Behavior of a Light Solid in a Rotating Horizontal Cylinder with Liquid Under Vibration

Dynamics of a cylindrical body in a rotating cavity is experimentally studied under transversal translational vibrations of the cavity rotation axis. Experiments are run at high rotation rate, when under the action of centrifugal force the body shifts to the rotation axis (the centrifuged state). In the absence of vibrations, the lagging rotation of the body is observed, due to the body radial shift from the axis of rotation caused by gravity. The body average rotation regime depends on the cavity rotation rate. The vibrations lead to the excitation of different regimes of body differential rotation (leading or lagging) associated with the excitation of its inertial oscillations. The dependence of the differential speed of the body rotation on the vibration frequency is investigated. The body dynamics has a complex character depending on the dimensionless vibration frequency. The analysis of body oscillation trajectory revealed that the body oscillatory motion consists of several modes, which contribute to the averaged dynamics of the body and the flows in the cavity.     

Vortex Flows in the Liquid Layer and Droplets on a Vibrating Flexible Plate

In certain conditions, in the layers and droplets of a liquid on a vibrating rectangular flexible plate, vortex flows are formed simultaneously with the excitation of capillary oscillations on the free surface of the liquid layers and droplets. Capillary oscillations in the form of two-dimensional standing waves form Faraday ripples on the free surface of the liquid layer. On the surface of the vibrating droplets, at the excitation of capillary oscillations a light spot reflected from a spotlight source moves along a trajectory in the form of a Lissajous figure observed with a microscope. When vortex flows visualized with graphite microparticles appear in the layer and droplets of a transparent liquid, the trajectory of the light spot on the layer and droplet surface is a two-dimensional trajectory in the form of an ellipse or a saddle. This indicates that the generation of the vortex flows in a liquid at vibrations is due to capillary oscillations in the orthogonally related directions. In the liquid layer and droplets on the surface of the flexible plate, the vibrations of which are generated by bending vibrations, the vortex flows appear due to the plate vibrations and the capillary oscillations of the surface of a layer or a droplet of the liquid. On the free surface of the liquid, the capillary waves, which are parametrically excited by the plate bending vibrations, are additionally modulated by the same bending vibrations in the transverse direction.     

Dynamics of Rotating Two-phase System Under Transversal Vibration

Mean dynamics of light granular matter in liquid in the rotating horizontal cylinder subjected to transversal vibrations is experimentally investigated. The excitation of outstripping and lagging azimuth motion of the interface with respect to the cavity is revealed at definite ratios of rotation and vibration frequencies ${\Omega _\upsilon } \mathord{\left/ {\vphantom {{\Omega _\upsilon } {\Omega_r }}} \right. \kern-0em} {\Omega _r }$ . The motion is generated by the inertial oscillations arising in the system in a resonant way. The formation of regular spatial structures on the interface is revealed at intensive outstripping motion. These structures have azimuth and axial periodicity and their shape depends on the type of inertial waves arising in the cavity. Intensity and direction of azimuth flows as well as shape of patterns on the granular matter–liquid interface are determined by the ratio $ {\Omega _\upsilon } \mathord{\left/ {\vphantom {{\Omega _\upsilon } {\Omega _r}}} \right. \kern-0em} {\Omega _r }$ . It is shown, that the lagging motion exists at $ {\Omega _\upsilon } \mathord{\left/ {\vphantom {{\Omega _\upsilon } {\Omega _r }}} \right. \kern-0em} {\Omega _r }<1$ , and the outstripping one exists at $ {\Omega _\upsilon } \mathord{\left/ {\vphantom {{\Omega _\upsilon } {\Omega _r }}} \right. \kern-0em} {\Omega _r }>1 $ . Combined action of vibrations and rotation provides an efficient mechanism of mass transfer control, the intensity of mean flows in the cavity frame can be of the same order of magnitude as the rotation velocity.     

Stability of Rimming Flow under Vibration

The structure of rimming flow in a horizontal rotating cylinder subjected to vibration is experimentally investigated. Under vibration liquid performs oscillations. In the resonant domain oscillations have a form of progressive two-dimensional azimuth wave which generates averaged flow in the direction of its propagation. It is found that the plane motion is unstable to the spatially periodic vortical flow appearance. The transition to the vortical flow is determined by the oscillatory liquid flow instability in viscous Stokes layer near cylindrical wall. The threshold of 2D flow instability and the structure of overcritical flows in a wide range of dimensionless parameters are investigated.     

Inertial Waves and Steady Flows in a Liquid Filled Librating Cylinder

The fluid flow in a non-uniformly rotating (librating) cylinder about a horizontal axis is experimentally studied. In the absence of librations the fluid performs a solid-body rotation together with the cavity. Librations lead to the appearance of steady zonal flow in the whole cylinder and the intensive steady toroidal flows near the cavity corners. If the frequency of librations is twice lower than the mean rotation rate the inertial waves are excited. The oscillating motion associated with the propagation of inertial wave in the fluid bulk leads to the appearance of an additional steady flow in the Stokes boundary layers on the cavity side wall. In this case the heavy particles of the visualizer are assembled on the side wall into ring structures. The patterns are determined by the structure of steady flow, which in turn depends on the number of reflections of inertial wave beams from the cavity side wall. For some frequencies, inertial waves experience spatial resonance, resulting in inertial modes, which are eigenmodes of the cavity geometry. The resonance of the inertial modes modifies the steady flow structure close to the boundary layer that is manifested in the direct rebuilding of patterns. It is shown that the intensity of zonal flow, as well as the intensity of steady flows excited by inertial waves, is proportional to the square of the amplitude of librations.     

Possibility of excitation of azimuthal surface waves in a magnetized plasma by annular ion beams

Excitation of the azimuthal surface eigenmodes with the extraordinary polarization for the ion plasma component is shown to be possible in cylindrical waveguides with metal walls, filled partially by a cold magnetoactive neon plasma. The interaction of the oscillations with the flows of alpha particles rotating around the plasma column in a narrow layer that separates the plasma from the waveguide walls is studied. If the external magnetic field is strong enough, the resonance interaction of the beam with the waves can be realized for three minimum values of the azimuthal mode number when the wave frequency normalized by neon ion cyclotron frequency is close to the factor of five (m _Ne/m _He ≈ 5).     

Effect of heating on parametric excitation of waves on the surface of a liquid

The threshold of excitation and the wave numbers of parametric waves on the surface of a layer of viscous incompressible liquid undergoing harmonic vibrations along a vertical axis are determined for an equilibrium temperature gradient.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 4, pp. 708–711, April, 1977.     

Digital simulation of road-vehicle systems

This paper investigates dynamics of road-vehicle systems via stochastic numerics, applying discrete integration schemes of first and second order. The ride on rough roads generates vertical car vibrations whose root mean squares become resonant for critical speeds. The investigations are extended to nonlinear wheel suspensions with cubic-progressive springs. For weak but still positive damping, the car vibrations become unstable in overcritical speed ranges detected by means of perturbation equations whose top Lyapunov exponent can become positive in the case of parameter resonances. This indicates that the stationary car vibrations bifurcate into stochastic chaos.     

Nonlinear oscillations in a thin ring — I. Three-wave resonant interactions

Summary Nonlinear resonant interactions between planar waves in a thin circular ring are investigated. It is found that a high-frequency azimuthal wave is unstable against a pair of secondary low-frequency waves. The secondary waves are of two types; either two bending or azimuthal and bending. These are in phase with the primary wave. All three together compose a resonant triad. Such kind of instability causes the stress amplification in the ring. The stress growth constant and the period of energy exchange between the waves are estimated based on analytical solutions to the evolution equations driving the triad. The lowest-order nonlinear approximation analysis predicts stability for bending waves. A good qualitative agreement of the obtained results with some known experimental data is observed.     

The wave characteristics of a nonisothermal film of liquid under conditions of jets forming on its surface

An eight-channel capacitive sensor is used for the first time, which enables one to investigate the dynamics of three-dimensional wave flows and the variation of the transverse profile of a nonisothermal film of liquid during formation of jets. Measurements are performed of the wave characteristics of the flow of a film of water on a vertical plate with a heater 150 × 150 mm in size. During the heating of falling liquid, the thermocapillary forces cause the formation of jets and of a thin film between them. The film thickness and wave amplitude in the interjet region decrease with increasing heat flux. Two ranges of the effect of the heat flux on the characteristics of wave flow are identified. Under conditions of low heat fluxes, the film flow hardly differs from isothermal. Under significant heat loads, an intensive formation of jets occurs. Three-dimensional waves propagate over the jet crests, where the film thickness and wave amplitude increase with increasing heat flux. In the interjet region of the film being heated, the average relative amplitude of waves increases with decreasing average thickness, and in the isothermal region this amplitude decreases. Comparison of the obtained results with experimental data for isothermal film reveals that the values of relative amplitude differ significantly in the interjet region at high densities of heat fluxes. Transverse temperature gradients cause a decrease in the liquid film thickness, and longitudinal gradients cause an increase in the relative amplitude of waves compared to isothermal flows. In the end, this leads to the emergence of dry spots and breakdown of film. The relative amplitude of waves on the jet surface decreases with increasing heat flux; this is true of isothermal film flows.     

Tkachenko waves

The existence of Tkachenko waves in rotating superfluid⁴He has been confirmed experimentally. Tkachenko waves are displacement waves in the vortex line array that exists in a rotating superfluid. The waves were excited and detected in resonant cavities formed by a stack of closely spaced parallel plates. The dispersion relation, studied as a function of rotation speed, disk spacing (which fixed one component of the wave vector), and temperature, is compared with existing theories and found to be in good agreement at low temperatures. The theories predict peaks in the density of states associated with a lattice of vortices; the resonant responses observed are found to correspond to these peaks. The need for a more complete theory is presented in the light of the behavior of the vortex resonances at elevated temperatures.This work was supported by NSF grant DMR-78-25409.     

Dynamic mechanical response of elastic spherical inclusions to impulsive acoustic radiation force excitation

Acoustic radiation force impulse imaging has been used clinically to study the dynamic response of lesions relative to their background material to focused, impulsive acoustic radiation force excitations through the generation of dynamic displacement field images. Dynamic displacement data are typically displayed as a set of parametric images, including displacement immediately after excitation, maximum displacement, time to peak displacement, and recovery time from peak displacement. To date, however, no definitive trends have been established between these parametric images and the tissues' mechanical properties. This work demonstrates that displacement magnitude, time to peak displacement, and recovery time are all inversely related to the Young's modulus in homogeneous elastic media. Experimentally, pulse repetition frequency during displacement tracking limits stiffness resolution using the time to peak displacement parameter. The excitation pulse duration also impacts the time to peak parameter, with longer pulses reducing the inertial effects present during impulsive excitations. Material density affects tissue dynamics, but is not expected to play a significant role in biological tissues. The presence of an elastic spherical inclusion in the imaged medium significantly alters the tissue dynamics in response to impulsive, focused acoustic radiation force excitations. Times to peak displacement for excitations within and outside an elastic inclusion are still indicative of local material stiffness; however, recovery times are altered due to the reflection and transmission of shear waves at the inclusion boundaries. These shear wave interactions cause stiffer inclusions to appear to be displaced longer than the more compliant background material. The magnitude of shear waves reflected at elastic lesion boundaries is dependent on the stiffness contrast between the inclusion and the background material, and the stiffness and size of the inclusion dictate when shear wave reflections within the lesion will interfere with one another. Jitter and bias associated with the ultrasonic displacement tracking also impact the estimation of a tissue's dynamic response to acoustic radiation force excitation.     

Nonstationary Nonlinear Phenomena on the Charged Surface of Liquid Hydrogen

Investigations of nonlinear phenomena on the charged surface of liquid hydrogen are reviewed. It is demonstrated that excitation of the surface by a low frequency AC electric field results in the formation of capillary waves in the high-frequency domain, and that the latter exhibit turbulence. The quasi-adiabatic decay of this capillary turbulence has been studied both experimentally and theoretically. It is shown that the processes of formation and decay of the turbulence are both controlled by the same relaxation mechanisms. For spectrally narrow pumping, the application of an additional low-frequency driving force causes a decrease of wave amplitude in the high-frequency domain of the turbulent spectrum and correspondingly decreases the width of the inertial range of energy transfer.      

Wave radiation and diffraction by a two-dimensional floating rectangular body with an opening in its bottom

The radiation and diffraction problem of a two-dimensional rectangular body with an opening in its bottom floating on a layer of water of finite depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for the potentials are obtained by the method of separation of variables, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The hydrodynamic coefficients and wave excitation forces are obtained and verified using the near-field and far-field methods and the symmetry properties of coupled hydrodynamic coefficients. The effect of the opening on the wave excitation force and hydrodynamic coefficients is investigated. Piston resonant behaviour and sloshing resonant behaviour are also investigated and their effect on the wave excitation force and hydrodynamic coefficients is discussed.     

High-frequency vibrations of piezoelectric plates driven by lateral electric fields

We study coupled face-shear and thickness-twist motions of piezoelectric plates of monoclinic crystals driven by lateral electric fields. The first-order theory of piezoelectric plates is used. Pure thickness modes and propagating waves in unbounded plates as well as vibrations of finite plates are studied. Both free vibrations and electrically forced vibrations are considered. Basic vibration characteristics including resonant frequencies, dispersion relations, frequency spectra and motional capacitance are obtained. Numerical results are presented for AT-cut quartz plates. The results are expected to be useful for the understanding and design of resonant piezoelectric devices using lateral field excitation.     

Noncontact Damage Detection of a Rotating Shaft Using the Magnetostrictive Effect

The objective of this investigation is to develop a cost-effective noncontact diagnostic method for rotating shafts in operation. Unlike most existing diagnostic methods developed for rotating shafts, longitudinal stress waves are used and processed for damage assessment. For the non-contact measurement of stress waves in rotating shafts, we propose to use magnetostrictive effect. Shaft rotations inevitably accompany lateral vibrations; thus the effects of the vibrations on the measurement accuracy of the sensor are studied to verify the validity of the magnetostrictive effect application to rotating shafts. For damage location estimation, we use the continuous wavelet transform of the measured wave signals. In particular, we propose to adopt the real-valued Gaussian wavelets as the mother wavelet in order to pinpoint accurately the arrival time of the reflected wave from a crack. Several case studies are considered to show the effectiveness of the present diagnostic method.     

Incremental harmonic balance method with multiple time variables for dynamical systems with cubic non‐linearities

The incremental harmonic balance method with multiple time variables is developed for analysis of almost periodic oscillations in multi‐degree‐of‐freedom dynamical systems with cubic non‐linearities, subjected to the external multi‐tone excitation. The method is formulated to treat non‐autonomous as well as autonomous dynamical systems. The almost periodic oscillations, which coexist with periodic oscillations in a rotating system model with cubic restoring force and an electromagnetic eddy‐current damper are analysed. The closed form solutions based on generalized Fourier series containing two incommensurate frequencies are obtained in the case of small non‐dimensional stiffness ratio. Almost periodic oscillations of a rotating system model in dependence on variable parameters are also analysed, where solutions are computed through an augmentation process including a greater number of harmonics and combination frequencies involved. Copyright © 2003 John Wiley & Sons, Ltd.     

Parametric array technique for microbubble excitation

This study investigates the use of an acoustic parametric array as a means for microbubble excitation. The excitation wave is generated during propagation in a nonlinear medium of two high-frequency carrier waves, whereby the frequency of the excitation wave is the difference frequency of the carrier waves. Carrier waves of around 10 and 25 MHz are used to generate low-frequency waves between 0.5 and 3.5 MHz at amplitudes in the range of 25 to 80 kPa in water. We demonstrate with high-speed camera observations that it is possible to induce microbubble oscillations with the low frequency signal arising from the nonlinear propagation process. As an application, we determined the resonance frequency of Definity contrast agent microbubbles with radius ranging from 1.5 to 5 μm by sweeping the difference frequency in the range from 0.5 to 3.5 MHz.     

Investigation of crossed SAW fields by scanning acoustic force microscopy

We used multimode scanning acoustic force microscopy (SAFM) for studying noncollinearly propagating Rayleigh and Love wave fields. By analyzing torsion and bending movement of SAFM cantilever, normal and in-plane wave oscillation components are accessible. The SAFM principle is the down-conversion of surface oscillations into cantilever vibrations caused by the nonlinearity of the tip-sample interaction. Through mixing of complementary oscillation components, phase velocities of crossed Rayleigh waves on GaAs and crossed Rayleigh and Love waves on the layered system SiO2/ST-cut quartz were obtained simultaneously. Now, it is possible to investigate elastic properties of submicron areas through multimode SAFM measurements. Finally, we present mixing experiments of four SAWs on GaAs and discuss the various influences on the measured SAFM amplitude and phase contrast.     

Resonant Acoustic Nonlinearity of Defects for Highly-Efficient Nonlinear NDE

In this paper, the effect of local defect resonance (LDR) on the nonlinear ultrasonic responses of defects is studied and applied for enhancement of sensitivity of nonlinear NDE. Unlike the resonance of the whole specimen, the LDR provides an efficient energy pumping from the wave directly to the defect and causes an efficient generation of the higher harmonics and wave mixing even at moderate input signals. At higher levels of excitation, a combined effect of LDR and nonlinearity results in qualitatively new “nonclassical” features characteristic of the nonlinear and parametric resonances. The resonant nonlinear defects demonstrate threshold dynamics of instable vibrations, hysteresis, super- and subharmonic resonances. Under nonlinear LDR conditions nearly total input energy can be converted into higher harmonic or subharmonic vibrations of the defect. This proposes nonlinear LDR application as an extremely efficient and sensitive mode for nonlinear imaging and NDE.