Dispersion Characteristics Of Waves Research Articles

Dynamics of thermoelastic Lamb waves in functionally graded nanoplates based on the modified nonlocal theory

Based on the integral form of the modified nonlocal theory, the dispersion and attenuation characteristics of thermoelastic Lamb waves in functionally graded material nanoplates are investigated. The improved Legendre polynomial series approach is presented to conquer the difficulty of the very time-consuming integration calculation, which contains the nonlocal factor, the Legendre polynomials, rectangular window function and their derivative. An iteration solution integration method is derived by using the properties of Legendre polynomials and the integration by parts. The proposed approach possesses the advantages of a small scale of the characteristic matrix and can directly obtain the complex wave number solutions without iteration. Comparisons with the available data indicate the validity of the proposed approach. Numerical examples show that the nonlocal effect on attenuation is more notable than that on phase velocity, especially at the frequency of the maximal attenuation. Besides, the nonlocal effect is very weak at the low frequency. Importantly, the escape frequency, which appears in the results from the differential form of modified nonlocal theory, does not exist in the integral form of modified nonlocal theory. In fact, the escape frequency originates from the approximate transformation from integral model to differential model.

An accurate method for dispersion characteristics of surface waves in layered anisotropic semi-infinite spaces

In this paper, we develop a novel method for the dispersion characteristics of surface waves in layered anisotropic semi-infinite spaces. Compared to solving the algebraic transcendental eigenequations directly, this method can find all surface waves accurately. For solving accurately, the first-order state equation is formed by introducing the dual variable. Some properties of the complex Hamiltonian matrix are presented and proved, then based on these properties, the radiation condition for the homogeneous anisotropic half-space is given. And, based on the scaling and squaring algorithm and mixed energy matrix, the precise integration method (PIM) is presented for solving accurately the eigenvalue problem of ordinary differential equations (ODEs) corresponding to surface waves. All eigenfrequencies can be found with certainty by using the concept of the eigenvalue count in the Wittrick-Williams (W-W) algorithm. Numerical examples show that the proposed method is highly accurate and efficient for solving dispersion relations of surface waves in layered anisotropic semi-infinite spaces, which involves the comparison of other previously published methods.

Wave Dispersion Behaviors of Multi-Scale CNT/Glass Fiber/Polymer Nanocomposite Laminated Plates.

In this paper, wave propagation in multi-scale hybrid glass fiber (GF)/carbon nanotube (CNT)/polymer nanocomposite plates is studied for the first time by means of refined higher-order plate theory. The hybrid nanocomposite consists of CNTs and glass fibers (GF) as reinforcing components distributed within a polymeric matrix. A hierarchical micromechanical approach is used to predict the effective mechanical properties of the hybrid nanocomposite, including the three-dimensional (3D) Mori-Tanaka method and the rule of mixture. Moreover, a refined-type higher-order shear deformation theory (HSDT) is implemented to take into account the influence of the shear deformation on the motion equations of the system. Then, the governing equations are achieved on the basis of the energy-based Hamilton's principle. Finally, the derived equations will be solved analytically for the purpose of extracting the natural frequency of the continuous system. A set of numerical examples are provided to cover the effects of various parameters on the wave dispersion characteristics of the plate. It can be declared that the hybrid nanocomposite system can achieve higher wave frequencies compared with other types of composite structures. Additionally, it is found that the selection of the lay-ups and length-to-diameter ratio plays a significant role in the determination of the sandwich plate's acoustic response.

Analysis on the dispersion characteristics of surface waves in a layered slope

For landslide detection and monitoring, surface wave methods (such as multichannel analysis of surface waves and array microtremor measurements), can be exploited to infer the subsurface shear-wave velocity (VS), which is a key physical parameter for calculating the soil vulnerability index and slope stability. To facilitate implementation, the seismic sources and geophones of survey lines traversing the slope of a landslide are commonly deployed along the direction of gravity. Considering that single (vertical)-geophones are extensively utilized in a variety of practical applications, it is meaningful to analyze the dispersion characteristics of the gravity-oriented component in a layered slope. Based on the stiffness matrix method and a coordinate rotation, we derive an explicit relationship for the gravity-oriented component in a layered slope. We further analyze the dispersion characteristics of the gravity-oriented component in three typical layered slopes by using a new developed tool comprising a seismic wavefield simulation and a modified frequency–Bessel transform. The results show that the dispersion spectra of the gravity-oriented component may be contaminated by Love waves, which can cause the Rayleigh wave dispersion curves to be misidentified. As the slope angle and the included angle between the survey line and dip direction increase, Love waves interfere more with the dispersion spectra of the gravity-oriented component. Numerical experiments indicate that if the slope angle is <17° or the angle between the survey line and dip direction is kept below a certain reasonable threshold, the dispersion spectra of the gravity-oriented component are determined mainly by Rayleigh waves. Moreover, we propose an azimuth filter method to suppress the interference of Love waves for passive surface wave dispersion measurements. The presented method offers useful guidance and emphasizes the great potential of surface wave methods in landslide detection and monitoring applications.

An Algebraic Wavenumber Identification (AWI) technique under stochastic conditions

This paper presents an inverse Algebraic Wavenumber Identification (AWI) technique for multi-modal 1D-periodic structures, which can extract complex wavenumbers from steady-state vibration measurements under stochastic conditions. These wave dispersion characteristics provide valuable vibroacoustic indicators for model updating, damage monitoring in operational conditions, or metamaterial design. Wavenumber extraction techniques are highly sensitive to noisy measurements, nonuniform sampling points, or geometrical uncertainties. The proposed formulation relies on algebraic parameters identification to enable the extraction of complex wavenumbers in four scenarios: (a) low Signal Noise Ratio; (b) small perturbation caused by uncertainties on sampling points’ coordinates; (c) unknown structural periodicity; (d) nonuniform sampling. This AWI is compared with Inhomogeneous Wave Correlation (IWC) method and INverse COnvolution MEthod (INCOME) to assess the robustness and accuracy of the method.

Bandgaps in functionally graded phononic crystals containing graphene origami-enabled metamaterials

This paper investigates the dispersion characteristics of elastic waves propagating along the thickness direction in functionally graded laminated phononic crystals (FGLPCs) containing novel auxetic metamaterials enabled by graphene origami that is created with the aid of hydrogenation. Both graphene weight fraction and hydrogen coverage which are the key parameters governing the auxetic property are nonuniformly distributed in unit cells of FGLPCs whose material properties are determined by genetic programming-assisted micromechanical models. The dispersion relations of elastic waves in the structure are obtained based on the state space approach and the method of reverberation-ray matrix. A comprehensive parametric study is conducted to discuss the effects of graphene origami weight fraction and hydrogen coverage on bulk waves in elastic solids made of the metamaterial and elastic waves in FGLPCs. It is found that introducing auxetic metamaterials into FGLPCs can effectively manipulate elastic waves. The graded distribution of weight fraction in FGLPCs can lead to bandgaps for both transverse and longitudinal waves, while a through-thickness graded pattern in hydrogen coverage can trigger broad bandgaps for longitudinal waves only with transverse waves nearly unchanged.

Phase-velocity and intercept-time scanning (PIS) technique for extracting experimental dispersion characteristics of surface waves

In active surface wave methods, the ability to extract the true dispersion trends from surface wave field data is critical for inferring accurate shear-wave velocity profiles. However, dispersion images such as those generated by the conventional wavefield transformation method are usually accompanied by numerical artifacts including side-lobes and aliasing, both of which decrease the dispersion image resolution and may lead to misinterpretation of dispersion modes. For example, the side lobes can be misinterpreted as higher or lower modes, which would introduce additional errors into the inverted stiffness profiles. A new experimental dispersion analysis method is presented to improve the resolution and sharpness of dispersion images and minimize the side lobes. The proposed method employs scanning of the phase-velocities and intercept-times of a series of harmonic signals obtained by Fourier transformation of raw multichannel data in the space-time (x-t) domain. Results obtained from synthetic and real field data demonstrate that the improved method can yield high-quality dispersion images compared to those of the conventional dispersion-imaging method. In addition, the improved method do not rely on the assumption that the impact point is the generation point of the Rayleigh waves, which is needed for the conventional method.

Identification of partial differential equations in structural mechanics theory through k-space analysis and design

This paper presents a method to identify wave equations’ parameters using wave dispersion characteristics (k-space) on two-dimensional domains. The proposed approach uses the minimization of the difference of an analytic formulation of the dispersion relation to wavenumbers calculated from solution fields. The implementation of partial differential equations (PDE) resolution on finite element software is explained and tested with analytic solutions in order to generate the test solution fields for the identification process. The coefficient identification is tested on solution fields generated by finite element solver for some 2nd- and 4th-order equations. In particular the test cases are the equations at different frequencies of deflection of isotropic and orthotropic membrane, flexion of isotropic and orthotropic plate and an original model of orthotropic plate equivalent to a bi-directional ribbed plate. In the limits of the spatial sampling rate and the domain size, the process allows an accurate retrieval of the wave equation parameters.

Wave dispersion characteristics of laminated carbon fiber reinforced polymer composite shells resting on viscoelastic foundations under thermal field

Wave dispersion characteristics of laminated composite shells resting on viscoelastic foundations in thermal environments are examined. Three types of temperature distributions (i.e., uniform, linear, and sinusoidal) along the thickness of the laminates are considered. Effective material properties of the carbon fiber reinforced polymer (CFRP) composite are calculated by the Mori-Tanaka homogenization method. The four-variable higher-order shear deformation theory (HSDT) and Hamilton principle are utilized to derive the equations of motion. The Navier approach in conjunction with wave solution is exploited to obtain the dispersion relations of the simply supported laminated shells with cross-ply and antisymmetric angle-ply arrangements. A comparative study is performed to demonstrate the validity of the present model. A parametric study is conducted with focus on the effects of curvature ratio, viscoelastic foundation parameters, carbon fiber volume fraction, number of layers, lamination scheme, temperature distribution, temperature difference, and fiber orientation on the wave dispersion behavior. Numerical results manifest that uniform temperature distribution reduces the phase velocity furthest. At low wave number, the extrema of phase velocity are determined by the curvature ratio and fiber orientation. The results can be used for the ultrasound detection techniques and structural health monitoring.

Realization of low-frequency stop band in Timoshenko beam with periodic IDVAs

The most prominent dynamic characteristic of metamaterials is that they possess the frequency pass bands and band gaps. In the bandgap, the elastic waves will attenuate significantly, and this property is potentially used to control low-frequency vibrations in civil engineering. To open the low-frequency bandgap of the Timoshenko beam, inerter-based dynamic vibration absorbers (IDVAs) are arranged periodically in the beam. An analytical methodology based on transfer matrix method was developed to predict the flexural wave dispersion characteristics, and was validated by test and numerical experiments. The band gaps can be simultaneously tuned by the parameters of the IDVAs, including spring stiffness, inertance and attached mass. Moreover, the band gaps generated by single IDVAs are independent of each other, and a super-wide bandgap can be achieved by splicing the band gaps for metamaterial beams with graded IDVAs. Explicit formulas with respect to the parameters of IDVAs have been developed to determine the condition of bandgap merging, which can broaden the bandwidth effectively. Finally, a computer-based program was presented to determine the reasonable design parameters.

Rapid assessment of fire damage to reinforced concrete structures using the surface wave method with contact and non-contact receivers

The study developed a rapid on-site assessment method for fire damage of reinforced concrete structures by using surface wave dispersion characteristics. A reinforced concrete slab containing four kinds of arrangement of steel-reinforced bars was cast. The gas furnace produced the fire damage by heating on one surface of the slab with a maximum temperature of 600˚C. The surface wave tests were carried out using an impact source and a receiver 0.5 m away from the impact location before and after the fire damage. The impactor is a small hammer embedded with a piezoelectric element to record the initial time of the impact. Contact and non-contact receivers were applied. The former is a displacement receiver, and the latter is a microphone. The surface wave response in the waveform was filtered out, and then processed by the short-time Fourier transform and reassigned method to obtain the group velocity spectrogram. The wave velocity-wavelength diagram of the surface wave was used for analysis. This study compares the results obtained by the two types of receivers before and after the fire. The influence of the relative directions between the survey line and the steel bars is also discussed. The results show that the test results obtained from the two types of receivers are similar under room temperature and 600˚C. However, the signal noise of the microphone is relatively large, and the consistency of repeated tests after a fire is poorer. The oblique angle between the measuring line and the steel bar is the most suitable choice because it can better distinguish the severity of fire damage and estimate the depth of deterioration.

Study on wave dispersion characteristics of piezoelectric sandwich nanoplates considering surface effects

Study on wave dispersion characteristics of piezoelectric sandwich nanoplates considering surface effects

Comparison of Peridynamics and Lattice Dynamics Wave Dispersion Relationships

Peridynamics is a non-local continuum formulation and material points inside an influence domain, named horizon, can interact with each other. Peridynamics also has a capability to represent wave dispersion which is observed in real materials especially at shorter wave lengths. Therefore, wave frequency and wave number have a nonlinear relationship in peridynamics. In this study, we present wave dispersion characteristics of peridynamics and compare with lattice dynamics to determine the horizon size for different materials including copper, gold, silver and platinum through an iterative process for the first time in the literature. This study also shows the superiority of peridynamics over classical continuum mechanics by having a length scale parameter, horizon, which allows peridynamics to represent the entire range of dispersion curves for both short and long wave lengths as opposed to limitation of classical mechanics to long wave lengths.

Nonreciprocal propagation of spin waves in a bilayer magnonic waveguide based on yttrium-iron garnet films

Objectives. Nonreciprocal spin wave effects can manifest themselves in metalized films of ferrite garnets. By studying the dynamics of spin waves in micro- and nano-scale magnetic films, the possibility of using multilayer dielectric films of yttrium iron garnet (YIG) to ensure the manifestation of the nonreciprocity effect is demonstrated. This approach offers advantages compared to the use of a layered YIG/metal structure due to significantly lower spin-wave losses in the two-layer YIG film consisting of layers with different values of magnetization. Such films can be used in logical elements to create controllable Mach-Zehnder interferometers based on magnonic principles. The purpose of this work is to reconcile the concept of nonreciprocal spin-wave propagation of a signal with the simultaneous manifestation of the effects arising from the propagation of spin waves in microwave guides formed by finite-width YIG films.Methods. We used an experimental microwave spectroscopy method based on a vector network analyzer along with a finite difference method to perform a numerical simulation of the dispersion characteristics of spin waves in two-layer magnonic microwave guides. An analytical model was also used to obtain a dispersion equation based on the magnetostatic approximation.Results. Based on measurements of the amplitude and phase responses, the possible coexistence of two frequency ranges for the propagation of a spin-wave signal in a two-layer magnon microwave guide based on a YIG film formed by two layers with different values of saturation magnetization was demonstrated. Regimes of nonreciprocal propagation of a spin-wave signal were revealed. A numerical model was using to study the formation mechanisms of spin wave modes in the spectrum of a two-layer structure formed due to the finite dimensions of the microwave guide. An analytical model was used to evaluate the transformation of the mode spectrum. The experimental data are in good agreement with the results of the proposed numerical and analytical models.Conclusions. The possibility of frequency-selective propagation of spin waves in a magnon microwaveguide consisting of two layers with different saturation magnetization values is demonstrated. Multimode propagation of spin waves can occur inside a two-layer structure in two frequency ranges. At the same time, this process is accompanied by a strong nonreciprocity of spin-wave signal propagation, which manifests itself in a change in the amplitude and phase responses when the direction of the external magnetic field is reversed. The proposed two-layer spin-wave waveguide concept can be used in the manufacture of magnon interconnects and magnon interferometers with the support of multiband regimes of operation.

Guided wave propagation in functionally graded viscoelastic polymer composite shells reinforced with graphite particles

Guided wave propagation in functionally graded (FG) viscoelastic polymer composite shells reinforced with spherical graphite particles (SGPs) is investigated. Under different distribution patterns, the layer-wise variation of SGP volume fraction through the thickness of the structure enables to achieve desired performance. Viscoelastic behavior of the structure is described by the Kelvin–Voigt model. Effective material properties of the particulate composite are precisely calculated via the differential scheme. The four-variable higher-order shear deformation theory and Hamilton’s principle are applied to obtain the governing equations of the laminated shell. Analytical solutions for the dispersion relations of guided waves are provided using Galerkin approach. The accuracy of the present model is verified by comparison with published results. A parametric study is conducted considering the effects of boundary condition, curvature ratio, SGP volume fraction, SGP distribution pattern, radius of curvature to length ratio and structure damping coefficient on the wave dispersion characteristics. The results highlight that the boundary conditions play a significant role in affecting phase velocity at low wave numbers, while the effect of structure damping coefficient becomes predominant at high wave numbers.

Surface wave dispersion in imperfectly bonded flexoelectric-piezoelectric/FGPM bi-composite in contact of Newtonian liquid

The present research article manifests the dissipation and dispersion characteristics of Love-type waves in a flexoelectric-piezoelectric/functionally graded piezomagnetic material structure, loaded with Newtonian liquid. The interface between the piezoelectric plate and the piezomagnetic substrate is considered mechanically and electromagnetically imperfect. Transcendental complex dispersion relations for electrically and magnetically open and short cases are obtained by rigorous analytical methods. A particular numerical example is considered and dispersion, as well as attenuation curves are obtained for it. Influences of mechanical and electromechanical imperfections, flexoelectricity, layer-thickness, and material gradient parameters on phase velocity and attenuation of Love-type waves are meticulously examined.

Analytical and experimental investigation of flexural waves in horizontal pipes conveying two-phase periodic intermittent flow

Two-phase flow in pipes can generate different geometric distribution of phases depending on the flow conditions, called flow patterns. The identification of such flow patterns is fundamental for designing operational conditions of complex oil and gas industrial plants for production and transport of such fluids by pipes. Amongst them, the intermittent flow is the most relevant for industrial applications as it can lead to increased vibration levels with catastrophic failures, and also to several flow assurance problems. In this flow condition, an elongated gas bubble travels along the pipe followed by a liquid slug with or without dispersed bubbles. The two-phase flow induced vibration research have been mostly focused on the modal approaches, which can be very sensitive to boundary and operational conditions thus limiting its practical applicability in field conditions. On the other hand, wave-based approaches can overcome this limitation since they are based on local properties. In this paper, bending wave propagation in horizontal ducts conveying intermittent flow is investigated. A periodic unit cell model is assumed to describe the intermittent flow and the mass density along the duct is thus given by a Fourier series, representing space and time fluctuations. Subsequently, the wave dispersion characteristics can be analytically calculated for a duct in bending conveying intermittent flow, assuming small mixture velocity when compared to the bending waves. The periodic flow creates a periodic dispersion diagram which is distorted by the flow velocity. This effect accounts for the asymmetry in the wave propagating along and against the flow direction. The wave dispersion curves are experimentally estimated for typical intermittent flow conditions and it is shown that they can be approximated by equivalent homogeneous fluid. In addition, this curve is sensitive to the gas fraction of the two-phase fluid. The presented approach introduces a new perspective on two-phase flow induced vibrations of pipes and opens the way for better understanding the effect of the periodic two-phase flow in the dynamic behaviour of pipes.

Numerical study of dispersion characteristics of dipole flexural waves in a cased hole with different cement conditions

Numerical study of dispersion characteristics of dipole flexural waves in a cased hole with different cement conditions

Theoretical and experimental investigation of circumferential guided waves in orthotropic annuli

The fiber composite materials fabricated by stacking the lamina structure obtain increasing attention in the industry, and at the same time, damage analysis is essential for safe operation. A proposed way to detect defects such as debonding and delamination is to induce circumferential guided waves. Accurate determination of the dispersion characteristics and wave fields is a prerequisite for using acoustic guided waves. The aim of this work is to provide such an accurate dispersion results in an arbitrarily thick cylindrically orthotropic homogeneous cylindrical shell of uniform thickness. Compared with the traditional SAFE method, the proposed method, which combines the two numerical methods, namely Floquet Boundary Condition (Floquet BC) Method and Sweeping Frequency Finite Element Modeling (SFFEM) method has obvious advantages. Through Floquet BC method, a theoretical result can be easily obtained without tedious code writing. Then SFFEM helps to verify the theoretical result in an experimental way. Besides, the slight gap between the theoretical and experimental results works as a basis for calibrating the elastic constants of composite materials provided in the manual. Simulations in COMSOL Multiphysics FE software supported by both methods and experiments by the latter have been carried out in this work. The calculated phase velocity dispersion curves demonstrated the efficiency of those two methods. The developed method can be adapted to other complex pipeline structures to extract circumferential guided wave dispersion characteristics by both simulation and experimental measurements.

Nonlocal and magneto effects on dispersion characteristics of Love-type waves in piezomagnetic media

Attributions of intrinsic nanoscale dimension in piezomagnetic structures, the small scale effects on the propagating wave are undeniable in their piezotronic applications. In this work, based on the nonlocal constitutive relations, the nanoscale size effects on the Love-type wave propagating in piezomagnetic structure are investigated. Dispersion equations are derived for magnetically open and short circuit cases. Particular results are deduced and validated with the existing results. Variation of phase velocity and group velocity versus the penetration depth has been distinctly marked. Influence of various parameters like nonlocal parameter, magneto parameters, magnetomechanical coupling coefficient associated with piezomagnetic media etc. on the dispersion characteristics for first three modes has been demonstrated graphically. This research shows that small scale effects have substantial effect on the phase velocity of the propagating wave. The results find its enormous possible applications in smart devices especially, nanoscale devices using wave propagation phenomena owing to representing outstanding magnetic and mechanical coupling performances.