Showing papers on "Longitudinal wave published in 2011"

Linear models of dissipation whose Q is almost frequency independent

Abstract: Laboratory experiments and field observations indicate that tlie Q of many non ferromagnetic inorganic solids is almost frequency independent in the range 10' to 10~2 cps; although no single substance has been investigated over the entire frequency spectrum. One of the purposes of this investigation is to find the analytic expression of a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges. This will be obtained by introducing fractional derivatives in the stress strain relation. Since the aim of this research is to also contribute to elucidating the dissipating mechanism in the earth free modes, we shall treat the cases of dissipation in the free purely torsional modes of a shell and the purely radial vibration of a solid sphere. The theory is checked with the new values determined for the Q of the spheroidal free modes of the earth in the range between 10 and 5 minutes integrated with the Q of the Railegh waves in the range between 5 and 0.6 minutes. Another check of the theory is made with the experimental values of the Q of the longitudinal waves in an alluminimi rod, in the range between 10-5 and 10-3 seconds. In both clicks the theory represents the observed phenomena very satisfactory.

Hybrid elastic solids

Abstract: The ability to withstand shear is one of the properties that distinguishes a solid from a liquid. The proposal of an elastic metamaterial that in one direction only supports compressional waves, and therefore is fluid-like, and in the other supports compressional as well as shear waves represents a hybrid between fluids and solids that may lead to new applications.

Elastic metamaterials with simultaneously negative effective shear modulus and mass density.

Abstract: We propose a type of elastic metamaterial comprising fluid-solid composite inclusions which can possess a negative shear modulus and negative mass density over a large frequency region. Such a material has the unique property that only transverse waves can propagate with a negative dispersion while longitudinal waves are forbidden. This leads to many interesting phenomena such as negative refraction, which is demonstrated by using a wedge sample and a significant amount of mode conversion from transverse waves to longitudinal waves that cannot occur on the interface of two natural solids.

Characterization of a surface dielectric barrier discharge plasma sustained by repetitive nanosecond pulses

Abstract: The paper discusses experimental characterization of a surface dielectric barrier discharge plasma sustained by repetitive, high-voltage, nanosecond duration pulses. The discharge pulse energy is controlled primarily by the pulse peak voltage and scales approximately linearly with the length of the electrodes. Images of the plasma generated during the discharge pulse, taken by a nanosecond gate ICCD camera, show that the plasma remains fairly uniform in the initial phase of the discharge and becomes filamentary at a later stage. The temperature rise in the discharge, operated in both continuous mode and in burst mode, is inferred from UV/visible emission spectra. Phase-locked schlieren images are used to measure the speed of the compression waves generated by the nanosecond pulse discharge and the density gradient in the wave. The density gradient is inferred from the schlieren images using absolute calibration by a pair of wedged windows. The results demonstrate that discharge filaments generate compression waves with higher amplitude and higher speed compared with waves produced in a diffuse discharge. The density gradient in the compression waves is compared with numerical modeling of propagating compression waves produced by short-pulse localized heating, and shows satisfactory agreement between the model and the experimental results.

Three-dimensional continuous particle focusing in a microfluidic channel via standing surface acoustic waves (SSAW).

Abstract: Three-dimensional (3D) continuous microparticle focusing has been achieved in a single-layer polydimethylsiloxane (PDMS) microfluidic channel using a standing surface acoustic wave (SSAW). The SSAW was generated by the interference of two identical surface acoustic waves (SAWs) created by two parallel interdigital transducers (IDTs) on a piezoelectric substrate with a microchannel precisely bonded between them. To understand the working principle of the SSAW-based 3D focusing and investigate the position of the focal point, we computed longitudinal waves, generated by the SAWs and radiated into the fluid media from opposite sides of the microchannel, and the resultant pressure and velocity fields due to the interference and reflection of the longitudinal waves. Simulation results predict the existence of a focusing point which is in good agreement with our experimental observations. Compared with other 3D focusing techniques, this method is non-invasive, robust, energy-efficient, easy to implement, and applicable to nearly all types of microparticles.

Information stored in Faraday waves: the origin of a path memory

Abstract: On a vertically vibrating fluid interface, a droplet can remain bouncing indefinitely. When approaching the Faraday instability onset, the droplet couples to the wave it generates and starts propagating horizontally. The resulting wave–particle association, called a walker, was shown previously to have remarkable dynamical properties, reminiscent of quantum behaviours. In the present article, the nature of a walker's wave field is investigated experimentally, numerically and theoretically. It is shown to result from the superposition of waves emitted by the droplet collisions with the interface. A single impact is studied experimentally and in a fluid mechanics theoretical approach. It is shown that each shock emits a radial travelling wave, leaving behind a localized mode of slowly decaying Faraday standing waves. As it moves, the walker keeps generating waves and the global structure of the wave field results from the linear superposition of the waves generated along the recent trajectory. For rectilinear trajectories, this results in a Fresnel interference pattern of the global wave field. Since the droplet moves due to its interaction with the distorted interface, this means that it is guided by a pilot wave that contains a path memory. Through this wave-mediated memory, the past as well as the environment determines the walker's present motion.

Three‐dimensional, nonhydrostatic numerical simulation of nonlinear internal wave generation and propagation in the South China Sea

Abstract: [1] We present the results of three-dimensional, nonhydrostatic simulations of internal tides and waves in the South China Sea (SCS) using the SUNTANS model. Model results accurately predict the observed wave arrival times at two mooring locations in the SCS. Internal wave amplitudes are underpredicted which causes underprediction of internal wave speeds due to a lack of amplitude dispersion. We show that the well-known A and B waves arise from the steepening of semidiurnal internal tides that are generated due to strong barotropic flow over ridges in the Luzon Strait. A wave generation is stronger in the southern portion of the Luzon Strait because diurnal internal tidal beams augment the amplitude of the semidiurnal A waves. B wave generation is stronger in the northern portion where the distance between the eastern and western ridges is approximately equal to one internal tidal wavelength and leads to semidiurnal internal tidal resonance. The orientation of the ridges produces large A waves that propagate into the northern portion of the western SCS basin and stronger B waves that propagate into the southern portion. When traced back in time along linear characteristics, A waves consistently line up close to peak ebb (eastward) barotropic currents, while B waves consistently line up with peak flood (westward) barotropic currents. This reinforces the notion that the lee wave mechanism and associated hydraulic or nonlinear effects are weak, as demonstrated by a simple linear model relating the amplitude of the simulated waves to the excursion parameter at the ridges.

Interaction of highly nonlinear solitary waves with linear elastic media.

Abstract: We study the interaction of highly nonlinear solitary waves propagating in granular crystals with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary and secondary reflected waves. Experimental tests are performed to correlate the linear medium geometry, materials, and mass with the formation and propagation of reflected waves. We compare the experimental results with theoretical analysis based on the long-wavelength approximation and with numerical predictions obtained from discrete particle models. Experimental results are found to be in agreement with theoretical analysis and numerical simulations. This preliminary study establishes the foundation for utilizing reflected solitary waves as novel information carriers in nondestructive evaluation of elastic material systems.

Steady Water Waves with Multiple Critical Layers

Abstract: We construct small-amplitude periodic water waves with multiple critical layers. In addition to waves with arbitrarily many critical layers and a single crest in each period, multimodal waves with several crests and troughs in each period are found. The setting is that of steady two-dimensional finite-depth gravity water waves with vorticity.

Phase and group velocity matching for cumulative harmonic generation in Lamb waves

Abstract: Owing to the enhanced sensitivity of nonlinear acoustic methods to material damage, the nonlinear Lamb wave propagation is pertinent to the nondestructive evaluation of platelike structures, and it is typically manifested as generation of higher harmonics. For dispersive waves such as Lamb waves, however, the cumulative growth of harmonics requires that the primary mode and the generated higher harmonic modes possess identical phase and group velocities. In this paper, this issue of the phase and group velocity matching in Lamb waves is explored based on a systematic analysis of the Rayleigh-Lamb frequency equations. The analysis shows that for certain values of the phase velocity, the Rayleigh-Lamb frequency equations are satisfied at equi-spaced frequencies which are multiples of the smallest. Such frequencies, together with the corresponding phase velocities and the Lamb modes, are determined analytically. Four such types of Lamb modes are identified: (i) Lame modes, (ii) symmetric modes with dominant longitudinal displacements, (iii) intersections of symmetric and antisymmetric modes and (iv) extra Rayleigh modes. For the first three types, it is also established that the primary and the harmonic modes have the same group velocity, and that the surface motion of the plate is featured with vanishing vertical or horizontal displacements. In contrast to these three types, the fourth type only exists for a special range of the transverse to longitudinal wave speeds of the solid. This type is not featured with a common group velocity, and neither of the vertical or horizontal displacement vanishes on the plate surfaces. The obtained results are summarized as tables, and demonstrated graphically on the dispersion curves for aluminum as well as iron plates.

Introduction to the Physics of Ultrasound

Abstract: From an acoustical point of view, bone is a complex medium as it is heterogeneous, anisotropic and viscoelastic. This chapter reviews the basic notions of physical acoustics which are necessary to tackle the problem of the ultrasonic propagation in bone, in the perspective of the application of quantitative ultrasound (QUS) techniques to bone characterization. The first section introduces the basic phenomena related to the field of medical ultrasound. Basic description of wave propagation is introduced. Mechanical bases are necessary to understand the elastodynamic nature of the interaction between bone and ultrasound. The physical determinants of the speed of sound of the different types of waves corresponding to the propagation in a liquid and in a solid are considered. The effects of boundary conditions (guided waves) are also detailed. The second section describes the physical interaction between an ultrasonic wave and bone tissue, by introducing reflection/refraction, attenuation and scattering phenomena.

Dirac cones at k⃗=0 in phononic crystals

Abstract: We show that two-dimensional phononic crystals exhibit Dirac cone dispersion at $\stackrel{P\vec}{k}=0$ by exploiting dipole and quadrupole accidental degeneracy. While the equifrequency surface of Dirac cone modes is almost isotropic, such systems exhibit super-anisotropy, meaning that only transverse waves are allowed along certain directions, while only longitudinal waves are allowed along some other directions. Only one mode, not two, is allowed near the Dirac point, and only two effective parameters, not four, are needed to describe the dispersion. Effective medium theory finds that the phononic crystals have effectively zero mass density and zero $1/{C}_{44}^{\mathrm{eff}}$ at the Dirac point. Numerical simulations are used to demonstrate the unusual elastic wave properties near the Dirac point frequency.

Numerical simulations of conversion to Alfven waves in sunspots

Abstract: We study the conversion of fast magneto-acoustic waves to Alfven waves by means of 2.5D numerical simulations in a sunspot-like magnetic configuration. A fast, essentially acoustic, wave of a given frequency and wave number is generated below the surface and propagates upward though the Alfven/acoustic equipartition layer where it splits into upgoing slow (acoustic) and fast (magnetic) waves. The fast wave quickly reflects off the steep Alfven speed gradient, but around and above this reflection height it partially converts to Alfven waves, depending on the local relative inclinations of the background magnetic field and the wavevector. To measure the efficiency of this conversion to Alfven waves we calculate acoustic and magnetic energy fluxes. The particular amplitude and phase relations between the magnetic field and velocity oscillations help us to demonstrate that the waves produced are indeed Alfven waves. We find that the conversion to Alfven waves is particularly important for strongly inclined fields like those existing in sunspot penumbrae. Equally important is the magnetic field orientation with respect to the vertical plane of wave propagation, which we refer to as "field azimuth". For field azimuth less than 90 degrees the generated Alfven waves continue upwards, but above 90 degrees downgoing Alfven waves are preferentially produced. This yields negative Alfven energy flux for azimuths between 90 and 180 degrees. Alfven energy fluxes may be comparable to or exceed acoustic fluxes, depending upon geometry, though computational exigencies limit their magnitude in our simulations.

Rogue waves in nonlinear hyperbolic systems (shallow-water framework)*

Abstract: The formation of rogue waves is studied in the framework of nonlinear hyperbolic systems with an application to nonlinear shallow-water waves. It is shown that the nonlinearity in the random Riemann (travelling) wave, which manifests in the steeping of the face-front of the wave, does not lead to extreme wave formation. At the same time, the strongly nonlinear Riemann wave cannot be described by the Gaussian statistics for all components of the wave field. It is shown that rogue waves can appear in nonlinear hyperbolic systems only in the result of nonlinear wave–wave or/and wave–bottom interaction. Two special cases of wave interaction with a vertical wall (interaction of two Riemann waves propagating in opposite directions) and wave transformation in the basin of variable depth are studied in detail. Open problems of the rogue wave occurrence in nonlinear hyperbolic systems are discussed.

The many faces of shear Alfvén wavesa)

Abstract: One of the fundamental waves in magnetized plasmas is the shear Alfven wave. This wave is responsible for rearranging current systems and, in fact all low frequency currents in magnetized plasmas are shear waves. It has become apparent that Alfven waves are important in a wide variety of physical environments. Shear waves of various forms have been a topic of experimental research for more than fifteen years in the large plasma device (LAPD) at UCLA. The waves were first studied in both the kinetic and inertial regimes when excited by fluctuating currents with transverse dimension on the order of the collisionless skin depth. Theory and experiment on wave propagation in these regimes is presented, and the morphology of the wave is illustrated to be dependent on the generation mechanism. Three-dimensional currents associated with the waves have been mapped. The ion motion, which closes the current across the magnetic field, has been studied using laser induced fluorescence. The wave propagation in inhomogeneous magnetic fields and density gradients is presented as well as effects of collisions and reflections from boundaries. Reflections may result in Alfvenic field line resonances and in the right conditions maser action. The waves occur spontaneously on temperature and density gradients as hybrids with drift waves. These have been seen to affect cross-field heat and plasma transport. Although the waves are easily launched with antennas, they may also be generated by secondary processes, such as Cherenkov radiation. This is the case when intense shear Alfven waves in a background magnetoplasma are produced by an exploding laser-produced plasma. Time varying magnetic flux ropes can be considered to be low frequency shear waves. Studies of the interaction of multiple ropes and the link between magnetic field line reconnection and rope dynamics are revealed. This manuscript gives us an overview of the major results from these experiments and provides a modern prospective for the earlier studies of shear Alfven waves.

The colours of cloaks

Abstract: We present a survey of results from various research groups under the unifying viewpoint of transformational physics, which has been recently introduced for the design of metamaterials in optics and acoustics. We illustrate the versatility of underlying geometric transforms in order to bridge wave phenomena (the different 'colours' of waves) ranging from transverse electric waves, to linear surface water waves at an air–fluid interface, to pressure waves in fluids and out-of-plane shear waves in elastic media: these waves are all governed by a second order scalar partial differential equation (PDE) invariant under geometric transform. Moreover, flexural waves propagating in thin plates represent a very peculiar situation whereby the displacement field satisfies a fourth order scalar PDE which also retains its form under geometric transform (unlike for the Navier equation in elastodynamics). Control of flexural wave trajectories is illustrated with a multilayered cloak and a carpet. Interestingly, the colours of waves can be revealed through an analysis of the band spectra of invisibility cloaks. In the context of acoustics, this suggests one can hear the shape of a drum. Alternative avenues towards cloaking based upon anomalous resonances of a negatively refracting coating (which can be seen as the result of folding the space back onto itself), and even plasmonic shells reducing the scattering cross-section of nano-objects are also addressed.

Hydroelastic solitary waves in deep water

Abstract: The problem of waves propagating on the surface of a two-dimensional ideal fluid of infinite depth bounded above by an elastic sheet is studied with asymptotic and numerical methods. We use a nonlinear elastic model that has been used to describe the dynamics of ice sheets. Particular attention is paid to forced and unforced dynamics of waves having near-minimum phase speed. For the unforced problem, we find that wavepacket solitary waves bifurcate from nonlinear periodic waves of minimum speed. When the problem is forced by a moving load, we find that, for small-amplitude forcing, steady responses are possible at all subcritical speeds, but for larger loads there is a transcritical range of forcing speeds for which there are no steady solutions. In unsteady computations, we find that if the problem is forced at a speed in this range, very large unsteady responses are obtained, and that when the forcing is released, a solitary wave is generated. These solitary waves appear stable, and can coexist within a sea of small-amplitude waves.

Tuned Passive Control of Acoustic Damping of Perforated Liners

Abstract: To suppress combustion instabilities, perforated liners can be fitted along the bounding walls of a combustor to provide acoustic damping. These liners are typically subjected to a low-Mach-number bias flow (a cooling flow through perforated holes), and they tend to be effective only over narrow frequency ranges. To investigate the damping effect of perforated liners on plane acoustic waves and to increase their effective frequency range, experiments and numerical simulations are carried out. An acoustically driven pipe system containing a lined section was designed and experimentally tested. The length of the pipe system, along with the bias flow rate, could be varied. The experimental results showed that the liner damping depended on both the pipe length and the bias flow rate, in agreement with predictions from the numerical model presented by (Eldredge, J. D., and Dowling, A. P., "The Absorption of Axial Acoustic Waves by a Perforated Liner with Bias Flow," Journal of Fluid Mechanics, Vol. 485, No. , 2003, pp. 307-335.). To maintain the acoustic damping of the liner in the presence of large frequency changes (corresponding to instability frequency changes in a combustor), real-time tuning of perforated liners was experimentally investigated. Both a pipe length parameter and the bias flow rate were sequentially tuned using a multiple-parameter tuning scheme. The scheme required two algorithms to be developed: one for characterizing the finer's acoustic damping in real time and another for sequentially determining the two optimum actuation signals for the damper tuning. The former involved developing a real-time version of the two-microphone technique for resolving the two plane acoustic wave strengths, which is widely applicable. On implementing these algorithms in the pipe system, optimal damping of the liner was achieved and maintained over a broad frequency range.

c-Axis Zig-Zag ZnO film ultrasonic transducers for designing longitudinal and shear wave resonant frequencies and modes

Abstract: A method for designing frequencies and modes in ultrasonic transducers above the very-high-frequency (VHF) range is required for ultrasonic non-destructive evaluation and acoustic mass sensors. To obtain the desired longitudinal and shear wave conversion loss characteristics in the transducer, we propose the use of a c-axis zig-zag structure consisting of multilayered c-axis 23° tilted ZnO piezoelectric films. In this structure, every layer has the same thickness, and the c-axis tilt directions in odd and even layers are symmetric with respect to the film surface normal. c-axis zig-zag crystal growth was achieved by using a SiO2 low-temperature buffer layer. The frequency characteristics of the multilayered transducer were predicted using a transmission line model based on Mason's equivalent circuit. We experimentally demonstrated two types of transducers: those exciting longitudinal and shear waves simultaneously at the same frequency, and those exciting shear waves with suppressed longitudinal waves.

Solitary waves in a magneto-electro-elastic circular rod

Abstract: A simple nonlinear model is proposed in this paper to study the solitary wave in a circular magneto-electro-elastic rod. Based on the constitutive relation for transversely isotropic piezoelectric and piezomagnetic materials, combined with the differential equations of motion, we derive the longitudinal wave motion equation in a long circular rod. The nonlinearity considered is geometrically associated with the nonlinear normal strain in the longitudinal rod direction and the transverse Poisson's effect is included by introducing the effective Poisson's ratio. The nonlinear solitary wave equation is solved by the Jacobi elliptic function expansion method and numerical examples demonstrate not only the existence of such a wave but also some interesting characteristics of the solitary wave in the rod made of different multiphase coupled materials.

Spatial damping of propagating kink waves due to resonant absorption: effect of background flow

Abstract: Observations show the ubiquitous presence of propagating magnetohydrodynamic (MHD) kink waves inthe solar atmosphere. Waves and flows are often observed simu ltaneously. Due to plasma inhomogeneity inthe perpendicular direction to the magnetic field, kink wave s are spatially damped by resonant absorption.The presence of flow may a ffect the wave spatial damping. Here, we investigate the effect of longitudinalbackground flow on the propagation and spatial damping of res onant kink waves in transversely nonuniformmagnetic flux tubes. We combine approximate analytical theo ry with numerical investigation. The analyticaltheory uses the thin tube (TT) and thin boundary(TB) approximationsto obtain expressions for the wavelengthand the damping length. Numerically, we verify the previously obtained analytical expressions by means ofthe full solution of the resistive MHD eigenvalue problem beyond the TT and TB approximations. We findthat the backward and forward propagating waves have different wavelengths and are damped on length scalesthat are inversely proportional to the frequency as in the static case. However, the factor of proportionalitydepends on the characteristics of the flow, so that the dampin g length differs from its static analogue. For slow,sub-Alfve´nic flows the backward propagating wave gets damped on a shorter length scale than in the absenceof flow, while for the forward propagating wave the damping le ngth is longer. The different properties of thewaves depending on their direction of propagation with respect to the background flow may be detected by theobservations and may be relevant for seismological applications.Subject headings: Sun: oscillations — Sun: corona — Sun: atmosphere — Magnetoh ydrodynamics (MHD)— Waves