ABSOLUTELY UNSTABLE WAVES IN INVISCID HYDROELASTIC SYSTEMS

The effect of inviscid plug flow on the stability of several hydroelastic systems is investigated by determining the absolute or convective nature of the instability from the linear dispersion relation. The fluid-structure systems consist of plates and membranes with bounded and unbounded flow. A method is proposed to derive systematically in parameter space the boundary between convective and absolute instability, based on the particular symmetries of the dispersion relation as originally noted by Crighton and Oswell. This method is then applied to the case of plates with superimposed tension, thick plates with rotary inertia and walls made of plates or membranes bounding channel flow, oscillating in a sinuous or varicose mode of deformation. A relation is drawn with solutions by previous authors for plates, for pipes and for the Kelvin-Helmholtz instability with surface tension. To illustrate these results some temporal evolutions are calculated by using an integration in the wavenumber space. Based on the large set of new cases solved in the paper some general trends are discussed as to the influence of flow velocity, confinement and structural stiffness on the existence of absolutely unstable waves in inviscid hydroelastic systems.     

Effects of hysteretic and aerodynamic damping on supersonic panel flutter of composite plates

The governing equation for the finite element analysis of the panel flutter of composite plates including structural damping is derived from Hamilton's principle. The first order shear deformable plate theory has been applied to structural modelling so as to obtain the finite element eigenvalue equation. The unsteady aerodynamic load in a supersonic flow is computed by using the linear piston theory. The critical dynamic pressures for composite plates have been calculated to investigate the effects of structural damping on flutter boundaries. The effects are dependent on fiber orientation because flutter mode can be weak or strong in the fiber orientation of composite plates. Structural damping plays an important role in flutter stability with low aerodynamic damping but would not affect the flutter boundary with high aerodynamic damping.     

Vibration and stability of sandwich beams with elastic bonding

This paper is a study of the vibration and stability of symmetrical sandwich cantilevers with elastic bonding. The horizontal displacements of the face layer and the core are discontinuous due to the elasticity of the interface bond. The shear traction at the interface is assumed to be proportional to the relative horizontal displacement of the layers. The core layer is subjected to a horizontal (conservative) or tangential (non-conservative) axial force at its free end. It is shown that a symmetrical sandwich beam with elastic bonding has two kinds of vibration modes: i.e., bending modes and longitudinal modes. Numerical results are given for a beam composed of FRP face layers and a syntactic-foam core layer. It is shown that the divergence and the flutter type instability loads, as well as the natural frequency, are affected considerably by the stiffness of the interface bond.     

Mathematical model for axisymmetric steady flow within layered structures with finite or infinitely high bulk viscosity

A mathematical model was developed for viscous incompressible medium; this model comprises a small parameter for regularization of ill-posed problem. Starting from the analogy with strain problems of axisymmetric laminar structures which include the elastic orthotropic and elastic volume-incompressible layers with a connection to viscous laminar fluid flow, we have developed a method providing a single algorithm for computation of velocity field, stresses, and other parameters of laminar composite material. The example of calculation for the binding agent flow during pultrusion formation is presented.     

The influence of the wake on the stability of cantilevered flexible plates in axial flow

Cantilevered flexible plates in axial flow lose stability through flutter. Using the inextensibility condition for the cantilevered nonlinear plate equation of motion and the unsteady lumped-vortex model to calculate the fluid loads, a flutter boundary has been obtained. In the time-domain analysis performed to this end, the wake behind the oscillating cantilevered plate is assumed to issue tangentially from the free trailing edge and extend downstream with an undulating form. The influence of the wake on system stability may be characterized in terms of the non-dimensional mass ratio, reduced flow velocity and flutter frequency. For large values of the mass ratio, the plate vibrates with high frequency and high-order mode content. It is shown that the wake has less influence on system stability for long plates than it does for short ones.     

Frequency maximization of laminated sandwich plates under general boundary conditions using layerwise optimization method with refined zigzag theory

The present paper extends the layerwise optimization (LO) procedure to the maximization problem of the fundamental frequencies of sandwich plates with fibrous composites and low stiffness core layers. Frequencies are calculated by the Ritz method based on a refined zigzag theory (RZT). Polynomial functions which satisfy at least geometrical boundary conditions with boundary indexes are employed as displacement functions, and they enable satisfying arbitrary sets of boundary conditions for rectangular plates. Results of the experimental modal analysis validate the accuracy of the present calculations, and a comparison with results of the classical laminated theory (CLPT) and the first order share deformation theory (FSDT) supports the effectiveness of the present method. Optimized results are compared with other typical sets of lay-up configurations and this shows the LO method as suitable means to the optimization problem for sandwich plates.     

Flutter of Finite-Span Flexible Plates in Uniform Flow

The flutter instability and response of finite-span flexible plates in uniform flow are investigated experimentally. The effects of the plate aspect ratio on its dynamic responses are mainly analyzed. A hysteretic phenomenon is observed and can be described such that the plate flutters spontaneously as the flow velocity is greater than a critical value UC and the plate returns to its stable state as the flow velocity is slowly decreased to another critical one UD. We find that the aspect ratio has a greater effect on UC than on UD. The flutter frequency decreases and the amplitude increases with the increase in the flow velocity. When the flutter instability of the plate occurs, three typical flutter modes are identified and are associated with the aspect ratio and the flow velocity.     

Aero-/hydro-elastic stability of flexible panels: Prediction and control using localised spring support

We study the effect of adding localised stiffness, via a spring support, on the stability of flexible panels subjected to axial uniform incompressible flow. Applications are considered that range from the hydro-elasticity of hull panels of high-speed ships to the aero-elasticity of glass panels in the curtain walls of high-rise buildings in very strong winds. A two-dimensional linear analysis is conducted using a hybrid of theoretical and computational methods that calculates the system eigen-states but can also be used to capture the transient behaviour that precedes these. We show that localised stiffening is a very effective means to increase the divergence-onset flow speed in both hydro- and aero-elastic applications. It is most effective when located at the mid-chord of the panel and there exists an optimum value of added stiffness beyond which further increases to the divergence-onset flow speed do not occur. For aero-elastic applications, localised stiffening can be used to replace the more destructive flutter instability that follows divergence at higher flow speeds by an extended range of divergence. The difference in eigen-solution morphology between aero- and hydro-elastic applications is highlighted, showing that for the former coalescence of two non-oscillatory divergence modes is the mechanism for flutter onset. This variation in solution morphology is mapped out in terms of a non-dimensional mass ratio. Finally, we present a short discussion of the applicability of the stabilisation strategy in a full three-dimensional system.     

Dynamics of microscale pipes containing internal fluid flow: Damping, frequency shift, and stability

This paper initiates the theoretical analysis of microscale resonators containing internal flow, modelled here as microfabricated pipes conveying fluid, and investigates the effects of flow velocity on damping, stability, and frequency shift. The analysis is conducted within the context of classical continuum mechanics, and the effects of structural dissipation (including thermoelastic damping in hollow beams), boundary conditions, geometry, and flow velocity on vibrations are discussed. A scaling analysis suggests that slender elastomeric micropipes are susceptible to instability by divergence (buckling) and flutter at relatively low flow velocities of ∼10 m/s.     

Subsonic flapping flutter

A mathematical model of two-dimensional flow through a flexible channel is analyzed for its stability characteristics. Linear theory shows that fluid viscosity, modelled by a Darcy friction factor, induces flutter instability when the dimensionsless fluid speed, S, attains a critical flutter speed, S₀. This is in qualitative agreement with experimental results, and it is at variance with previous analytical studies where fluid viscosity was neglected and divergence instability was predicted. The critical flutter speed and the associated critical flutter frequency depend on three other dimensionless parameters: the ratio of fluid to wall damping; the ratio of wall to fluid mass; and the ratio of wall bending resistance to elastance. Non-linear theory predicts stable, finite amplitude flutter for S>S₀, which increases in frequency and amplitude as S increases. Both symmetric and antisymmetric modes of deformation are discussed.     

Dynamic stability of elastically supported pipes conveying pulsating fluid

The effect of support flexibility on the dynamic behaviour of pipes conveying fluid is investigated for both steady and pulsatile flows. The pipes are built-in at the upstream end and supported at the other by both a translational and a rotational spring. For the steady flow condition, the critical flow velocities, the frequencies and flow induced damping patterns that are associated with the different vibration modes of selected pipe systems are determined as functions of the flow velocity. The results from steady flow cases show that the pipes may first lose stability by either buckling or flutter, depending on the values of the rotational and translational spring constants and their relative magnitudes. In the case of pulsatile flow, the Floquet theory is utilized for the stability analysis of the selected pipe-fluid systems. Numerical results are presented to illustrate the effects of the amount of translational and rotational resiliences at the elastic support on the regions of parametric and combination resonances of the pipes. The results more of the interesting aspects of the behaviour of non-conservative systems.     

Experimental Study on Physical Mechanism of Drag Reduction of Hydrophobic Materials in Laminar Flow

We experimentally study the physical mechanism of the drag reduction of hydrophobic materials in the macroscopic scale. The experiment includes the drag and velocity measurements of laminar boundary layer flow over flat plates, and the observation of air bubbles on the surfaces. The plate surfaces have different wetting and roughness properties. In the drag measurements, the plates with bubbles on the surfaces lead to drag reduction, but not for those without bubbles. Velocity measurement confirms that the flow is laminar and gives apparent fluid slip on the plate wall with bubbles. In observation, air bubbles in macroscopic size emerge and enlarge on hydrophobic surfaces but not on hydrophilic surfaces. Therefore, the drag reduction of hydrophobic materials is explained by the generation of air bubbles of macroscopic size that cause the apparent velocity slip.     

Scattering of sound by an elastic plate with flow

An elastic plate, set in an infinite baffle and immersed in a fluid moving with a uniform subsonic velocity, is excited by an acoustic source. The scattered sound field is analyzed when fluid-plate coupling is large, and a solution is found by the use of matched asymptotic expansions. The far field is found to approximate to the solution obtained when the elastic plate is absent. At a plate resonance, however, the outer field must include eigensolutions with singularities at the plate edges, and close to the plate the dominant terms are travelling plate waves. These plate waves are found to have a wavelength independent of the frequency of the source. It is also shown that a plate resonance corresponds to a divergence instability of aerodynamic flutter theory and that the stability results found in this paper are in agreement with those obtained by using modal expansions. The limit as the Mach number goes to zero is found to be singular, suggesting an analysis of the model for small flow velocity. This calculation is performed and the results match smoothly to the respective solutions for a stationary fluid and for a large subsonic flow.     

Propagation of elastic waves in layered composites with microdefect concentration zones and their simulation with spring boundary conditions

The possibility is studied of applying spring boundary conditions to describe propagation of elastic waves in layered composites with nonperfect contact of components or in the presence of groups of microdefects at the interface. Stiffnesses in spring boundary conditions are determined by crack density, the average size of microdefects, and the elastic properties of the materials surrounding them. In deriving the values of the effective stiffness parameters, the Baik-Thompson and Boström-Wickham approaches are applied, as well as the integral approach. The components of the stiffness matrices are derived from consideration of an incident, at a random angle to the interface, plane wave in the antiplane case, and at a normal angle in the plane case. The efficiency of this model and the possibility of using its results in the three-dimensional case are discussed.     

多孔表面推迟高超声速边界层转捩的机理

利用线性稳定性理论分析（LST）结合直接数值模拟（DNS）研究高超声速多孔表面边界层流动的失稳特征,分析多孔表面推迟高超声速边界层转捩的机理.在Ma=6,Re=2.0×10⁴（参考长度为入口处边界层位移厚度）条件下获得平板边界层及不同孔隙排列情形下平板边界层的典型流动特征,并采用LST方法分析光滑平板及多孔平板扰动的增长率及累计放大率.研究表明三维顺排及错排多孔表面都可以抑制第二模扰动的发展,推迟高超声速边界层转捩,但顺排多孔表面推迟高超声速边界层转捩能力更强.     

AEROELASTIC FLUTTER OF CIRCULAR ROTATING DISKS: A SIMPLE PREDICTIVE MODEL

This paper is an attempt to predict aeroelastic flutter of a rotating disk in an unbounded fluid. In the first part of the paper, the linear vibration of a rotating, potential fluid driven by transverse, harmonic motion of a rotating disk is solved. We extend the existing solution for a rigid disk to include flexible disks and compare alternative numerical evaluation schemes. Our principal interest in this problem is the identification of possible physical mechanisms for aeroelastic flutter. In the forced vibration problem considered here, fluid rotation renders the governing equations hyperbolic for low-frequency oscillation. As a result, the fluid motion may be discontinuous along the two characteristics that emanate from the rim of the disk. These discontinuities suggest the presence of previously unrecognized boundary layers near the rim of the disk that may be important for aeroelastic flutter. This idea is used to develop a simple mathematical model for predicting aeroelastic flutter. The model and its dependence on the dimensionless parameters describing the system are derived from first principles except for the compressible boundary layer, which is described by a simple function whose magnitude is empirically determined by fitting experimental data. Although the model is simple, its predictions are quantitatively similar to the experimental evidence and gives analytic predictions of aeroelastic flutter that are within an order of magnitude of the experimental values.     

Natural vibrations and stability of shells of revolution interacting with an internal fluid flow

A finite-element algorithm is proposed to investigate the dynamic behavior of elastic shells of revolution containing a quiescent or a flowing inviscid fluid in the framework of linear theory. The fluid behavior is described using the perturbed velocity potential. The shell behavior is treated in the framework of the classical shell theory and variational principle of virtual displacements incorporating a linearized Bernoulli equation for calculation of hydrodynamic pressure acting on the shell. The problem reduces to evaluation and analysis of the eigenvalues in the connected system of equations obtained by coupling the equations for velocity perturbations with the equations for shell displacements. For cylindrical shells, the results of numerical simulations are compared with recently published experimental, analytical and numerical data. The paper also reports the results of studying the dynamic behavior of shells under various boundary conditions for the perturbed velocity potential. The investigation made for conical shells has shown that under certain conditions an increase in the cone angle can change a divergent type of instability to a flutter type.     

Stability of flat plate boundary layer over monolithic viscoelastic coatings

It is well known that compliant coatings of a wetted surface can affect the stability of hydrodynamic flows. The mechanism of this influence is related to viscoelastic properties of the coatings particularly to their reaction on the disturbing impact. However, the majority of corresponding studies are devoted to investigation of the effect of soft compliant coatings which are unpractical. Moreover, up to now only model computations of flow stability over the compliant coatings have been performed, as experimental data on viscoelastic properties (the modulus of elasticity E characterizing the elastic features, and the loss tangent ?? characterizing the viscous or damping features) as functions of frequency for the coatings promising from the point of view of their practical application have been absent. Such data were obtained only last years for some materials (silicon rubbers) in a series of studies [1?C3]. The coatings are prospective first of all because of their adequate stiffness (about 1 MPa). In the present paper, results of computations of boundary layer stability performed for the first time for the flow developed over compliant coatings with real properties.     

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.     

Shear instability in the subsurface layer of a material in friction

The shear instability in subsurface layers of a material in friction has been investigated. As the friction surface is approached, several characteristic regions can be distinguished in the bulk of the metal: the region of plastic deformation and texturing (I), the region of severe fragmentation (II), the region of turbulent flow (III), and the region of laminar flow (IV). Regions I and II can be referred to as regions of conventional plastic deformation, whereas regions III and IV correspond to regions of the development of shear instability of the Kelvin-Helmholtz type at the shear boundary. The possibility of implementing this phenomenon within the hydrodynamic approach has been evaluated.