Coherent structures in the boundary layer of a flat thick plate

We use POD and EPOD (extended POD) analysis to extract the main features of the flow over a thick flat plate simulated with an LES. Our goal is to better understand the coupling between the velocity field and the surface pressure field. We find that POD modes based on the full velocity and energy fields contain both flapping and shedding frequencies. Pressure modes are found to be uniform in the spanwise direction and the most intense variations take place at the mean reattachment point. Velocity modes educed from the pressure modes with EPOD are seen to correspond to eddies shed by the recirculation bubble.     

Non-linear vibrations of free-edge thin spherical shells: Experiments on a 1:1:2 internal resonance

This study is devoted to the experimental validation of a theoretical model of large amplitude vibrations of thin spherical shells described in a previous study by the same authors. A modal analysis of the structure is first detailed. Then, a specific mode coupling due to a 1:1:2 internal resonance between an axisymmetric mode and two companion asymmetric modes is especially addressed. The structure is forced with a simple-harmonic signal of frequency close to the natural frequency of the axisymmetric mode. The experimental setup, which allows precise measurements of the vibration amplitudes of the three involved modes, is presented. Experimental frequency response curves showing the amplitude of the modes as functions of the driving frequency are compared to the theoretical ones. A good qualitative agreement is obtained with the predictions given by in the model. Some quantitative discrepancies are observed and discussed, and improvements of the model are proposed.     

Transient responses of repeated impact of a beam against a stop

The transient behavior of a cantilever beam, driven by periodic force and repeated impacting against a rod-like stop, is the subject of this investigation. As impact and separation phase take place alternately, the transient waves induced either by impacts or by separations will travel in more complicated ways. Thus the transient responses of both the beam and the rod during repeated impact become an important issue. In both impact phase and separation phase, the transient wave propagations are solved by the expansion of transient wave functions in a series of Eigenfunctions (wave modes). From the solutions, the answer of impact force is derived directly, so that the divergence problem, encountered in solving impact force numerically by a strongly non-linear equation coupled the unknown impact force with motions, has been avoided. Numerical results show the convergence of the time-step size and truncation number of wave modes in the calculations of impact force by the present method. As the transient wave effect is considered, the numerical results can show several transient phenomena involving the propagation of transient impact-induced waves, sub-impact phases, long-term impact motion, chatter, sticking motion, synchronous impact, non-synchronous impact (including asynchronous impact) and impact loss.     

Co-simulation coupling spectral/finite elements for 3D soil/structure interaction problems

The coupling between an implicit finite elements (FE) code and an explicit spectral elements (SE) code has been explored for solving the elastic wave propagation in the case of soil/structure interaction problem. The coupling approach is based on domain decomposition methods in transient dynamics. The spatial coupling at the interface is managed by a standard coupling mortar approach, whereas the time integration is dealt with an hybrid asynchronous time integrator. An external coupling software, handling the interface problem, has been set up in order to couple the FE software Code_Aster with the SE software EFISPEC3D.     

Numerical simulations of a filament in a flowing soap film

Experiments concerning the properties of soap films have recently been carried out and these systems have been proposed as experimental versions of theoretical two‐dimensional liquids. A silk filament introduced into a flowing soap film, was seen to demonstrate various stable modes, and these were, namely, a mode in which the filament oscillates and one in which the filament is stationary and aligns with the flow of the liquid. The system could be forced from the oscillatory mode into the non‐ oscillatory mode by varying the length of the filament. In this article we use numerical and computational techniques in order to simulate the strongly coupled behaviour of the filament and the fluid. Preliminary results are presented for the specific case in which the filament is seen to oscillate continuously for the duration of our simulation. We also find that the filament oscillations are strongly suppressed when we reduce the effective length of the filament. We believe that these results are reminiscent of the different oscillatory and non‐oscillatory modes observed in experiment. The numerical solutions show that, in contrast to experiment, vortices are created at the leading edge of the filament and are preferentially grown in the curvature of the filament and are eventually released from the trailing edge of the filament. In a similar manner to oscillating hydrofoils, it seems that the oscillating filaments are in a minimal energy state, extracting sufficient energy from the fluid to oscillate. In comparing numerical and experimental results it is possible that the soap film does have an effect on the fluid flow especially in the boundary layer where surface tension forces are large. Copyright © 2004 John Wiley & Sons, Ltd.     

Diffraction of high-frequency waves by the edge of a perfectly conducting sheet located on a cylindrical dielectric interface

An important class of electromagnetic structures involves metallic sheets on the surface of a curved dielectric interface. At high frequencies, the behavior of such structures can be analyzed by the geometrical theory of diffraction (GTD) provided that the various wave and ray species excited by a single edge are known. This problem is addressed here by determining the line source Green's function for a thin perfectly conduvting half plane wrapped around a dielectric cylinder in an infinitely extended (nonperiodic) angular space. The formally exact solution is evaluated asymptotically to yield the GTD field in various ray-optical domains, with emphasis on those wave and ray species (creeping waves, whispering gallery modes, edge scattered fields, etc.) attributed to the presence of the edge. When the dielectric contrast is reduced to zero, all expressions are found to agree with those known for a curved sheet in a homogeneous medium.     

On stability and non-uniqueness of the dilatation states of a compressible isotropic unit cube subjected to dead loading

This paper considers a unit elastic cube, made of compressible isotropic material, with its faces subjected to certain dead-load tractions that produce a possible equilibrium state of non-uniform dilatation. It is seen that, at the considered equilibrium state, the cube material acquires properties of pseudo-transverse isotropy. Conditions are obtained for the stability of such an equilibrium state with respect to superimposed pure homogeneous deformations having principal directions parallel to the cube edges. The problem of non-uniqueness of the cube dilatation states is also addressed, and non-uniqueness is illustrated in an example application dealing with an isotropic cube made of the Blatz-Ko material. The nature and the stability features of these equilibrium states are studied in depth.     

Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence

The vortex formation and shedding process in the near wake region of a 2D square-section cylinder at incidence has been investigated by means of particle image velocimetry (PIV). Proper orthogonal decomposition (POD) is used to characterize the coherent large-scale flow unsteadiness that is associated with the wake vortex shedding process. A particular application of the POD analysis is to extract the vortex-shedding phase of individual velocity fields, which were acquired at asynchronous low rate with respect to the vortex shedding cycle. The phase of an individual flow field is determined from its projection on the first pair of POD modes, allowing phase averaging of the measurement data to be performed. In addition, a low-order representation of the flow, constructed from the mean and the first pair of POD modes, is found to be practically equivalent to the phase-averaged results. It is shown that this low-order representation corresponds to the basic Fourier component of the flow field ensemble with respect to the reconstructed phase. The phase-averaged flow representations reveal the dominant flow features of the vortex-shedding process and the effect of the angle of incidence upon it.     

Vibration analysis of a spinning disk using image-derotated holographic interferometry

This paper reports on the application of image-derotated holographic interferometry to study the resonant response of a rotating steel disk at speeds up to 8000 rpm. The rotational motion of the disk is optically removed by passing the image of the rotating disk through a prism that is traveling at half the rotational speed of the disk. Off-axis, double-pulsed, laser holography is then used to record the disk resonant-vibratory response. The first five diametrical modes and one complex mode of disk vibration are obtained at various rpm. The effects of disk imbalance, misalignment of optical and mechanical axes of rotation and system-excited modes of vibration are also addressed. Selected experimental results are compared to those obtained using finite element analysis.     

Non-quadratic Kelvin modes based plasticity criteria for anisotropic materials

Novel (non-quadratic) plasticity criteria based on Kelvin modes are formulated here for anisotropic materials. As an example, such a macroscopic criterion is applied with success to the case of FCC nickel-base single crystals. Indeed, relying on the cubic symmetry of the material, the Kelvin decomposition of elasticity tensor easily allows for the definition of an objective and loading independent criterion. The criterion identification is performed from different loading cases for CMSX2 single crystal superalloy. Tension-torsion yield surfaces at room temperature and yield stress dependence on crystal orientation are modeled. The Kelvin modes based criterion is compared to experimental data, to Hill and Barlat and coworkers macroscopic criteria and to Schmid law predictions. The results show that a simple three-parameter yield function built thanks to von Mises equivalent Kelvin stresses accounts for a satisfying plasticity criterion for such alloys.Non-quadratic norm ∥·∥_a plasticity framework is addressed. Intrinsic generalizations of Hershey-Hosford criterion are proposed for cubic material symmetry.     

Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities

We study the resonant dynamics of a two-degree-of-freedom system composed of a linear oscillator weakly coupled to a strongly non-linear one, with an essential (non-linearizable) cubic stiffness non-linearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show that the undamped system possesses stable and unstable synchronous periodic motions (non-linear normal modes—NNMs), as well as, asynchronous periodic motions (elliptic orbits—EOs). Furthermore, we show that when damping is introduced certain NNMs produce resonance capture phenomena, where a trajectory of the damped dynamics gets ‘captured’ in the neighborhood of a damped NNM before ‘escaping’ and becoming an oscillation with exponentially decaying amplitude. In turn, these resonance captures may lead to passive non-linear energy pumping phenomena from the linear to the non-linear oscillator. Thus, sustained resonance capture appears to provide a dynamical mechanism for passively transferring energy from one part of the system to another, in a one-way, irreversible fashion. Numerical integrations confirm the analytical predictions.     

Hydroelastic vibration of two annular plates coupled with a bounded compressible fluid

A theoretical study on a linear hydroelastic vibration of two annular plates coupled with a bounded fluid is presented. The proposed method, based on the Rayleigh–Ritz method and the finite Hankel transform, is verified through a finite element analysis by using a commercial computer code, with an excellent accuracy. It is assumed that plates with an unequal thickness and with an unequal inner radius are clamped along their edges and an inviscid compressible fluid fills the space between the annular plates and the outer rigid vessel. When the two annular plates are identical, distinct in-phase and out-of-phase modes are observed. By increasing the difference in the plate thickness, the symmetric in-phase and out-of-phase modes with respect to the middle plane of the system are gradually shifted to pseudo in-phase and out-of-phase modes, and eventually they are changed to mixed modes. It is found that the natural frequencies decrease with an increase of the fluid compressibility, and additional modes due to a fluid concentration are observed when the plates are coupled with a compressible fluid. The fluid compressibility effect on the natural frequency is dominant in the out-of-phase modes and the higher modes. Also, the effects of the fluid thickness or the distance between the plates and the inner radius of the plates on the natural frequencies of the wet modes are investigated.     

Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency

This paper investigates the energy harvested from the flutter of a plate in an axial flow by making use of piezoelectric materials. The equations for fully coupled linear dynamics of the fluid–solid and electrical systems are derived. The continuous limit is then considered, when the characteristic length of the plate's deformations is large compared to the piezoelectric patches' length. The linear stability analysis of the coupled system is addressed from both a local and global point of view. Piezoelectric energy harvesting adds rigidity and damping on the motion of the flexible plate, and destabilization by dissipation is observed for negative energy waves propagating in the medium. This result is confirmed in the global analysis of fluttering modes of a finite-length plate. It is finally observed that waves or modes destabilized by piezoelectric coupling maximize the energy conversion efficiency.     

Acoustic waves in a cylindrical duct with periodically varying cross section

The null field approach is used to study the propagation of acoustic waves in a rotationally symmetric hard-walled duct with a periodically varying cross section. For a radius that varies sinusoidally along the axial distance, numerical computations give the axial wave number and the passbands and stopbands of the modes of the duct. In particular, small passbands are seen to exist even for very large variations in radius, and probably all the way to the point where the duct is cut off. We also present some plots which show the pressure pattern inside the duct.     

Parametric resonances in a base-excited double pendulum

Two parametrically-induced phenomena are addressed in the context of a double pendulum subject to a vertical base excitation. First, the parametric resonances that cause the stable downward vertical equilibrium to bifurcate into large-amplitude periodic solutions are investigated extensively. Then the stabilization of the unstable upward equilibrium states through the parametric action of the high-frequency base motion is documented in the experiments and in the simulations. It is shown that there is a region in the plane of the excitation frequency and amplitude where all four unstable equilibrium states can be stabilized simultaneously in the double pendulum. The parametric resonances of the two modes of the base-excited double pendulum are studied both theoretically and experimentally. The transition curves (i.e., boundaries of the dynamic instability regions) are constructed asymptotically via the method of multiple scales including higher-order effects. The bifurcations characterizing the transitions from the trivial equilibrium to the periodic solutions are computed by either continuation methods and or by time integration and compared with the theoretical and experimental results.     

Modal analysis of measurements from a large-scale VIV model test of a riser in linearly sheared flow

Large-scale model testing of a tensioned steel riser in well-defined sheared current was performed at Hanøytangen outside Bergen, Norway in 1997. The length of the model was 90 m and the diameter was 3 cm. The aim of the present work is to look into this information and try to improve the understanding of vortex-induced vibrations (VIV) for cases with very high order of responding modes, and in particular to study if and under which circumstances the riser motions would be single-mode or multi-mode. The measurement system consisted of 29 biaxial gauges for bending moment. The signals are processed to yield curvature and displacement and further to identify modes of vibration. A modal approach is used successfully employing a combination of signal filtering and least-squares fitting of precalculated mode-shapes. As a part of the modal analysis, it is demonstrated that the equally spaced instrumentation limited the maximum mode number to be extracted to be equal to the number of instrumentation locations. This imposed a constraint on the analysis of in-line (IL) vibration, which occurs at higher frequencies and involves higher modes than cross-flow (CF). The analysis has shown that in general the riser response was irregular (i.e. broad-banded) and that the degree of irregularity increases with the flow speed. In some tests distinct spectral peaks could be seen, corresponding to a dominating mode. No occurrences of single-mode (lock-in) were seen. The IL response is more broad-banded than the CF response and contains higher frequencies. The average value of the displacement r.m.s over the length of the riser is computed to indicate the magnitude of VIV motion during one test. In the CF direction the average displacement is typically 1/4 of the diameter, almost independent of the flow speed. For the IL direction the values are in the range 0.05–0.08 of the diameter. The peak frequency taken from the spectra of the CF displacement at riser midpoint show approximately to be equal to the Strouhal frequency. The peak frequency in IL direction was typically twice the Strouhal frequency.     

A numerical study of mixed convection in a horizontal channel with a discrete heat source in an open cavity

This article aims to numerically investigate mixed convection heat transfer in a two-dimensional horizontal channel with an open cavity. A discrete heat source is considered to be located on one of the walls of the cavity. Three different heating modes are considered which relate to the location of the heat source on three different walls (left, right and bottom) of the cavity. The analysis is carried out for a range of Richardson numbers and cavity aspect ratios. The results show that there are noticeable differences among the three heating modes. When the heat source is located on the right wall, the cavity with an aspect ratio of two has the highest heat transfer rate compared to other cavity heating modes. Moreover, when the heat source is located on the bottom wall, the flow field in the cavity with an aspect ratio of two experiences a fluctuating behaviour for Richardson number of 10. The results also show that at a fixed value of Richardson number, all three different heating modes show noticeable improvements in the heat transfer mechanism as the cavity aspect ratio increases.     

Flow induced oscillation of two rigid rectangular plates in a side-by-side configuration

The present work is an experimental study of two oscillating rigid plates placed in side-by-side configuration, hinged at their leading edges, subjected to low subsonic flow. This problem is investigated using smoke-wire flow visualization, hot-wire anemometry, and time resolved particle image velocimetry. It is found that beyond a critical Reynolds number, the plates set into oscillatory motion. This critical Reynolds number depends on the gap between the plates. It is also seen that this value of Reynolds number, at lower values of gap to thickness ratio (<7) is significantly higher than that of the single plate configuration value. The frequency and amplitude of the oscillating plates at various gaps and Reynolds numbers have been studied and compared with the characteristics of an oscillating single plate. It is also found that depending on the gap and acceleration of the free-stream, there exist two modes of oscillation - (i) in-phase and (ii) out-of-phase. For gap to thickness ratio less than 10, only in-phase oscillations take place for all values of free-stream velocity considered in the present work, whereas, when this ratio is greater than 10, the mode of oscillation depends on the initial conditions up to a certain free-stream velocity, beyond which the plates switch to in-phase mode. Smoke wire flow visualization technique along with time resolved particle image velocimetry reveal that the vorticity distributions around the plates are responsible for the initiation of the two modes of oscillations.     

Responses of a non-linearly coupled pitch-roll ship model under harmonic excitation

Stationary responses of nonlinearly coupled pitch and roll ship modes are studied using a modified averaging method, along with two second order multiple time scale (MTS) methods for comparison. Stability of the solutions is also studied. In the case of harmonic excitation all the three methods give fairly accurate results to the original problem but the averaging method is the most efficient. Analytic solutions are obtained from the averaged equations, which can be used to predict stationary responses both for small and for large excitations. From the averaging method several qualitatively different phenomena which cannot be addressed by the first order theory have been obtained: (i) the saturation phenomenon is lost, (ii) the bifurcation points are altered and (iii) a drift term is present which, although small, appears to have a significant effect on the accuracy of the solutions.     

Effect of a biasing electric field on the propagation of antisymmetric Lamb waves in piezoelectric plates

Based on the theories of anisotropic elasticity, piezoelectricity and elastic waves in solids, the propagation of antisymmetric Lamb waves in a biasing electric field is investigated in this paper. By solving the coupled differential equations of motion under a biasing electric field, the phase velocity equations of antisymmetric Lamb wave modes for electrically open and shorted cases are obtained, respectively. The beating effect arising from the difference between the phase velocity of the zero-order symmetric mode and antisymmetric mode exists in the plate when the plate has a thickness comparable to or slightly larger than the wavelength. The influence of the biasing electric field on the phase velocity, beat wavelength, mechanical displacement and stress fields for the lowest two antisymmetric modes of Lamb waves are discussed in detail. From the calculated results, it is seen that the phase velocity of the fundamental antisymmetric mode is especially sensitive to the applied biasing electric field.