Vibration-induced granular segregation: a phenomenon driven by three mechanisms

The segregation of large spheres in a granular bed under vertical vibrations is studied. In our experiments, we systematically measure rise times as a function of density, diameter, and depth, for two different sinusoidal excitations. The measurements reveal that, at low frequencies, inertia and convection are the only mechanisms behind segregation. Inertia (convection) dominates when the relative density is greater (less) than one. At high frequencies, where convection is suppressed, fluidization of the granular bed causes either buoyancy or sinkage and segregation occurs.     

Controllable equilibrium of an inhomogeneously heated liquid in a vibrational field

Equations of thermal vibrational convection of an inhomogeneously heated liquid are analytically solved for arbitrary orientation of vectors determining the heating direction, force of gravity, and vibrations in a closed cavity in the shape of an infinite horizontal cylinder. It is demonstrated that for any orientation of these vectors in the plane perpendicular to the cylinder, the gravitational and vibrational convection mechanisms can completely compensate each other. The ratio is determined between the vibrational and the gravitational Grashof numbers such that mechanical equilibrium conditions are satisfied. This ratio is proved by direct numerical calculation of complete equations of thermal vibrational convection.     

An analytical study of rotor dynamics coupled with thermal effect for a continuous rotor shaft

This paper presents an analytical analysis of a continuous rotor shaft subjected to universal temperature gradients. To this end, an analytical model is derived to investigate the generic thermal vibrations of rotor structures. The analytical solutions are obtained in a rotating frame and include parameters related with both the thermal environment and the rotor dynamic structures. This provides an insight into the mechanisms for the rotor thermal vibration. Furthermore, numerical results based on the analytical solutions are given. An index denoting the temperature gradients is proposed for the occasions with nonlinear cross-sectional temperature distributions. Finally, the factors influencing the thermal vibrations are analyzed. The results show that the thermal vibration is affected by many factors including the shaft size, rotational speeds, heating locations, critical speed, etc. Moreover, it is investigated how the convection coefficient and the heat conductivity influence the thermal vibrations in order to provide an insight into the management of thermal vibrations from the perspective of thermal aspects.     

Stochastic solutions of Navier-Stokes equations: an experimental evidence

An electrodynamic loudspeaker has been operated in anharmonic regime indicated by the nonlinear ordinary differential equation when spring constant γ in restoring term, as well as, viscoelasticity of the membrane material, increases with displacement. For driving currents in the range of 2.8-3.3 A, doubling of the vibration period appears, while for currents in the range of 3.3-3.6 A, multiple sequences of subharmonic vibrations begin with f/4 and 3f/4. An application of currents higher than 3.6 A results in a spectrum, characteristic for the chaotic state. The loudspeaker was then operated in a closed chamber, and subharmonic vibrations disappeared by an evacuation. Subsequent injection of air revoked them again at ～ 120 mbar (Re(')=476) when air viscous forces dominate the Morse convection. At 430 mbar (Re=538) single vibration state was restored, and the phenomenon is in an agreement with prediction of the five mode truncation procedure applied to the Navier-Stokes equations describing a two-dimensional incompressible fluid.     

Convective instability of the thermovibrational flow of binary mixture in the presence of the Soret effect

The convective instability of the thermovibration flow in a plane horizontal layer filled with an incompressible binary gaseous mixture is investigated. The study takes into account the effect of thermal diffusion or the Ludwig-Soret effect. Several instability mechanisms are discussed. To determine the instability threshold with respect to cell and long-wave perturbations, the Floquet theory was applied to the linearized equations of convection formulated in the Boussinesq approximation. We found that regime parametric instability can occur owing to the finite frequency vibrations. The evolution of plane, spiral and three-dimensional disturbances is studied. We demonstrated that, because of the properties of the system, the subharmonic response of plane disturbances to the external periodic action cannot be observed. The instability can be associated only with synchronous or quasiperiodic modes. Depending on the vibration parameters, modulations can stabilize or destabilize the base state. For spiral perturbations the stability boundary does not depend on the amplitude and frequency of vibrations. In the case of long-wave instability we apply the regular perturbation approach with the wavenumber as a small parameter in power expansions. The stability boundaries are found.     

Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids

In this paper, we study flexural vibrations of a cantilever beam with thin rectangular cross section submerged in a quiescent viscous fluid and undergoing oscillations whose amplitude is comparable with its width. The structure is modeled using Euler–Bernoulli beam theory and the distributed hydrodynamic loading is described by a single complex-valued hydrodynamic function which accounts for added mass and fluid damping experienced by the structure. We perform a parametric 2D computational fluid dynamics analysis of an oscillating rigid lamina, representative of a generic beam cross section, to understand the dependence of the hydrodynamic function on the governing flow parameters. We find that increasing the frequency and amplitude of the vibration elicits vortex shedding and convection phenomena which are, in turn, responsible for nonlinear hydrodynamic damping. We establish a manageable nonlinear correction to the classical hydrodynamic function developed for small amplitude vibration and we derive a computationally efficient reduced order modal model for the beam nonlinear oscillations. Numerical and theoretical results are validated by comparison with ad hoc designed experiments on tapered beams and multimodal vibrations and with data available in the literature. Findings from this work are expected to find applications in the design of slender structures of interest in marine applications, such as biomimetic propulsion systems and energy harvesting devices.     

Acoustic streaming induced by ultrasonic flexural vibrations and associated enhancement of convective heat transfer

Acoustic streaming induced by ultrasonic flexural vibrations and the associated convection enhancement are investigated. Acoustic streaming pattern, streaming velocity, and associated heat transfer characteristics are experimentally observed. Moreover, analytical analysis based on Nyborg's formulation is performed along with computational fluid dynamics (CFD) simulation using a numerical solver CFX 4.3. Two distinctive acoustic streaming patterns in half-wavelength of the flexural vibrations are observed, which agree well with the theory. However, acoustic streaming velocities obtained from CFD simulation, based on the incompressible flow assumption, exceed the theoretically estimated velocity by a factor ranging from 10 to 100, depending upon the location along the beam. Both CFD simulation and analytical analysis reveal that the acoustic streaming velocity is proportional to the square of the vibration amplitude and the wavelength of the vibrating beam that decreases with the excitation frequency. It is observed that the streaming velocity decreases with the excitation frequency. Also, with an open-ended channel, a substantial increase in streaming velocity is observed from CFD simulations. Using acoustic streaming, a temperature drop of 40 degrees C with a vibration amplitude of 25 microm at 28.4 kHz is experimentally achieved.     

Angular vibrations of cryogenically cooled double‐crystal monochromators

The effect of angular vibrations of the crystals in cryogenically cooled monochromators on the beam performance has been studied theoretically and experimentally. A simple relation between amplitude of the vibrations and size of the focused beam is developed. It is shown that the double‐crystal monochromator vibrations affect not only the image size but also the image position along the optical axis. Several methods to measure vibrations with the X‐ray beam are explained and analyzed. The methods have been applied to systematically study angular crystal vibrations at monochromators installed at the PETRA III light source. Characteristic values of the amplitudes of angular vibrations for different monochromators are presented.     

分离比对混合流体Rayleigh-Bénard对流解的影响

混合流体Rayleigh-Bénard对流是研究非平衡对流的非线性动力学特性的典型模型之一.基于流体力学方程组的数值模拟,首先探讨了矩形腔体中具有强Soret效应(分离比Ψ=-0.60)的混合流体行波对流的分叉特性及斑图演化,沿着分叉曲线的上部分支,随着相对瑞利数的增加,此系统依次出现了局部行波对流、具有缺陷的行波对流、行波对流、摆动行波对流及定常对流5种行波对流解.然后,研究了分离比Ψ对对流解的影响,与弱Soret效应(Ψ=-0.11)时的对流解相比较,强Soret效应(Ψ=-0.60)时出现的对流解更丰富.由于有强Soret效应的对流的复杂性,Ψ=-0.60时的对流解与Ψ=-0.20,-0.4时的对流解不同.     

Pressure effects on inter‐ and intramolecular vibrations in hydrogen‐bonded L‐ascorbic acid crystal

Pressure effects on the Raman spectra due to the inter‐ and intramolecular vibrations of the L ‐ascorbic acid crystal were studied. The intensity of the Raman bands due to the intermolecular vibrations varies in three different ways by application of pressure. The bands of the first group become stronger, those of the second one become weaker and the third group shows no prominent change in their intensity with increasing pressure. The bands due to the intermolecular vibrations show a blue shift, while the bands due to the intramolecular vibrations shift to the blue or red depending on the vibrational modes by application of pressure. The bands assigned to the O H stretching vibrations shift to the red, the bands assigned to the CO and CC stretching vibrations shift a little to the red and the bands assigned to the other vibrations shift to the blue under high pressure. The following conclusions were derived. (1) The hydrogen bonds forming helixes become stronger and the isolated hydrogen bond becomes weaker with increasing pressure. (2) The bands of the first group owing to the intermolecular vibrations are ascribed to the vibrations related to the helix hydrogen bonds and the second group bands to the isolated hydrogen bond. (3) The CO stretching vibration couples with the CC stretching vibration. (4) The phase transitions take place at 1.8 and 4 GPa in the crystal. Copyright © 2007 John Wiley & Sons, Ltd.     

Fermi resonance of optical one-phonon and acoustic two-phonon vibrations in light metals

It is shown that the anharmonicity of crystal lattice vibrations in light metals such as beryllium, can give rise to a Fermi resonance of optical one-phonon and acoustic two-phonon vibrations. New hybridized vibrational states are formed as a result of such a resonance interaction: biphonon and quasibiphonon vibrations and renormalized optical vibrations. Depending on the wave vector, these vibrational states can be both damped and stationary. The corresponding dispersion equation is obtained, whose solution made it possible to determine the spectrum of these vibrations (dispersion curves and the wave vector dependence of the damping for damped vibrations). It is shown that ultrafast damping of optical vibrations, similar to the well-known superradiance effect for Frenkel’ and Wannier-Mott excitons, is possible. Fiz. Tverd. Tela (St. Petersburg) 39, 542–546 (March 1997)     

Isotopic dependence of the shape of Se nuclei in the collective-model representation

The energy structure of low-lying excited states in the nuclei of even selenium isotopes is considered on the basis of a soft-nucleus model. The nuclei are treated as nonaxial rotors, longitudinal and transverse vibrations of their surface being taken into account in the quadrupole-deformation approximation featuring an admixture of an octupole deformation. The parameters of a phenomenological collective model for the ^{72,74,76,78,80,82}Se nuclei are found both in the case of β vibrations (longitudinal vibrations) and in the presence of additional γ vibrations (transverse vibrations) of the nuclear surface.     

Anharmonicity of lattice vibrations induced by charged nickel impurities in II–VI semiconductors

The lattice vibrations induced by nickel impurities with a negative charge relative to the lattice in ZnSe: Ni, ZnO: Ni, ZnS: Ni, and CdS: Ni semiconductors are investigated using very sensitive field-induced vibronic spectroscopy. This technique is based on the interaction of lattice vibrations with impurity excitons and the effect of an ac electric field on these excitons. The phonon replicas of the zero-phonon line (ZPL) of impurity excitons (including intense peaks of combination replicas up to the eighth order) in the experimental spectra of the system under investigation are observed for the first time. These spectra make it possible to analyze the interaction between different vibrations. The experimental results are interpreted in terms of model calculations of the vibrations in a lattice with a charged impurity center and vibrations in a monoatomic chain with a strong anharmonicity. It is demonstrated that charged impurity centers initiate new lattice vibrations, namely, extrinsic anharmonic modes with a considerable third-or fourth-order anharmonicity.     

Chaotic vibrations of a vocal fold model with a unilateral polyp

A nonlinear model was proposed to study chaotic vibrations of vocal folds with a unilateral vocal polyp. The model study found that the vocal polyp affected glottal closure and caused aperiodic vocal fold vibrations. Using nonlinear dynamic methods, aperiodic vibrations of the vocal fold model with a polyp were attributed to low-dimensional chaos. Bifurcation diagrams showed that vocal polyp size, stiffness, and damping had important effects on vocal fold vibrations. An increase in polyp size tended to induce subharmonic patterns and chaos. This study provides a theoretical basis to model aperiodic vibrations of vocal folds with a laryngeal mass.     

Local vibrations in fcc crystals with two-parametric substitutional impurities

The threshold parameters of defects (the mass defect and the relative change in the force constants) are determined at which local vibrations start to occur in an fcc crystal with substitutional impurities. The characteristics of local vibrations are investigated, and the influence of the defect parameters on the frequency of local vibrations and their decay rate with distance from the impurity atom is analyzed. The frequencies and the intensities of local vibrations are calculated for the nearest neighboring atoms of an impurity, which, combined with the impurity atom, form a defect cluster.     

Vibrations of inclined bars with end constraint

Considered are vibrations of inclined bars with the bottom end fixed and the top end having a constraint that this end can move only in the vertical direction. During the vibrations of such bars, the axial and lateral motions are coupled. The frequencies of the coupled vibrations of small amplitudes of inclined bars with different end conditions are presented along with the normal functions. The application of the method of normalfunction expansion to the forced as well as transient vibrations of the inclined bars is also outlined.     

水平圆管通道内热磁对流的实验研究

由于温度分布不均匀而导致磁场中的磁性流体受到非平衡的磁场力作用,而发生流动的现象,称为热磁对流。它是一种由体积力驱动的类似自然对流的流动,可以通过设计合适的磁场来控制热磁对流的强度和方向。本文对水平圆管通道内热磁对流进行了实验研究,测量了通道内及壁面的温度分布,并通过两种不同的方法根据实验测得的温度分布估算了热磁对流的流量和速度的大小。     

Dynamics of Front Driven by Convection Field in Bistable Media

The front dynamics driven by a convection field in a model of FitzHugh-Nagumo type is studied both analytieMly and numerically. Saddle-node bifurcation induced by the convection field is found by using a singular perturbation analysis of front solutions. Convection field accelerates the B1och front propagating opposite the direction of convection field, but inhibits the Bloch front propagating along the direction of convection field. In addition convection field drives Ising front to travel opposite the direction of convection field.     

Effect of ultrasound on sodium arsenate induction time and crystallization property during solution crystallization processes

The effect of ultrasound vibrations on the cooling crystallization of sodium arsenate in supersaturated solutions was investigated. In particular, the effects of ultrasound vibrations on induction time and crystal size distribution were studied using a laser-based apparatus with relative supersaturation ranging from 1.3 to 1.8. The results show that ultrasound vibrations have a significant effect on reducing induction time and crystal size distribution. The application of ultrasound vibrations to the system resulted in a small change in surface tension; however, the induction time and crystal size significantly decreased. The mean size of sodium arsenate crystals decreased from 398.87 ± 3.27 to 168.68 ± 2.07 μm, as the ultrasound power increases from 26 to 130 W. Ultrasound vibrations significantly reduced the induction time in a highly supersaturated solution compared to that in a low supersaturated solution.     

Free localized vibrations of a semi-infinite cylindrical shell

Free vibrations of a semi-infinite cylindrical shell, localized near the edge of the shell are investigated. The dynamic equations in the Kirchhoff-Love theory of shells are subjected to asymptotic analysis. Three types of localized vibrations, associated with bending, extensional, and super-low-frequency semi-membrane motions, are determined. A link between localized vibrations and Rayleigh-type bending and extensional waves, propagating along the edge, is established. Different boundary conditions on the edge are considered. It is shown that for bending and super-low-frequency vibrations the natural frequencies are real while for extensional vibrations they have asymptotically small imaginary parts. The latter corresponds to the radiation to infinity caused by coupling between extensional and bending modes.