Showing papers on "Longitudinal wave published in 2016"

On the complex and hyperbolic structures of the longitudinal wave equation in a magneto-electro-elastic circular rod

Abstract: In this study, we improve a new analytical method called the 'Modified exp expansion function method'. This method is based on the exp expansion function method. We obtain new analytical solutions expressed by hyperbolic, complex and complex hyperbolic function solutions to the nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod. We plot two- and three-dimensional surfaces of analytical solutions by using Wolfram Mathematica 9.

Polarization bandgaps and fluid-like elasticity in fully solid elastic metamaterials.

Abstract: Elastic waves exhibit rich polarization characteristics absent in acoustic and electromagnetic waves. By designing a solid elastic metamaterial based on three-dimensional anisotropic locally resonant units, here we experimentally demonstrate polarization bandgaps together with exotic properties such as ‘fluid-like’ elasticity. We construct elastic rods with unusual vibrational properties, which we denote as ‘meta-rods’. By measuring the vibrational responses under flexural, longitudinal and torsional excitations, we find that each vibration mode can be selectively suppressed. In particular, we observe in a finite frequency regime that all flexural vibrations are forbidden, whereas longitudinal vibration is allowed—a unique property of fluids. In another case, the torsional vibration can be suppressed significantly. The experimental results are well interpreted by band structure analysis, as well as effective media with indefinite mass density and negative moment of inertia. Our work opens an approach to efficiently separate and control elastic waves of different polarizations in fully solid structures. Controlling elastic waves in medium is essential to many applications in mechanical to earthquake engineering. Ma et al. demonstrate selective suppression of different vibrational modes in a three-dimensional rod-shape structure, which shows fluid-like elasticity with only longitudinal waves propagating.

Charged particle behavior in the growth and damping stages of ultralow frequency waves: theory and Van Allen Probes observations

Abstract: Ultralow frequency (ULF) electromagnetic waves in Earth's magnetosphere can accelerate charged particles via a process called drift resonance. In the conventional drift resonance theory, a default assumption is that the wave growth rate is time independent, positive, and extremely small. However, this is not the case for ULF waves in the real magnetosphere. The ULF waves must have experienced an earlier growth stage when their energy was taken from external and/or internal sources, and as time proceeds the waves have to be damped with a negative growth rate. Therefore, a more generalized theory on particle behavior during different stages of ULF wave evolution is required. In this paper, we introduce a time-dependent imaginary wave frequency to accommodate the growth and damping of the waves in the drift resonance theory, so that the wave-particle interactions during the entire wave lifespan can be studied. We then predict from the generalized theory particle signatures during different stages of the wave evolution, which are consistent with observations from Van Allen Probes. The more generalized theory, therefore, provides new insights into ULF wave evolution and wave-particle interactions in the magnetosphere.

Rich eight-branch spectrum of the oblique propagating longitudinal waves in partially spin-polarized electron-positron-ion plasmas.

Abstract: We consider the separate spin evolution of electrons and positrons in electron-positron and electron-positron-ion plasmas. We consider the oblique propagating longitudinal waves in these systems. Working in a regime of high-density n(0) ∼ 10(27) cm(-3) and high-magnetic-field B(0)=10(10) G, we report the presence of the spin-electron acoustic waves and their dispersion dependencies. In electron-positron plasmas, similarly to the electron-ion plasmas, we find one spin-electron acoustic wave (SEAW) at the propagation parallel or perpendicular to the external field and two spin-electron acoustic waves at the oblique propagation. At the parallel or perpendicular propagation of the longitudinal waves in electron-positron-ion plasmas, we find four branches: the Langmuir wave, the positron-acoustic wave, and a pair of waves having spin nature, they are the SEAW and the wave discovered in this paper, called the spin-electron-positron acoustic wave (SEPAW). At the oblique propagation we find eight longitudinal waves: the Langmuir wave, the Trivelpiece--Gould wave, a pair of positron-acoustic waves, a pair of SEAWs, and a pair of SEPAWs. Thus, for the first time, we report the existence of the second positron-acoustic wave existing at the oblique propagation and the existence of SEPAWs.

Longitudinal elastic wave propagation characteristics of inertant acoustic metamaterials

Abstract: Longitudinal elastic wave propagation characteristics of acoustic metamaterials with various inerter configurations are investigated using their representative one-dimensional discrete element lattice models. Inerters are dynamic mass-amplifying mechanical elements that are activated by a difference in acceleration across them. They have a small device mass but can provide a relatively large dynamic mass presence depending on accelerations in systems that employ them. The effect of introducing inerters both in local attachments and in the lattice was examined vis-a-vis the propagation characteristics of locally resonant acoustic metamaterials. A simple effective model based on mass, stiffness, or their combined equivalent was used to establish dispersion behavior and quantify attenuation within bandgaps. Depending on inerter configurations in local attachments or in the lattice, both up-shift and down-shift in the bandgap frequency range and their extent are shown to be possible while retaining static mass addition to the host structure to a minimum. Further, frequency-dependent negative and even extreme effective-stiffness regimes are encountered. The feasibility of employing tuned combinations of such mass-delimited inertant configurations to engineer acoustic metamaterials that act as high-pass filters without the use of grounded elements or even as complete longitudinal wave inhibitors is shown. Potential device implications and strategies for practical applications are also discussed.

Ultrafast magnetoelastic probing of surface acoustic transients

Abstract: We generate in-plane magnetoelastic waves in nickel films using the all-optical transient grating technique. When performed on amorphous glass substrates, two dominant magnetoelastic excitations can be resonantly driven by the underlying elastic distortions, the Rayleigh surface acoustic wave and the surface skimming longitudinal wave. An applied field, oriented in the sample plane, selectively tunes the coupling between magnetic precession and one of the elastic waves, thus demonstrating selective excitation of coexisting, large-amplitude magnetoelastic waves. Analytical calculations based on the Green's function approach corroborate the generation of multiple surface acoustic transients with disparate decay dynamics.

Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types

Abstract: In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.

Micromechanics of seismic wave propagation in granular materials

Abstract: In this study experimental data on a model soil in a cubical cell are compared with both discrete element (DEM) simulations and continuum analyses. The experiments and simulations used point source transmitters and receivers to evaluate the shear and compression wave velocities of the samples, from which some of the elastic moduli can be deduced. Complex responses to perturbations generated by the bender/extender piezoceramic elements in the experiments were compared to those found by the controlled movement of the particles in the DEM simulations. The generally satisfactory agreement between experimental observations and DEM simulations can be seen as a validation and support the use of DEM to investigate the influence of grain interaction on wave propagation. Frequency domain analyses that considered filtering of the higher frequency components of the inserted signal, the ratio of the input and received signals in the frequency domain and sample resonance provided useful insight into the system response. Frequency domain analysis and analytical continuum solutions for cube vibration show that the testing configuration excited some, but not all, of the system’s resonant frequencies. The particle scale data available from DEM enabled analysis of the energy dissipation during propagation of the wave. Frequency domain analysis at the particle scale revealed that the higher frequency content reduces with increasing distance from the point of excitation.

On the steady-state nearly resonant waves

Abstract: The steady-state nearly resonant water waves with time-independent spectrum in deep water are obtained from the full wave equations for inviscid, incompressible gravity waves in the absence of surface tension by means of a analytic approximation approach based on the homotopy analysis method (HAM). Our strategy is to mathematically transfer the steady-state nearly resonant wave problem into the steady-state exactly resonant ones. By means of choosing a generalized auxiliary linear operator that is a little different from the linear part of the original wave equations, the small divisor, which is unavoidable for nearly resonant waves in the frame of perturbation methods, is avoided, or moved far away from low wave frequency to rather high wave frequency with physically negligible wave energy. It is found that the steady-state nearly resonant waves have nothing fundamentally different from the steady-state exactly resonant ones, from physical and numerical viewpoints. In addition, the validity of this HAM-based analytic approximation approach for the full wave equations in deep water is numerically verified by means of the Zakharov’s equation. A thought experiment is discussed, which suggests that the essence of the so-called ‘wave resonance’ should be reconsidered carefully from both of physical and mathematical viewpoints.

Global MHD modeling of resonant ULF waves: Simulations with and without a plasmasphere

Abstract: We investigate the plasmaspheric influence on the resonant mode coupling of magnetospheric ultralow frequency (ULF) waves using the Lyon-Fedder-Mobarry (LFM) global magnetohydrodynamic (MHD) model. We present results from two different versions of the model, both driven by the same solar wind conditions: one version that contains a plasmasphere (the LFM coupled to the Rice Convection Model, where the Gallagher plasmasphere model is also included) and another that does not (the stand-alone LFM). We find that the inclusion of a cold, dense plasmasphere has a significant impact on the nature of the simulated ULF waves. For example, the inclusion of a plasmasphere leads to a deeper (more earthward) penetration of the compressional (azimuthal) electric field fluctuations, due to a shift in the location of the wave turning points. Consequently, the locations where the compressional electric field oscillations resonantly couple their energy into local toroidal mode field line resonances also shift earthward. We also find, in both simulations, that higher-frequency compressional (azimuthal) electric field oscillations penetrate deeper than lower frequency oscillations. In addition, the compressional wave mode structure in the simulations is consistent with a radial standing wave oscillation pattern, characteristic of a resonant waveguide. The incorporation of a plasmasphere into the LFM global MHD model represents an advance in the state of the art in regard to ULF wave modeling with such simulations. We offer a brief discussion of the implications for radiation belt modeling techniques that use the electric and magnetic field outputs from global MHD simulations to drive particle dynamics.

Slow electrostatic solitary waves in Earth's plasma sheet boundary layer

Abstract: We modeled Cluster spacecraft observations of slow electrostatic solitary waves (SESWs) in the Earth's northern plasma sheet boundary layer (PSBL) region on the basis of nonlinear fluid theory and fluid simulation. Various plasma parameters observed by the Cluster satellite at the time of the SESWs were examined to investigate the generation process of the SESWs. The nonlinear fluid model shows the coexistence of slow and fast ion acoustic waves and the presence of electron acoustic waves in the PSBL region. The fluid simulations, performed to examine the evolution of these waves in the PSBL region, showed the presence of an extra mode along with the waves supported by the nonlinear fluid theory. This extra mode is identified as the Buneman mode, which is generated by relative drifts of ions and electrons. A detailed investigation of the characteristics of the SESWs reveals that the SESWs are slow ion acoustic solitary waves.

Structure and location of branch point singularities for Stokes waves on deep water

Abstract: The Stokes wave is a finite-amplitude periodic gravity wave propagating with constant velocity in an inviscid fluid. The complex analytical structure of the Stokes wave is analysed using a conformal mapping of a free fluid surface of the Stokes wave onto the real axis with the fluid domain mapped onto the lower complex half-plane. There is one square root branch point per spatial period of the Stokes wave located in the upper complex half-plane at a distance from the real axis. The increase of Stokes wave height results in approaching zero with the limiting Stokes wave formation at . The limiting Stokes wave has a power-law singularity forming a radians angle on the crest which is qualitatively different from the square root singularity valid for arbitrary small but non-zero , making the limit of zero highly non-trivial. That limit is addressed by crossing a branch cut of a square root into the second and subsequently higher sheets of the Riemann surface to find coupled square root singularities at distances from the real axis at each sheet. The number of sheets is infinite and the analytical continuation of the Stokes wave into all of these sheets is found together with the series expansion in half-integer powers at singular points within each sheet. It is conjectured that a non-limiting Stokes wave at the leading order consists of an infinite number of nested square root singularities which also implies the existence in the third and higher sheets of additional square root singularities away from the real and imaginary axes. These nested square roots form a power-law singularity of the limiting Stokes wave as vanishes.

Whistler waves with angular momentum in space and laboratory plasmas and their counterparts in free space

Abstract: Electromagnetic waves with helical phase surfaces arise in different fields of physics such as space plasmas, laboratory plasmas, solid-state physics, atomic, molecular and optical sciences. Their common features are the wave orbital angular momentum associated with the circular wave propagation around the axis of wave propagation. In plasmas these waves are called helicons. When particles or waves change the field momentum they experience a pressure and a torque which can lead to useful applications. In plasmas electrons can damp or excite rotating whistlers, depending on the electron distribution function in velocity space. A magnetized plasma is an anisotropic medium in which electromagnetic waves propagate differently than in space. Phase and group velocities are different such that wave focusing and wave reflections are different from those in free space. Electrons experience Doppler shifts and cyclotron resonance which creates wave damping and growth. All media exhibit nonlinear effects whic...

Solitary waves in a peridynamic elastic solid

Abstract: The propagation of large amplitude nonlinear waves in a peridynamic solid is analyzed. With an elastic material model that hardens in compression, sufficiently large wave pulses propagate as solitary waves whose velocity can far exceed the linear wave speed. In spite of their large velocity and amplitude, these waves leave the material they pass through with no net change in velocity and stress. They are nondissipative and nondispersive, and they travel unchanged over large distances. An approximate solution for solitary waves is derived that reproduces the main features of these waves observed in computational simulations. It is demonstrated by numerical studies that the waves interact only weakly with each other when they collide. Wavetrains composed of many non-interacting solitary waves are found to form and propagate under certain boundary and initial conditions.

Stick-slip at soft adhesive interfaces mediated by slow frictional waves

Abstract: Stick-slip is a friction instability that governs diverse phenomena from squealing automobile brakes to earthquakes. At soft adhesive interfaces, this instability has long been attributed to Schallamach waves, which are a type of slow frictional wave. We use a contact configuration capable of isolating single wave events, coupled with high speed in situ imaging, to demonstrate the existence of two new stick-slip modes. It is shown that these modes also correspond to the passage of slow waves-separation pulse and slip pulse-with distinct nucleation and propagation characteristics. The slip pulse, characterized by a sharp stress front, propagates in the same direction as the Schallamach wave. In contrast, the separation pulse, involving local interface detachment and resembling a tensile neck, travels in exactly the opposite direction. A change in the stick-slip mode from the separation to the slip pulse is effected simply by increasing the normal force. Taken together, the three waves constitute all possible stick-slip modes in low-velocity sliding. The detailed observations enable us to present a phase diagram delineating the domains of occurrence of these waves. We suggest a direct analogy between the observed slow frictional waves and well known muscular locomotory waves in soft bodied organisms. Our work answers basic questions about adhesive mechanisms of frictional instabilities in natural and engineered systems, with broader implications for slow surface wave phenomena.

A parametric study for the generation of ion Bernstein modes from a discrete spectrum to a continuous one in the inner magnetosphere. I. Linear theory

Abstract: Ion Bernstein modes, also known as magnetosonic waves in the magnetospheric community, are considered to play an important role in radiation belt electron acceleration. The detailed properties of perpendicular magnetosonic waves excited in the inner magnetosphere by a tenuous proton ring distribution are investigated in a two series paper with a combination of the linear theory and one-dimensional particle-in-cell simulations. Here, in this paper, we study the properties of the excited magnetosonic waves under different plasma conditions with the linear theory. When the proton to electron mass ratio or the ratio of the light speed to the Alfven speed is small, the excited magnetosonic waves are prone to having a discrete spectrum with only several wave modes. With the increase of the proton to electron mass ratio or the ratio of the light speed to the Alfven speed, the lower hybrid frequency also increases, which leads to the increase of both the number and frequency of the excited wave modes. Meanwhile, the growth rate of these wave modes also increases. When the proton to electron mass ratio or the ratio of the light speed to the Alfven speed is sufficiently large, the spectrum of the excited magnetic waves becomes continuous due to the overlapping of the adjacent wave modes. The increase of the density of the protons with the ring distribution can also result in the increase of the growth rate, which may also change the discrete spectrum of the excited waves to a continuous one, while the increase of the ring velocity of the tenuous proton ring distribution leads to a broader spectrum, but with a smaller growth rate.

Theoretical and experimental correlation of mechanical wave formation on beams

Abstract: Mechanical waves can be broadly categorized into traveling waves and standing waves. In this study, the nature of the waves in a finite solid medium is investigated to reveal the excitation parameters that influence their behavior. Theoretical and experimental analysis is conducted to find the conditions for generating traveling waves using piezoelectric ceramics as the actuation agent in piezo-structural-coupled systems. A continuous electromechanical model is developed in order to predict the structural dynamics and is validated through experiments. The results from this study provide the fundamental physics behind the generation of mechanical waves and their propagation through finite mediums.

Higher order acoustoelastic Lamb wave propagation in stressed plates

Abstract: Modeling and experiments are used to investigate Lamb wave propagation in the direction perpendicular to an applied stress. Sensitivity, in terms of changes in velocity, for both symmetrical and anti-symmetrical modes was determined. Codes were developed based on analytical expressions for waves in loaded plates and they were used to give wave dispersion curves. The experimental system used a pair of compression wave transducers on variable angle wedges, with set separation, and variable frequency tone burst excitation, on an aluminum plate 0.16 cm thick with uniaxial applied loads. The loads, which were up to 600 μe, were measured using strain gages. Model results and experimental data are in good agreement. It was found that the change in Lamb wave velocity, due to the acoustoelastic effect, for the S1 mode exhibits about ten times more sensitive, in terms of velocity change, than the traditional bulk wave measurements, and those performed using the fundamental Lamb modes. The data presented demonstrate the potential for the use of higher order Lamb modes for online industrial stress measurement in plate, and that the higher sensitivity seen offers potential for improved measurement systems.

On resonant triad interactions of acoustic–gravity waves

Abstract: The propagation of wave disturbances in water of uniform depth is discussed, accounting for both gravity and compressibility effects. In the linear theory, free-surface (gravity) waves are virtually decoupled from acoustic (compression) waves, because the speed of sound in water far exceeds the maximum phase speed of gravity waves. However, these two types of wave motion could exchange energy via resonant triad nonlinear interactions. This scenario is analysed for triads comprising a long-crested acoustic mode and two oppositely propagating subharmonic gravity waves. Owing to the disparity of the gravity and acoustic length scales, the interaction time scale is longer than that of a standard resonant triad, and the appropriate amplitude evolution equations, apart from the usual quadratic interaction terms, also involve certain cubic terms. Nevertheless, it is still possible for monochromatic wavetrains to form finely tuned triads, such that nearly all the energy initially in the gravity waves is transferred to the acoustic mode. This coupling mechanism, however, is far less effective for locally confined wavepackets.

Plate-Angle Effects on Acoustic Waves from Supersonic Jets Impinging on Inclined Plates

Abstract: The effects of plate angle on acoustic waves from a supersonic jet impinging on an inclined flat plate at angles of 30, 45, and 60 deg are numerically investigated. Three-dimensional compressible Navier–Stokes equations are solved using the modified weighted compact nonlinear scheme. Similar to previous studies, the acoustic fields indicate that there are at least three types of acoustic waves in all of the cases considered herein: 1) Mach waves generated from the shear layer of the main jet, 2) acoustic waves generated from the impingement region, and 3) Mach waves generated from the shear layer of the supersonic flow downstream of the jet impingement. Acoustic waves (2) are generated from two different acoustic sources: 1) the interaction between the plate shock wave and the shear layer, and 2) the interaction between the bubble-induced shock waves and the shear layer. The frequency characteristics of acoustic waves are related to the thickness of the shear layer in the impingement region. The results o...

Analytical study of solitons in magneto-electro-elastic circular rod

Abstract: The nonlinear longitudinal wave equation, describing the propagation of optical solitons in magneto-electro-elastic circular rod, is investigated analytically. Two integration tools that are traveling wave hypothesis and G\(^{\prime }\)/G expansion scheme are recruited to extract explicit soliton solutions. The existence conditions are derived.

Frequency-wavenumber spectrum of the free surface of shallow turbulent flows over a rough boundary

Abstract: Data on the frequency-wavenumber spectra and dispersion relation of the dynamic water surface in an open channel flow are very scarce. In this work, new data on the frequency-wavenumber spectra were obtained in a rectangular laboratory flume with a rough bottom boundary, over a range of subcritical Froude numbers. These data were used to study the dispersion relation of the surface waves in such shallow turbulent water flows. The results show a complex pattern of surface waves, with a range of scales and velocities. When the mean surface velocity is faster than the minimum phase velocity of gravity-capillary waves, the wave pattern is dominated by stationary waves that interact with the static rough bed. There is a coherent three-dimensional pattern of radially propagating waves with the wavelength approximately equal to the wavelength of the stationary waves. Alongside these waves, there are freely propagating gravity-capillary waves that propagate mainly parallel to the mean flow, both upstream and downstream. In the flow conditions where the mean surface velocity is slower than the minimum phase velocity of gravity-capillary waves, patterns of non-dispersive waves are observed. It is suggested that these waves are forced by turbulence. The results demonstrate that the free surface carries information about the underlying turbulent flow. The knowledge obtained in this study paves the way for the development of novel airborne methods of non-invasive flow monitoring.