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.     

Resonant interaction of elastic oscillations of a thin plate with a hydrodynamic flow

It is demonstrated that the wind instability in a nonuniform flow with a velocity profile can give rise to elastic oscillations of a thin plate with a characteristic wavelength. The dispersion relations and the instability increment with a maximum in the long-wavelength range are obtained. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 77–80, July, 2007.     

Prolonged acousto-optic interaction with Lamb waves in crystalline plates

The propagation and acousto-optic interaction of Lamb modes in an anisotropic plate of tellurium dioxide (TeO2) are studied numerically and analytically. In the case of a Y-cut X-propagating TeO2 plate, the very high elastic anisotropy of the crystal greatly modifies the dispersion curves, giving rise to their multiple oscillations. The existence ranges of backward Lamb modes increase with the mode order contrary to the case of isotropic plates. The quasi-collinear light scattering by Lamb waves is considered. Owing to the structure of Lamb wave field, a simultaneous light diffraction at two different optical frequencies can take place while Lamb waves are excited only at the single frequency. It is demonstrated with the Z-cut (110)-propagating plate that a small change in the acoustic frequency can result in a significant shift in the frequency of the scattered light.     

Stochastic nonlinear aeroelastic analysis of a supersonic lifting surface using an adaptive spectral method

An adaptive stochastic spectral projection method is deployed for the uncertainty quantification in limit-cycle oscillations of an elastically mounted two-dimensional lifting surface in a supersonic flow field. Variabilities in the structural parameters are propagated in the aeroelastic system which accounts for nonlinear restoring force and moment by means of hardening cubic springs. The physical nonlinearities promote sharp and sudden flutter onset for small change of the reduced velocity. In a stochastic context, this behavior translates to steep solution gradients developing in the parametric space. A remedy is to expand the stochastic response of the airfoil on a piecewise generalized polynomial chaos basis. Accurate approximation andaffordable computational costs are obtained using sensitivity-based adaptivity for various types of supersonic stochastic responses depending on the selected values of the Mach number on the bifurcation map. Sensitivity analysis via Sobol' indices shows how the probability density function of the peak pitch amplitude responds to combined uncertainties: e.g. the elastic axis location, torsional stiffness and flap angle. We believe that this work demonstrates the capability and flexibility of the approach for more reliable predictions of realistic aeroelastic systems subject to a moderate number of uncertainties.     

Transient Dynamics of Super Bloch Oscillations of a 1D Holstein Polaron under the Influence of an External AC Electric Field

Theoretical formalism for DC‐field polaron dynamics is extended to the dynamics of a 1D Holstein polaron in an external AC electric field using multiple Davydov trial states. Effects of carrier–phonon coupling on detuned and resonant scenarios are investigated for both phase and nonzero phase. For slightly off‐resonant or detuned cases, a beat between the usual Bloch oscillations and an AC driving force results in super Bloch oscillations, that is, rescaled Bloch oscillations in both the spatial and the temporal dimension. Super Bloch oscillations are damped by carrier–phonon coupling. For resonant cases, if the carrier is created on two nearest‐neighboring sites, the carrier wave packet spreads with small‐amplitude oscillations. Adding carrier–phonon coupling localizes the carrier wave packet. If an initial broad Gaussian wave packet is adopted, the centroid of the carrier wave packet moves with a certain velocity and with its shape unchanged. Adding carrier–phonon coupling broadens the carrier wave packet and slows down the carrier movement. Our findings may help provide guiding principles on how to manipulate the dynamics of the super Bloch oscillations of carriers in semiconductor superlattice and optical lattices by modifying DC and AC field strengths, AC phases, and detuning parameters.     

The two-mode waveguide formed by a rigid plane and an elastic plate

The structure of the acoustic field formed in the gap between a rigid plane and an elastic plate excited by a point force is considered. Special attention is given to the frequency range near the coincidence frequency in the case of the small values of the load parameter characterizing the plate loading with the medium. Expressions for the energy fluxes in the plate and in the gap are obtained, and the characteristic length of the energy transfer into the gap, as well as the degree of completeness of such a transfer, is determined.     

A simple nonlinear element model

We study experimentally the behavior of a nonlinear element, a light plate pressed to the opening in the cavity of an acoustic resonator. Measurements of field oscillations inside and outside the cavity have shown that for large amplitudes, they become essentially anharmonic. The time dependences of displacement of the plate with increasing amplitude of the exciting voltage demonstrates a gradual change in the shape of vibrations from harmonic to half-period oscillation. A constant component appears in the cavity: rarefaction or outflow of the medium through the orifice. We construct a theory for nonlinear oscillations of a plate taking into account its different elastic reactions to compression and rarefaction with allowance for monopole radiation by the small-wave-size plate or radiation of a plane wave by the plate. We calculate the amplitudes of the harmonics and solve the problem of low-frequency stationary noise acting on the plate. We obtain expressions for the correlation function and mean power at the output given a normal random process at the input.     

Regimes of bubble volume oscillations in a pipe

The effect of an acoustically driven bubble on the acoustics of a liquid-filled pipe is theoretically analyzed and the dimensionless groups of the problem are identified. The different regimes of bubble volume oscillations are predicted theoretically with these dimensionless groups. Three main regimes can be identified: (1) For small bubbles and weak driving, the effect of the bubble oscillations on the acoustic field can be neglected. (2) For larger bubbles and still small driving, the bubble affects the acoustic field, but due to the small driving, a linear theory is sufficient. (3) For large bubbles and large driving, the two-way coupling between the bubble and the flow dynamics requires the solution of the full nonlinear problem. The developed theory is then applied to an air bubble in a channel of an inkjet printhead. A numerical model is developed to test the predictions of the theoretical analysis. The Rayleigh-Plesset equation is extended to include the influence of the bubble volume oscillations on the acoustic field and vice versa. This modified Rayleigh-Plesset equation is coupled to a channel acoustics calculation and a Navier-Stokes solver for the flow in the nozzle. The numerical simulations indeed confirm the predictions of the theoretical analysis.     

A PIV study of a supersonic impinging jet

The characteristics of supersonic impinging jets are investigated using Particle Image Velocimetry (PIV). The purpose of the experiments is to understand the jet induced forces on STOVL aircraft while hovering close to the ground. For this purpose, a large diameter circular plate was attached at the nozzle exit. The oscillations of the impinging jet generated due to a feedback loop are captured in the PIV images. The instantaneous velocity field measurements are used to describe flow characteristics of the impinging jet. The important flow features such as oscillating shock waves, slipstream shear layers and large scale structures are captured clearly by the PIV. The presence of large scale structures in the impinging jet induced high entrainment velocity in the near hydrodynamic field, which resulted in lift plate suction pressures. A passive control device is used to interfere with the acoustic waves travelling in the ambient medium to suppress the feedback loop. As a consequence, the large scale vortical structures disappeared completely leading to a corresponding reduction in the entrainment.     

Generation of Extremely Short Pulses upon Excitation of a Resonant Medium by a Superluminal Light Spot

The possibility of generation of quasi-unipolar extremely short pulses (with a duration of several periods of field oscillations) is theoretically analyzed for the excitation of a circular, nonlinear, and resonant medium with a light spot. The light spot rotates along a circle with a velocity that exceeds the speed of light in vacuum, while particles of the medium are distributed uniformly along the circle. It is shown that, by introducing a delay in the form of a phase plate into the system, one can control the shape, the duration, and the amplitude of generated pulses.     

Numerical study of plasma-wall transition using an Eulerian Vlasov code

A one-dimensional Eulerian Vlasov code is used to study the self-consistent solution of a plasma facing a floating collector, in the absence of an external magnetic field. Both electrons and ions are treated with a kinetic equation. A Bhatnagar-Gross-Krook (BGK) collision term is used to describe the collisions. Acceleration of the ion flow at the Debye sheath entrance is observed together with the formation of a stable steep negative electric field in front of the floating collector. This negative electric field acts to accelerate the positive ions towards the plate, pushing back the negative electrons, such that at steady state the total current collected at the plate is zero. The codes are run for a sufficiently long time on the ions time scale to ensure the ions (argon) distribution function is reaching a steady state. For the different parameters used, the solution shows the existence of persistent regular oscillations of constant amplitude when the electron collisions are very small or negligible. These oscillations will be studied. The increase in the electron collisions damps these oscillations and helps the system reach an equilibrium.Received: 16 October 2003, Published online: 26 May 2004PACS: 52.65.Ff Fokker-Planck and Vlasov equation     

Scattering of spatially inhomogeneous sound waves by a spherical particle

The problem of monopole, dipole, and rotational scattering of a spatially inhomogeneous time-harmonic sound field by an arbitrary spherical particle is solved for the cases of the medium being a viscous compressible liquid or an isotropic elastic medium. Equations for the spherical mean fields at the particle are obtained. These equations are used to derive the formulas for the scattered fields. Different limiting cases of particle behavior are considered. In particular, it is shown that the dipole scattering is determined by two components of particle oscillations, one of which corresponds to translational oscillatory motion and the other to oscillations of two antiphase monopoles. For these types of particle oscillations, a scattering matrix, which determines the scattering of an arbitrary field by a particle, is constructed. The matrix allows the formalization of the processes of multiple sound scattering by particles and is valid for any distances between the particles down to their contact.     

Study of second-harmonic generation of shear horizontal modes using modal analysis

In this work a modal analysis was employed to study generation of the second harmonics of shear horizontal (SH) modes in a solid plate. Under second order perturbation, second-harmonic generation will occur accompanying SH mode propagation due to the bulk elastic non-linearity of plate material. In solid plate the total second-harmonic fields of a SH mode propagation are regarded as sum of the fields of a series of double frequency Lamb modes (DFLMs). The contribution of each DFLM component to the total second-harmonic fields is dependent of the difference of phase velocities of the corresponding DFLM and SH mode. The analysis results show that the DFLM field component may have cumulative growth effect once its phase velocity exactly or approximately equals that of a SH mode. It is also found that the fields of the total second harmonics of a SH mode are only symmetrical. The examples of field distributions of several DFLMs on the plate surface are considered.     

Capillary oscillations of a drop in an electric field

The capillary oscillations of a conducting spheroidal drop with small eccentricity in an electric field are studied. The effect of the electric field is to lower the natural frequencies of oscillations and the damping coefficient.     

Investigating RF and microwave nonlinear magnetoelastic interactions in a three-layer structure

The problem of hypersound excitation in a structure consisting of three magnetic layers is considered. Motion equations and boundary conditions for the components of magnetization and elastic displacement when there is an arbitrary angle of magnetization vector precession are obtained. The development of oscillations over time in an alternating field is considered.     

Flexural edge waves in semi-infinite elastic plates

This paper presents a detailed analysis of the dispersion for flexural edge waves in semi-infinite isotropic elastic plates. A solution to the dynamic equations of motion is constructed by the superposition of two partial solutions, each providing zero shear stresses at the plate faces. A dispersion equation is expressed via the determinant of an infinite system of linear algebraic equations. The system is reduced to a finite one by taking into account the asymptotic behaviour of unknown coefficients. The accuracy of the solution is confirmed by a good agreement with the available experimental data and by a proper satisfaction of the prescribed boundary conditions.A detailed analysis of dispersion properties for the edge wave and corresponding displacements at various frequencies is carried out. In addition to the well-known results it is shown that the plate height does not influence the existence of the edge wave at high frequencies and, as the frequency increases, the phase velocity of the edge wave in a semi-infinite plate asymptotically approaches the velocity of an edge wave in a right-angled wedge. The performed analysis allows evaluating the plate theories such as the Kirchhoff theory or other refined plate theories developed for modeling edge waves in semi-infinite elastic plates at low frequencies.     

Laser-fluctuation measurements in a bath of strong Gaussian noise

Remarkable intensity fluctuations were observed in the LiNdP₄O₁₂ (LNP) laser by placing a moving ground-glass plate across the ouput beam. Resonance-like behaviors were also observed by tuning the moving velocity of the ground-glass plate, with respect to relaxation oscillations. Classical rate equations including the modulation term were given to explain the observed phenomena. Similar intensity fluctuations corresponding to relaxation oscillations were observed when the LNP laser light beam was coupled to an optical fiber.     

Effect of a liquid on the characteristics of antisymmetric lamb waves in thin piezoelectric plates

The effect of a perfectly elastic nonviscous nonconducting liquid on the characteristics of a zero-order antisymmetric Lamb wave (the A ₀ wave) in a 128YX LiNbO₃ plate, whose thickness is small compared to the wavelength, is studied both theoretically and experimentally. A method for calculating the velocity and attenuation of this wave depending on the value of the parameter hf (h is the plate thickness and f is the wave frequency) is proposed. In addition, the characteristics of an A ₀ wave in a piezoelectric plate that is in contact with two different perfectly elastic nonviscous nonconducting liquids on its two sides are investigated. A possibility for the development of a proximate analyzer of liquids on the basis of such a structure is indicated.     

Anomalous compressibility and magnetostriction of beryllium under the conditions of diamagnetic domain formation

Magnetostriction oscillations are measured for a single-crystal beryllium sample shaped like a plate perpendicular to the direction of the magnetic field. In the range of 2–5 T at a temperature of 1.5 K, i.e., in the region of diamagnetic domain formation (Condon domains), the striction signal has the saw-tooth shape corresponding to the alternation of homogeneous and nonhomogeneous (domain) states. The formation of the domain structure is accompanied by an anomalous increase in compressibility; the oscillations in this coefficient are more than one hundred times greater than the value given by the standard theory. An analysis of the results indicates that the domain wall width should increase with increasing plate thickness.     

Edge flames stabilized in a non-premixed microcombustor

The dynamics of an edge flame confined in a non-premixed microcombustor model is studied numerically within the context of a diffusive-thermal model. Fuel and oxidizer, separated upstream by a thin plate, flow through a channel with a prescribed velocity. At the tip of the plate, the fuel and oxidizer mix and, when ignited, an edge flame is sustained at some distance from the plate. The objective in this work is to consider the effects of confinement, differential diffusion, and heat loss on the dynamics of an edge flame in a narrow channel. We consider a wide range of channel widths and allow for changing Lewis numbers, and both adiabatic conditions and heat losses along the channel walls. The results illustrate how the flame shape and standoff distance are affected by the channel width, by mixture composition through variations in Lewis numbers and by heat losses. Conditions for flame stabilization, flame oscillations and flame extinction or blowoff are predicted.