Bifurcations in a vocal fold model

An autonomous fourth order model of vocal fold vibrations is proposed. Each fold is represented by a lower and upper mass, and the aerodynamic forces are derived from a modified Bernoulli equation. The model exhibits many features of normal phonation in a wide parameter region. At the borderlines of this region coexistence of limit cycles, period-doubling and chaos are observed. Implications for an understanding of pathological voices are discussed.     

A reduced-order flow model for vocal fold vibration: From idealized to subject-specific models

We present a reduced-order model for fluid–structure interaction (FSI) simulation of vocal fold vibration during phonation. This model couples the three-dimensional (3D) tissue mechanics and a one-dimensional (1D) flow model that is derived from the momentum and mass conservation equations for the glottal airflow. The effects of glottal entrance and pressure loss in the glottis are incorporated in the flow model. We consider both idealized vocal fold geometries and subject-specific anatomical geometries segmented from the MRI images of rabbits. For the idealized vocal fold geometries, we compare the simulation results from the 1D/3D hybrid FSI model with those from the full 3D FSI simulation based on an immersed-boundary method. For the subject-specific geometries, we incorporate previously estimated tissue properties for individual samples and compare the results with those from the high-speed imaging experiment of in vivo phonation. In both setups, the comparison shows good agreement in the vibration frequency, amplitude, phase delay, and deformation pattern of the vocal fold, which suggests potential application of the present approach for future patient-specific modeling.     

Three-dimensional laryngeal flow fields induced by a model vocal fold polyp

Pathological laryngeal flow fields are investigated in a dynamically-driven, scaled-up model of the vocal folds. Disruption of the flow field due to the presence of a geometric protuberance, representative of a sessile unilateral polyp, is investigated in both the streamwise and transverse flow directions using phase-averaged particle image velocimetry. It is shown that the protuberance disrupts the normal flow behavior of the glottal jet throughout the phonatory cycle. During the divergent portions of the glottal cycle, the flow is characterized by the formation of hairpin vortices downstream of the protuberance. The protuberance also introduces significant velocity gradients in the anterior-posterior direction, which cover ∼30 − 40% of the vocal fold length. It is proposed that the disruption of the normal velocity behavior owing to the presence of a polyp will adversely impact the aerodynamic loadings that drive vocal fold motion, contributing to the temporal and spatial vocal fold asymmetries that are clinically-observed in patients with unilateral polyps.     

Chaotic flow-induced vibration of a flexible tube with end mass

Experimental evidence for chaotic vibrations of a hanging tube with a rigid cylindrical end weight attached is presented. A series of end-mass weights is examined. Bifurcations subsequent to the initial flutter instability result in a variety of complex motions in various domains of the parameter space. The system generically follows a quasi-periodic route to chaos. The data for one particular case is examined in some detail, documenting the quasi-periodic route to chaos with delay-embedding reconstructions of the attractors, dimension calculations and spectral analyses.     

Computational simulation of the flow-induced vibration of a circular cylinder subjected to wake interference

In this work, we considered the flow around two circular cylinders of equal diameter placed in tandem with respect to the incident uniform flow. The upstream cylinder was fixed and the downstream cylinder was completely free to move in the cross-stream direction, with no spring or damper attached to it. The centre-to-centre distance between the cylinders was four diameters, and the Reynolds number was varied from 100 to 645. We performed two- and three-dimensional simulations of this flow using a Spectral/hp element method to discretise the flow equations, coupled to a simple Newmark integration routine that solves the equation of the dynamics of the cylinder. The differences of the behaviours observed in the two- and three-dimensional simulations are highlighted and the data is analysed under the light of previously published experimental results obtained for higher Reynolds numbers.     

Experimental investigation of the flow-induced vibration of a curved cylinder in convex and concave configurations

Experiments have been conducted to investigate the two-degree-of-freedom vortex-induced vibration (VIV) response of a rigid section of a curved circular cylinder with low mass-damping ratio. Two curved configurations, a concave and a convex, were tested regarding the direction of the flow, in addition to a straight cylinder that served as reference. Amplitude and frequency responses are presented versus reduced velocity for a Reynolds number range between 750 and 15 000. Results for the curved cylinders with concave and convex configurations revealed significantly lower vibration amplitudes when compared to the typical VIV response of a straight cylinder. However, the concave cylinder showed relatively higher amplitudes than the convex cylinder which were sustained beyond the typical synchronisation region. We believe this distinct behaviour between the convex and the concave configurations is related to the wake interference taking place in the lower half of the curvature due to perturbations generated in the horizontal section when it is positioned upstream. Particle-image velocimetry (PIV) measurements of the separated flow along the cylinder highlight the effect of curvature on vortex formation and excitation revealing a complex fluid–structure interaction mechanism.     

Measurement of flow-induced pressures on the surface of a model in a flow visualization water tunnel

Flow-induced pressures were measured on the surface of a delta wing in a flow visualization water tunnel, and at the same time the vortical flow over the wing was visualized using dye. For a free-stream velocity of 0.1 m/s used in the experiments, the pressures were small (less than 15 Pa). This is believed to be the first time that flow-induced pressures have been measured in a water tunnel at such a low velocity. Measured pressure distributions can now be properly interpreted in terms of observed detailed flow patterns, without having to undertake complementary wind tunnel experiments to measure model loading.Symbols   c   centreline chord of the delta wing (c=300.0 mm) - C _p   pressure coefficient on the surface of the delta wing - f   frequency (Hz) - p _ref   static pressure measured by the reference static-pressure probe (Pa) - P _ref   total pressure measured by the reference total-pressure probe (Pa) - p _wing   flow-induced pressure at a pressure tapping on the delta wing (Pa) - R   Reynolds number for the delta wing in water (R=Uc/v _w) - s   local semi-span of the delta wing (mm) - U   free-stream velocity in the test section of the water tunnel (m/s) - x   chordwise distance from the apex of the delta wing (mm) - y   spanwise distance from the centreline chord of the delta wing (mm) -   angle of attack of the delta wing (deg) -   angle of sideslip of the delta wing (deg) - v _w   kinematic viscosity of water (m²/s) - _a   density of air (kg/m³) - _w   density of water (kg/m³)

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The role of vortex wake dynamics in the flow-induced vibration of tube arrays

Potential flow and 2-D Navier–Stokes calculations are used to investigate the role of vortex shedding in the non-resonant flow-induced vibration of periodic tube arrays. This dual approach untangles the effects of potential and vortical flow. The negative damping theory is shown to be inconsistent with the Navier–Stokes simulations, and allowing only a single degree of freedom in tube motion significantly overestimates the critical velocity. In contrast, Navier–Stokes simulations which allow all tubes to move in both the transverse and streamwise directions give results in good agreement with experiment. Somewhat surprisingly, potential flow calculations including an artificial phase lag between fluid force and tube motion give reasonably accurate results for a wide range of phase lags. This may be due to the fact that the most unstable mode at onset appears to be streamwise anti-phase (not whirling), as observed in the potential flow case.     

Experimental investigation of flow-induced vibration on isolated and tandem circular cylinders fitted with strakes

The effect of varying the geometric parameters of helical strakes on vortex-induced vibration (VIV) is investigated in this paper. The degree of oscillation attenuation or even suppression is analysed for isolated circular cylinder cases. How a cylinder fitted with strakes behaves when immersed in the wake of another cylinder in tandem arrangement is also investigated and these results are compared to those with a single straked cylinder. The experimental tests are conducted at a circulating water channel facility and the cylindrical models are mounted on a low-damping air bearing elastic base with one degree-of-freedom, restricted to oscillate in the transverse direction to the channel flow. Three strake pitches (p) and heights (h) are tested: p=5, 10, 15d, and h=0.1, 0.2, 0.25d. The mass ratio is 1.8 for all models. The Reynolds number range is from 1000 to 10 000, and the reduced velocity varies up to 21. The cases with h=0.1d strakes reduce the amplitude response when compared to the isolated plain cylinder, however the oscillation still persists. On the other hand, the cases with h=0.2, 0.25d strakes almost completely suppress VIV. Spanwise vorticity fields, obtained through stereoscopic digital particle image velocimetry (SDPIV), show an alternating vortex wake for the p=10d and h=0.1d straked cylinder. The p=10d and h=0.2d cylinder wake has separated shear layers with constant width and no roll-up close to the body. The strakes do not increase the magnitude of the out-of-plane velocity compared to the isolated plain cylinder. However, they deflect the flow in the out-of-plane direction in a controlled way, which can prevent the vortex shedding correlation along the span. In order to investigate the wake interference effect on the strake efficiency, an experimental arrangement with two cylinders in tandem is employed. The centre-to-centre distance for the tandem arrangement varies from 2 to 6. When the downstream p=10d and h=0.2d cylinder is immersed in the wake of an upstream fixed plain cylinder, it loses its effectiveness compared with the isolated case. Although the oscillations have significant amplitude, they are limited, which is a different behaviour from that of a tandem configuration with two plain cylinders. For this particular case, the amplitude response monotonically increases for all gaps, except one, a trait usually found in galloping-like oscillations. SDPIV results for the tandem arrangements show alternating vortex shedding and oscillatory wake.     

Fully coupled flow-induced vibration of structures under small deformation with GMRES method

Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual （GMRES） method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GiViRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.     

Nonlinear characteristics of circular-cylinder piezoelectric power harvester near resonance based on flow-induced flexural vibration mode

The nonlinear behaviors of a circular-cylinder piezoelectric power harvester （CCPPH） near resonance are analyzed based on the flow-induced flexural vibration mode. The geometrically-nonlinear effect of the cylinder is studied with considering the in-plane extension incidental to the large defection. The boundary electric charges generated from two deformation modes, flexure and in-plane extension, were distinguished with each other because the charge corresponding to the latter mode produces no contribution to the output current. Numerical results on output powers show that there are multi- valuedness and jump behaviors.     

THE EXISTENCE OF PERIODIC SOLUTION OF THE FOURTH ORDINARY NONLINEAR DIFFERENTIAL EQUATION CAUSED BY FLOW－IN

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Influence of a finite strain on vibration of a bounded Timoshenko beam

The goal of this work is to study the eigenmodes of shearable beams with initial finite strain. A three dimensional model is developed on the base of Cosserat continuum mechanics. The characteristics of waves propagation superimposed upon finite pre-stress are obtained using the (rigorous) calculation of the Hamiltonian action. The results are applied on vibration of beam supporting a finite longitudinal strain. Nonlinear effect according to the pre-stress is obtained for various boundary conditions and through a nondimensional formalism.     

Chaotic vibration of a nonlinear full-vehicle model

The present work investigates the chaotic responses of a nonlinear seven degree-of-freedom ground vehicle model. The disturbances from the road are assumed to be sinusoid and the time delay between the disturbances is investigated. Numerical results show that the responses of the vehicle model could be chaotic. With the bifurcation phenomenon detected, the chaotic motion is confirmed with the dominant Lyapunov exponent. The results can be useful in dynamic design of a vehicle.     

The influence of temperature on flow-induced forces on quartz-crystal-microbalance sensors in a Chinese liquor identification electronic-nose: three-dimensional computational fluid dynamics simulation and analysis

An electronic-nose is developed based on eight quartz-crystal-microbalance(QCM) gas sensors in a sensor box, and is used to detect Chinese liquors at room temperature. Each sensor is a highly-accurate and highly-sensitive oscillator that has experienced airflow disturbances under the condition of varying room temperatures due to unstable flow-induced forces on the sensors surfaces. The three-dimensional(3D) nature of the airflow inside the sensor box and the interactions of the airflow on the sensors surfaces at different temperatures are studied by computational fluid dynamics(CFD) tools. Higher simulation accuracy is achieved by optimizing meshes, meshing the computational domain using a fine unstructural tetrahedron mesh. An optimum temperature, 30°C, is obtained by analyzing the distributions of velocity streamlines and the static pressure, as well as the flow-induced forces over time, all of which may be used to improve the identification accuracy of the electronic-nose for achieving stable and repeatable signals by removing the influence of temperature.     

Measurement of flow separation in a human vocal folds model

The paper provides experimental data on flow separation from a model of the human vocal folds. Data were measured on a four times scaled physical model, where one vocal fold was fixed and the other oscillated due to fluid–structure interaction. The vocal folds were fabricated from silicone rubber and placed on elastic support in the wall of a transparent wind tunnel. A PIV system was used to visualize the flow fields immediately downstream of the glottis and to measure the velocity fields. From the visualizations, the position of the flow separation point was evaluated using a semiautomatic procedure and plotted for different airflow velocities. The separation point position was quantified relative to the orifice width separately for the left and right vocal folds to account for flow asymmetry. The results indicate that the flow separation point remains close to the narrowest cross-section during most of the vocal fold vibration cycle, but moves significantly further downstream shortly prior to and after glottal closure.     

Quantitative evaluation of flow-induced structural vibration and noise in turbomachinery by full-scale weakly coupled simulation

This article reports on a full-scale structural simulation of flow-induced mechanical vibrations and noise in a 5-stage centrifugal pump. An interior flow field is simulated by an LES-based CFD program, which can be found elsewhere. We developed a data-interface tool to enable mesh matching and data transfer between the fluid and structure meshes. The vibration of the pump's structure was simulated using a parallel explicit dynamic FEM code. This provided a time series of pressure fluctuations on the internal surface as force-boundary conditions. The calculated vibration of the outer surface of the structure agrees reasonably well with measured data. Using Fourier transformation, the vibration modes at blade passing frequencies (BPFs) were extracted and presented as a visual image. The simulation clarified the mechanisms of resonant noise generation and propagation, which can then be used for noise reduction. This study shows that it is feasible to use fluid–structure weakly coupled simulations to estimate the flow-induced noise generated in turbomachinery.