.The study showed that the acoustic output from these various rotor devices can be described by a common characteristic spectrum. In particular, the minimum broad band noise generated by ducted and free field rotors corresponds to laminar and turbulent boundary layer shedding, and discrete excess noise is generated by various degrees of impulsive blade loading. Finally the study showed that aerodynamic details can be interpreted from the acoustic spectra, and as a result, new insight into the mechanisms of rotor noise has been formed.     

The influence of the thermal wake due to pulsating optical discharge on the aerodynamic-drag force

The influence of a thermal wake due to gas injection and due to a pulsating optical discharge (POD) on the aero-dynamic-drag force of a body in a supersonic air flow with Mach number M = 1.45 are experimentally examined. With the help of a single-component aerodynamic balance, the influence of the injected subsonic jet and the thermal wake produced by POD on the aerodynamic drag of a hemisphere-on-cylinder model was studied. It is shown that the observed aerodynamic-force reduction phenomenon can be made more pronounced by increasing the laser power and pulse repetition frequency, or by decreasing the distance between the model and the pulsating optical discharge. The maximum aerodynamic-force reduction (up to 15%) due to the thermal-wake action was observed at a maximum laser-radiation power of W = 2.3 kW and at a pulse rate of f = 90 kHz. The joint effect due to the argon jet and due to the POD caused an aerodynamic-drag force reduction reaching 30%.     

DPIV in the wake of a tandem arrangement of two flexible circular cylinders

Abstract  

Visualization of the wake of a system of two circular cylinders in tandem is presented through Digital Particle Image Velocimetry results in a plane perpendicular to the models’ axes. Both cylinder models have an aspect ratio (length over diameter) of almost 100, a mass ratio (mass divided by mass of displaced fluid) under 2, and they are flexible and free to move in the in-line and cross-flow directions. A supporting structure provided attachment of both models through universal joints at each end and the cylinders were exposed to a uniform flow profile over the lower 45% of their lengths, producing vortex-induced vibrations with wake interactions. The centre to centre separation between the models could be varied and data is shown here for three separations of 2, 3 and 4 diameters.     

Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments

This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid–structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.     

轴向剪切流对Z箍缩等离子体瑞利-泰勒不稳定性的抑制

利用理想磁流体力学模型对有轴向剪切流的Z箍缩等离子体不稳定性进行了分析。给出了可压缩模型的色散关系,分别对可压缩及不可压缩模型中轴向剪切流对Z箍缩等离子体瑞利-泰勒不稳定性的抑制作用进行了比较,讨论了可压缩性对含有轴向剪切流系统不稳定性的影响。结果表明,可压缩性能够减缓瑞利-泰勒P凯尔文-亥姆霍兹(RTPKH)模扰动的增长,因而使得轴向剪切流对系统不稳定性的抑制作用表现得更为突出。计算结果还说明,在RT不稳定性线性增长阶段,等离子体温度较低,使用可压缩模型能够更真实地描述系统的状态。     

The influence of unipolar axial magnetic field on the behavior of vacuum arcs

The behavior of vacuum arcs under the influence of unipolar axial magnetic field (AMF) has been investigated. In experimental investigations, the vacuum arc mode is studied at different arc currents by using high-speed charge-coupled device (CCD) video images. In spite of the AMF, first sign of arc constriction appears at relatively small currents of about 15 kA (RMS). Three different arc modes were found. Based on generalized Ohm's law, the current density distribution in the vacuum arc with unipolar axial magnetic field is computed using three-dimensional finite-element method (FEM) software. The calculated current distribution is confirmed by the vacuum arc appearance taken from CCD video film. The distribution of AMF can be optimized by such experiments and theoretical analysis.