Showing papers on "Longitudinal wave published in 2018"

Internal Gravity Waves

Abstract: The study of internal gravity waves provides many challenges: they move along interfaces as well as in fully three-dimensional space, at relatively fast temporal and small spatial scales, making them difficult to observe and resolve in weather and climate models. Solving the equations describing their evolution poses various mathematical challenges associated with singular boundary value problems and large amplitude dynamics. This book provides the first comprehensive treatment of the theory for small and large amplitude internal gravity waves. Over 120 schematics, numerical simulations and laboratory images illustrate the theory and mathematical techniques, and 130 exercises enable the reader to apply their understanding of the theory. This is an invaluable single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

Abstract: This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

Band transition and topological interface modes in 1D elastic phononic crystals.

Abstract: In this report, we design a one-dimensional elastic phononic crystal (PC) comprised of an Aluminum beam with periodically arranged cross-sections to study the inversion of bulk bands due to the change of topological phases. As the geometric parameters of the unit cell varies, the second bulk band closes and reopens forming a topological transition point. This phenomenon is confirmed for both longitudinal waves and bending waves. By constructing a structural system formed by two PCs with different topological phases, for the first time, we experimentally demonstrate the existence of interface mode within the bulk band gap as a result of topological transition for both longitudinal and bending modes in elastic systems, although for bending modes, additional conditions have to be met in order to have the interface mode due to the dispersive nature of the bending waves in uniform media compared to the longitudinal waves.

Intrinsic spin of elastic waves

Abstract: Unveiling spins of physical systems usually gives people a fundamental understanding of the geometrical properties of waves from classical to quantum aspects. A great variety of research has shown that transverse waves can possess nontrivial spins and spin-related properties naturally. However, until now, we still lack essential physical insights about the spin nature of longitudinal waves. Here, demonstrated by elastic waves, we uncover spins for longitudinal waves and the mixed longitudinal-transverse waves that play essential roles in spin-momentum locking. Based on this spin perspective, several abnormal phenomena beyond pure transverse waves are attributed to the hybrid spin induced by mixed longitudinal-transverse waves. The unique hybrid spin reveals the complex spin essence in elastic waves and advances our understanding about their fundamental geometrical properties. We also show that these spin-dependent phenomena can be exploited to control the wave propagation, such as nonsymmetric elastic wave excitation by spin pairs, a unidirectional Rayleigh wave, and spin-selected elastic wave routing. These findings are generally applicable for wave cases with longitudinal and transverse components.

Transmodal elastic metasurface for broad angle total mode conversion

Abstract: It has been long believed that a total mode conversion between longitudinal and shear elastic waves can only be achieved at a certain incidence angle. Here, we show that a total mode conversion can be achieved for a broad range of incidence angles by a specially designed elastic metasurface, namely, transmodal metasurface. From the generalized reflection law, we found that the incident longitudinal wave can be totally converted to a reflected shear wave over a broad range of incidence angles if a sufficiently large phase gradient is introduced at the boundary. Numerical and experimental investigations with a specially engineered transmodal metasurface showed that the total mode conversion can be achieved for wide incidence angles from 19 ° to 90 °, which was impossible to be achieved previously. The proposed idea of the transmodal metasurface can open up an advanced avenue for tailoring elastic wave modes as an outstanding alternative to generating shear waves.It has been long believed that a total mode conversion between longitudinal and shear elastic waves can only be achieved at a certain incidence angle. Here, we show that a total mode conversion can be achieved for a broad range of incidence angles by a specially designed elastic metasurface, namely, transmodal metasurface. From the generalized reflection law, we found that the incident longitudinal wave can be totally converted to a reflected shear wave over a broad range of incidence angles if a sufficiently large phase gradient is introduced at the boundary. Numerical and experimental investigations with a specially engineered transmodal metasurface showed that the total mode conversion can be achieved for wide incidence angles from 19 ° to 90 °, which was impossible to be achieved previously. The proposed idea of the transmodal metasurface can open up an advanced avenue for tailoring elastic wave modes as an outstanding alternative to generating shear waves.

Tuning Elastic Waves in Soft Phononic Crystal Cylinders via Large Deformation and Electromechanical Coupling

Abstract: Soft electroactive materials can undergo large deformation subjected to either mechanical or electrical stimulus, and hence they can be excellent candidates for designing extremely flexible and adaptive structures and devices. This paper proposes a simple one-dimensional soft phononic crystal cylinder made of dielectric elastomer to show how large deformation and electric field can be used jointly to tune the longitudinal waves propagating in the PC. A series of soft electrodes are placed periodically along the dielectric elastomer cylinder, and hence the material can be regarded as uniform in the undeformed state. This is also the case for the uniformly pre-stretched state induced by a static axial force only. The effective periodicity of the structure is then achieved through two loading paths, i.e. by maintaining the longitudinal stretch and applying an electric voltage over any two neighbouring electrodes, or by holding the axial force and applying the voltage. All physical field variables for both configurations can be determined exactly based on the nonlinear theory of electroelasticity. An infinitesimal wave motion is further superimposed on the pre-deformed configurations and the corresponding dispersion equations are derived analytically by invoking the linearized theory for incremental motions. Numerical examples are finally considered to show the tunability of wave propagation behavior in the soft PC cylinder. The outstanding performance regarding the band gap (BG) property of the proposed soft dielectric PC is clearly demonstrated by comparing with the conventional design adopting the hard piezoelectric material. Note that soft dielectric PCs are susceptible to various kinds of failure (buckling, electromechanical instability, electric breakdown, etc.), imposing corresponding limits on the external stimuli.

Frequency and wavenumber selective excitation of spin waves through coherent energy transfer from elastic waves

Abstract: Using spin-wave tomography (SWaT), we have investigated the excitation and the propagation dynamics of optically excited magnetoelastic waves, i.e., hybridized modes of spin waves and elastic waves, in a garnet film. By using time-resolved SWaT, we reveal the excitation dynamics of magnetoelastic waves through coherent-energy transfer between optically excited pure-elastic waves and spin waves via magnetoelastic coupling. This process realizes frequency and wavenumber selective excitation of spin waves at the crossing of the dispersion relations of spin waves and elastic waves. Finally, we demonstrate that the excitation mechanism of the optically excited pure-elastic waves, which are the source of the observed magnetoelastic waves, is dissipative in nature.

Waves in Solar Coronal Loops

Abstract: Recent observations have revealed the ubiquitous presence of magnetohydrodynamic (MHD) waves and oscillations in the solar corona. The aim of this review is to present recent progress in the observational study of four types of wave (or oscillation) phenomena mainly occurring in active region coronal loops, including (i) flare-induced slow mode oscillations, (ii) fast kink mode oscillations, (iii) propagating slow magnetoacoustic waves, and (iv) ubiquitous propagating kink (Alfvenic) waves. This review not only comprehensively outlines various aspects of these waves and coronal seismology, but also highlights the topics that are newly emerging or hotly debated, thus can provide readers a useful guidance on further studies of their interested topics.

The Role of Localized Compressional Ultra‐low Frequency Waves in Energetic Electron Precipitation

Abstract: Typically, Ultra-Low Frequency (ULF) waves have historically been invoked for radial diffusive transport leading to acceleration and loss of outer radiation belt electrons. At higher frequencies, Very-Low Frequency (VLF) waves are generally thought to provide a mechanism for localized acceleration and loss through precipitation into the ionosphere of radiation belt electrons. In this study we present a new mechanism for electron loss through precipitation into the ionosphere due to a direct modulation of the loss cone via localized compressional ULF waves. We present a case study of compressional wave activity in tandem with riometer and balloon-borne electron precipitation across keV-MeV energies to demonstrate that the experimental measurements can be explained by our new enhanced loss cone mechanism. Observational evidence is presented demonstrating that modulation of the equatorial loss cone can occur via localized compressional wave activity, which greatly exceeds the change in pitch angle through conservation of the first and second adiabatic invariants. The precipitation response can be a complex interplay between electron energy, the localisation of the waves, the shape of the phase space density profile at low pitch angles, ionospheric decay timescales, and the time-dependence of the electron source; we show that two pivotal components not usually considered are localized ULF wave fields and ionospheric decay timescales. We conclude that enhanced precipitation driven by compressional ULF wave modulation of the loss cone is a viable candidate for direct precipitation of radiation belt electrons without any additional requirement for gyroresonant wave-particle interaction. Additional mechanisms would be complementary and additive in providing means to precipitate electrons from the radiation belts during storm-times.

Dispersion Energy Analysis of Rayleigh and Love Waves in the Presence of Low-Velocity Layers in Near-Surface Seismic Surveys

Abstract: High-frequency surface-wave analysis methods have been effectively and widely used to determine near-surface shear (S) wave velocity. To image the dispersion energy and identify different dispersive modes of surface waves accurately is one of key steps of using surface-wave methods. We analyzed the dispersion energy characteristics of Rayleigh and Love waves in near-surface layered models based on numerical simulations. It has been found that if there is a low-velocity layer (LVL) in the half-space, the dispersion energy of Rayleigh or Love waves is discontinuous and ‘‘jumping’’ appears from the fundamental mode to higher modes on dispersive images. We introduce the guided waves generated in an LVL (LVL-guided waves, a trapped wave mode) to clarify the complexity of the dispersion energy. We confirm the LVL-guided waves by analyzing the snapshots of SH and P–SV wavefield and comparing the dispersive energy with theoretical values of phase velocities. Results demonstrate that LVL-guided waves possess energy on dispersive images, which can interfere with the normal dispersion energy of Rayleigh or Love waves. Each mode of LVL-guided waves having lack of energy at the free surface in some high frequency range causes the discontinuity of dispersive energy on dispersive images, which is because shorter wavelengths (generally with lower phase velocities and higher frequencies) of LVL-guided waves cannot penetrate to the free surface. If the S wave velocity of the LVL is higher than that of the surface layer, the energy of LVL-guided waves only contaminates higher mode energy of surface waves and there is no interlacement with the fundamental mode of surface waves, while if the S wave velocity of the LVL is lower than that of the surface layer, the energy of LVL-guided waves may interlace with the fundamental mode of surface waves. Both of the interlacements with the fundamental mode or higher mode energy may cause misidentification for the dispersion curves of surface waves.

Nonlinear non-collinear ultrasonic detection and characterisation of kissing bonds

Abstract: The development of cost effective and reliable bonded structures ideally requires an NDT method to detect the presence of poor quality, weak bonds or kissing bonds If these bonds are more compliant in tension than in compression stress-strain nonlinearities provide a possible route to detection with the use of nonlinear ultrasonic techniques This paper focuses on the kissing bond case and the resulting contact acoustic nonlinearity of the interface A kissing bond is created by compression loading of two aluminium blocks Non-collinear mixing of two shear waves producing a sum frequency longitudinal wave is the method of stimulation of contact acoustic nonlinearity in this research The parametric space of the nonlinear mixing is measured in terms of interaction angle of the input beams and the ratio of their frequencies creating a ‘fingerprint’ of the sample's bulk and interface properties in the region where the beams overlap The scattering fingerprint of a classically nonlinear solid is modelled analytically and a kissing interface is modelled numerically; these results are compared with experimentally measured values The experimental interface is tested with varied interfacial loading, resulting in an increase in scattering amplitude as load is increased Secondary peaks in the parameter space also appeared as loading increased, as well as other changes in the fingerprint pattern

On the solitary wave solutions to the longitudinal wave equation in MEE circular rod

Abstract: This study investigates the longitudinal wave equation in a magneto-electro-elastic circular rod by using the extended sinh-Gordon equation expansion method. Topological, non-topological and singular soliton solutions are extracted. To illustrate the physical appearance of the obtained solutions, 2D, 3D and the contour graphs to some of the obtained solutions are plotted. The reported results may be useful in explaining the physical meaning of the studied models and other nonlinear physical models arising in nonlinear sciences.

Elastic wave manipulation by using a phase-controlling meta-layer

Abstract: In this work, a high pass meta-layer for elastic waves is proposed. An elastic phase-controlling meta-layer is theoretically realized using parallel and periodically arranged metamaterial sections based on the generalized Snell's law. The elastic meta-layer is composed of periodically repeated supercells, in which the frequency dependent elastic properties of the metamaterial are used to control a phase gradient at the interface between the meta-layer and conventional medium. It is analytically and numerically demonstrated that with a normal incident longitudinal wave, the wave propagation characteristics can be directly manipulated by the periodic length of the meta-layer element at the sub-wavelength scale. It is found that propagation of the incident wave through the interface is dependent on whether the working wavelength is longer or shorter than the periodic length of the meta-layer element. Specifically, a mode conversion of the P-wave to an SV-wave is investigated as the incident wave passes throu...

Numerical study on static component generation from the primary Lamb waves propagating in a plate with nonlinearity

Abstract: Under the discipline of nonlinear ultrasonics, in addition to second harmonic generation, static component generation is another frequently used nonlinear ultrasonic behavior in non-destructive testing (NDT) and structural health monitoring (SHM) communities. However, most previous studies on static component generation are mainly based on using longitudinal waves. It is desirable to extend static component generation from primary longitudinal waves to primary Lamb waves. In this paper, static component generation from the primary Lamb waves is studied. Two major issues are numerically investigated. First, the mode of static displacement component generated from different primary Lamb wave modes is identified. Second, cumulative effect of static displacement component from different primary Lamb wave modes is also discussed. Our study results show that the static component wave packets generated from the primary S0, A0 and S1 modes share the almost same group velocity equal to the phase velocity of S0 mode tending to zero frequency c plate . The finding indicates that whether the primary mode is S0, A0 or S1, the static components generated from these primary modes always share the nature of S0 mode. This conclusion is also verified by the displacement filed of these static components that the horizontal displacement field is almost uniform and the vertical displacement filed is antisymmetric across the thickness of the plate. The uniform distribution of horizontal displacement filed enables the static component, regardless of the primary Lamb modes, to be a promising technique for evaluating microstructural damages buried in the interior of a structure. Our study also illustrates that the static components are cumulative regardless of whether the phase velocity of the primary and secondary waves is matched or not. This observation indicates that the static component overcomes the limitations of the traditional nonlinear Lamb waves satisfying phase velocity matching condition to achieve cumulative second harmonic generation. This nature also enables the primary Lamb waves excited at a low center frequency to generate static component used for inspecting large-scale structures with micro-scale damages.

Nonlinear Bloch waves and balance between hardening and softening dispersion

Abstract: The introduction of nonlinearity alters the dispersion of elastic waves in solid media In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals consisting of layers with alternating material properties Considering longitudinal waves and ignoring lateral effects, the exact nonlinear dispersion relation in each homogeneous layer is first obtained and subsequently used within the transfer matrix method to derive an approximate nonlinear dispersion relation for the overall periodic medium The result is an amplitude-dependent elastic band structure that upon verification by numerical simulations is accurate for up to an amplitude-to-unit-cell length ratio of one-eighth The derived dispersion relation allows us to interpret the formation of spatial invariance in the wave profile as a balance between hardening and softening effects in the dispersion that emerge due to the nonlinearity and the periodicity, respectively For example, for a wave amplitude of the order of one-eighth of the unit-cell size in a demonstrative structure, the two effects are practically in balance for wavelengths as small as roughly three times the unit-cell size

Nondestructive measurement of elastic modulus for thermally sprayed WC-Ni coatings based on acoustic wave mode conversion by small angle incidence

Abstract: a nondestructive method for characterization of thermally sprayed coatings is developed using an ultrasonic small angle incidence scheme in coatings of four layers and three interfaces. Through wave mode conversion analysis, the longitudinal and the transverse waves at the interfaces are simultaneously derived at an incident angle of 4.1°. The ultrasonic reflection coefficient amplitude spectrum (URCAS) is used to determine the thickness and longitudinal wave velocity of specimens through a two-parameter inversion utilizing the cross-correlation algorithm. The elastic modulus and Poisson's ratio of coatings were calculated utilizing the inversion results and modified density. Ultrasonic experiments were carried out on four WC-Ni specimens sprayed using the high velocity oxygen fuel (HVOF) method at spray angles of 30°, 45°, 60°, and 90°. The thicknesses measured by the ultrasonic method were in good agreement with those observed by optical microscopy with less than 10% error. The porosities determined from cross-section SEM photographs were 4.67%, 1.76%, 0.92%, and 0.19%, respectively with increasing spray angle. The elastic moduli of the specimens measured by the ultrasonic method were in the range of 315 GPa–351 GPa, and the Poisson's ratios were during 0.221–0.245. Metallurgical analysis indicated that increasing the spray angle increases both the density and the bond strength between particles which leads to an enhancement of the elastic modulus of the coatings. The proposed ultrasonic method is valid for nondestructive characterization of the elastic modulus and Poisson's ratio of the coatings.

An improved ultrasonic method for plane stress measurement using critically refracted longitudinal waves

Abstract: An improved ultrasonic method was developed theoretically and experimentally for plane stress measurement using critically refracted longitudinal (LCR) waves. Cruciform specimen method, combined with a digital image correlation (DIC) method, was applied to confirm the validity of this method. Based on the acoustoelastic theory, LCR waves with arbitrary detection directions were considered and relations between time-of-fight and biaxial principal stresses were described. To generate the LCR wave in cruciform specimen, a regular octagon polymethyl-methacrylate (PMMA) wedge was designed in accordance with Snell's law. Finally, validation experiments were performed under different step loads using cruciform specimens. In these experiments, the strain fields of cruciform specimens were extracted by DIC method and used to calculate the reference values of plane stress. By comparing the measured principal stresses with the reference values, the validation and precision of the improved ultrasonic method presented in this work were demonstrated.

Evaluation of Fatigue Crack Orientation Using Non-collinear Shear Wave Mixing Method

Abstract: In this paper, a non-collinear shear wave mixing technique is proposed for evaluation of fatigue crack orientation. Numerical analysis of the nonlinear interaction of two shear waves with crack is performed using two-dimensional finite-element simulations. The simulation results show that the nonlinear interaction of the two shears waves with cracks leads to the generation of transmitted and reflected sum-frequency longitudinal waves (SFLW), moreover the propagation direction of reflected SFLW is correlated with the orientation of crack, which can be used for crack orientation evaluation. Non-collinear wave-mixing experiments were conducted on specimens with fatigue crack. The experimental results show that the directivity of the generated SFLW agrees well with the simulation results, and non-collinear shear wave mixing has potential use in fatigue crack orientation evaluation.

Engineered metabarrier as shield from longitudinal waves: band gap properties and optimization mechanisms

Abstract: Phononic crystals that prevent the propagation of waves in a band gap have been widely applied in wave propagation control. In this paper, we propose the use of a metabarrier, based on a locally resonant phononic crystal mechanism, as a floating-slab track bearing to shield the infrastructure in a floating-slab track system from longitudinal waves from the slab, thereby improving mitigation of ground-borne vibrations. The locally resonant band gap properties of the metabarrier were studied based on the finite element method, and the shielding performance was verified by the transmission spectrum. Simplified models for band gap boundary frequencies were built according to the wave modes. Furthermore, a 3D half-track model was built to investigate the overall vibration mitigation performance of the floating-slab track with the metabarrier. An optimization mechanism for the band gap boundary frequencies is proposed. As the low-frequency ground-borne vibrations induced by subways carry the most energy, multi-objective genetic algorithm optimization was conducted to obtain a lower and wider band gap for a better shielding performance. The results show that the retained vibration isolation performance of the low natural frequency, the shielding performance of the band gap, and the controllability of band gap boundary frequencies all contribute to an improvement in overall vibration mitigation performance. The vertical static stiffness of the metabarrier was close to that of the existing bearing of the floating-slab track. An optimized locally resonant band gap from 50 to 113 Hz was generated using the optimization mechanism.

Finite amplitude steady-state wave groups with multiple near resonances in deep water

Abstract: In this paper, finite amplitude steady-state wave groups with multiple nearly resonant interactions in deep water are investigated theoretically. The nonlinear water wave equations are solved by the homotopy analysis method (HAM), which imposes no constraint on either the number or the amplitude of the wave components, to resolve the small-divisor problems caused by near resonances. A new kind of auxiliary linear operator in the framework of the HAM is proposed to transform the small divisors associated with the non-trivial nearly resonant components to singularities associated with the exactly resonant ones. Primary components, exactly resonant components together with nearly resonant components are considered as the initial non-trivial components, since all of them are homogeneous solutions to the auxiliary linear operator. For wave groups with weak nonlinearity, the energy transfer between nearby nearly resonant components is remarkable. As the nonlinearity increases, the number of steady-state wave groups increases as more components join the near resonance. This indicates that the probability of existence of steady-state resonant waves increases with the nonlinearity of wave groups. The frequency band broadens and spectral asymmetry becomes more and more pronounced. The amplitude of each component may either increase or decrease with the nonlinearity of wave groups, while the amplitude of the whole wave group increases continuously and finite amplitude wave groups are obtained. This work shows the wide existence of steady-state waves when multiple nearly resonant interactions are considered.