Dispersion Behavior Of Waves Research Articles

On the dispersion of bulk wave in hygrothermally affected poroelastic gymnastics beams based on refined higher-order shear deformation theory during athlete training

Poroelastic materials have gained prominence due to their beneficial characteristics, prompting the authors to investigate their behavior in wave propagation. Additionally, the balance beam used in gymnastics is a classic example of a beam structure. It is designed to support the weight of the gymnast while providing stability and strength. This paper focuses on analyzing wave dispersion behavior in a hygrothermally excited poroelastic gymnastics beam. It is considered that the beam is made of a composition of Alumina and Aluminum as ceramic and metallic phases, respectively. Initially, the basic characteristics are determined using an improved power-law homogenization scheme. Subsequently, a poroelastic beam is modeled based on a refined higher-order shear deformation theory, and based on it and Hamilton’s principle, the kinetic relations are obtained. The obtained governing equations are then solved through analytical schemes using harmonic functions, and the outcomes are presented. These results are afterward verified through comprehensive comparisons with existing literature. Furthermore, this paper findings shows that the phase velocity and wave frequency of the beam are influenced by gradient parameters, porosity, and environmental factors like temperature and humidity to gain further insights.

Monitoring early age concrete hydration through time-dependent wave dispersion

This paper explores into the intricate realm of wave dispersion behavior within the early stages of fresh concrete, with a specific focus on the dynamic interplay between micro-structure evolution and rheological properties in the quasi-solid state. Based on the characteristic of wave dispersion is factored by impulse frequency, the range used for the experiment is from 40 kHz to 100 kHz, where the wavelength is enough to be influenced by the medium. The time-dependent analytical solution and FE simulation show more linear changes in phase velocity at different times during the quasi-solid state. On the other hand, experimental data exhibits more dispersion behavior, likely due to the effect of viscoplasticity. To simulate the viscoplasticity effect, the FE simulation is compared between cases with applied viscoplasticity and without viscoplasticity. The phase velocity in the viscoplasticity case decreases by approximately 30% compared to the non-viscoplasticity case. This demonstrates that the effect of viscoplasticity cannot be overlooked in the quasi-solid state of concrete. The wave dispersion behavior in the early stages is predominantly influenced by particles and viscoplasticity, causing changes in phase velocity over time and impulse frequency. The highest phase velocity is observed between 50 kHz to 60 kHz. As the concrete undergoes hydration and hardening, both group velocity and phase velocity generally increase with the same frequency impulse. This study aims to unravel the complexities inherent in these phenomena, shedding light on the fundamental mechanisms governing wave dispersion in quasi-solid materials.

Influence of MWCNT’s waviness and aggregation factors on wave dispersion response of MWCNT-strengthened nanocomposite curved beam

This article focuses on the impact of waviness and aggregation of nanofillers on wave dispersion behavior of the nanocomposite curved beam strengthened with multi-walled carbon nanotubes (MWCNTs). In fact, the aggregation phenomenon is an inevitable subject in the manufacturing process of strengthened nanocomposite materials. Furthermore, in reality, usage of straight nanoreinforcements is almost impossible. So, MWCNTs can be wavy. These noted topics can significantly affect mechanical behavior of reinforced nanocomposite structures. In the current investigation, aggregation and waviness factors are accounted for through a modified Halpin-Tsai micromechanical homogenization model. The relations of kinetic and kinematic of MWCNTs-reinforced nanocomposite curved beam are expressed by employing Euler-Bernoulli beam theory. The governing equations are obtained by using Hamiltonian approach. The obtained equations are solved via an analytical solution to attain the wave dispersion values. The precision of the obtained outcomes is verified by the reported outcomes in the literature. Finally, the impacts of various important parameters such as aggregation and waviness factor, wave number and opening angles are examined.

Wave Dispersion Behavior in Quasi-Solid State Concrete Hydration.

This paper aims to investigate wave dispersion behavior in the quasi-solid state of concrete to better understand microstructure hydration interactions. The quasi-solid state refers to the consistency of the mixture between the initial liquid-solid stage and the hardened stage, where the concrete has not yet fully solidified but still exhibits viscous behavior. The study seeks to enable a more accurate evaluation of the optimal time for the quasi-liquid product of concrete using both contact and noncontact sensors, as current set time measurement approaches based on group velocity may not provide a comprehensive understanding of the hydration phenomenon. To achieve this goal, the wave dispersion behavior of P-wave and surface wave with transducers and sensors is studied. The dispersion behavior with different concrete mixtures and the phase velocity comparison of dispersion behavior are investigated. The analytical solutions are used to validate the measured data. The laboratory test specimen with w/c = 0.5 was subjected to an impulse in a frequency range of 40 kHz to 150 kHz. The results demonstrate that the P-wave results exhibit well-fitted waveform trends with analytical solutions, showing a maximum phase velocity when the impulse frequency is at 50 kHz. The surface wave phase velocity shows distinct patterns at different scanning times, which is attributed to the effect of the microstructure on the wave dispersion behavior. This investigation delivers profound knowledge of hydration and quality control in the quasi-solid state of concrete with wave dispersion behavior, providing a new approach for determining the optimal time of the quasi-liquid product. The criteria and methods developed in this paper can be applied to optimal timing for additive manufacturing of concrete material for 3D printers by utilizing sensors.

The effect of fluid flow in the longitudinal fracture along a borehole axis on Stoneley wave propagation

The characterization of fractures is essential to increase the production of hydrocarbon and geothermal resources. In this study, we investigate the effect of the fluid flow in the longitudinal fracture along a borehole on the dispersion and attenuation behavior of Stoneley waves using numerical experiments. In general, incorporating a fracture with the aperture of several tens to hundreds of micrometers into 3D seismic modeling is challenging with high calculational costs. We develop a novel numerical scheme that includes a 2D fluid flow simulation embedded into a 3D wave propagation modeling to address this problem. We devise an approach for capturing the effects of the fluid flow in the fractures of arbitrary aperture widths, which could be much thinner than the grid spacing of a 3D wave propagation simulation. A comparison of the numerical results from our scheme with the analytical solution indicates good agreement, supporting the method’s validity. This developed scheme is applied to the coupled simulation between the Stoneley wave propagation along the borehole axis and induced fluid flow inside a longitudinal fracture with different fracture apertures, fluid viscosity, and dynamic hydraulic conductivity. The modified matrix pencil algorithm applied to the recorded waveforms estimates the dispersion and attenuation of the Stoneley mode. The numerical results reveal the effect of the fracture aperture and fluid viscosity on the dispersion and attenuation behavior of the Stoneley waves. Based on the results, we demonstrate our scheme is an innovative method for estimating the aperture of the fracture and viscosity of the fluid by analyzing the dispersion and attenuation properties of the Stoneley waves.

Nonlocal wave propagation analysis of a rotating nanobeam on a Pasternak foundation

In this paper, the wave propagation analysis of a cantilever rotating nanobeam modeled as a thin beam based on the Euler–Bernoulli theory on a Pasternak foundation has been investigated using the nonlocal theory of elasticity. The governing partial differential equation of motion for a uniform rotating nanobeam is derived using the Hamilton principle considering the nonlocal parameter of small scale effect. The Spectrum and dispersion relations of non-dimensional wave number are obtained analytically. The effect of changes of different parameters including nonlocal scale parameter, non-dimensional rotational speed, non-dimensional rotational wave frequency ratio, and shear stiffness of the Pasternak foundation on the wave dispersion behavior of the non-dimensional wave number and phase and group speeds dispersions for the rotating nanotube have been studied. It is observed that the wave dispersion characteristics of the rotating nanobeam are extremely influenced by rotational speed, wave number, nonlocal length scale parameter, and shear stiffness of the Pasternak foundation. Moreover, the propagated flexural wave has been shown to exhibit non-dispersive behavior at very high rotational speeds.

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.

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.

Multi-scale dispersive gradient elasticity model with rotation for the particulate composite

Research on the characteristics of composites material has received enormous interest in recent years. The multi-scale nature of composite material leads to employing advanced techniques. Moreover, the presence of a wave with the high-frequency source adds complexity to the analysis. In this paper, a novel multi-scale elasticity model was developed to predict the wave dispersion property of particulate composites. The methodology was based on the simultaneous participation of translational and rotational degrees of freedom in motion equations. The method scheme of gaining motion equations was accomplished by using Taylor's expansion as a continualization method. The framework of the motion equations and restrictions determined the layout of the lattice. The obtained lattice was a network of polydispersive particles in three-dimensional as a unit cell. The model proposed the inertia coefficient and dimension coefficient, which reflected the heterogeneity on the particulate composite. The theoretical results were then validated with experimental results. For this aim, concrete and mortar with the various classes of heterogeneity were nominated as a sample of particulate composite material. The nominated composites were prepared with different mixture schemes from geopolymer paste. The wave dispersion behavior of geopolymer specimens was established by measuring phase velocity in various frequencies. In addition to geopolymer products, experimental results from independent literature were scrutinized for concrete and mortar with cement binder. In the end, the capability of the presented parameters was indicated for realizing the state of concrete curing and features of the binder.

Small amplitude rayleigh-lamb wave propagation in a finitely deformed viscoelastic dielectric elastomer (DE) layer

In recent years, Dielectric elastomers (DEs) have received much interest for the dynamics applications as waveguide. However, predicting the wave propagation behavior in a DE medium is very challenging due to the complexity of the problem, which involves the delicate interplay between electromechanical coupling, large deformation, and particularly the intrinsic material viscoelasticity. In this paper, by integrating the state-of-art finite-deformation viscoelasticity theory into the framework of small-amplitude wave propagation superimposed on a finitely deformed medium, the Rayleigh-Lamb wave propagation in a viscoelastic DE medium is investigated. Simulation results demonstrate the effects of material viscosity, status of relaxation, external electrical load, and mechanical pre-stretch on the dispersion behavior of the wave. It is found that for both purely elastic and viscoelastic DE media, waves with certain frequencies could be filtered by actively tuning the electrical loads. Moreover, some interesting findings conclude that the material viscoelasticity may cause some significant changes in the wave dispersion behavior. Therefore, incorporating the material viscosity in modeling DE waveguide is expected to provide more accurate prediction on their performance. This work will help to better understand the fundamentals of wave propagation in DE media and trigger more innovative and optimal design for DE waveguide.

Wave propagation properties of rotationally symmetric lattices with curved beams.

In this study, we design a type of rotationally symmetric lattice with curved beams and investigate the wave propagation properties of the structure. The analytical model of the structure is established to obtain the mass and stiffness matrices first. Because the dimensions of the mass and stiffness matrices will become very large if the structure is meshed with a number of small elements, we introduce the symplectic solution method to overcome the above difficulties of solving the eigenvalue problem. The effects of geometrical parameters and slenderness ratios on the distributions of bandgaps and variations of group velocities are investigated. We also numerically investigate the dynamic wave dispersion behavior and the transient responses of displacement and transmission coefficients in lattices subjected to excitations. Excellent agreement is obtained between the results obtained by the symplectic solution method and numerical simulations. The special wave-attenuation property of this type of structure is demonstrated and validated through experimental testing. The measured transmission coefficients in lattices with different geometrical parameters and slenderness ratios are in good agreement with the numerical simulations. The work provides a method for calculating wave behaviors in lattices and obtains lower bandgaps and directional wave propagation.

Electron-Acoustic Solitary Waves in Fermi Plasma With Two-Temperature Electrons

Electron Acoustic waves in Fermi Plasma with two temperature electrons have various applications in space and laboratory-made plasma. In some dense plasma systems like the inside of compact stars, Fermi plasma is important. We have studied Fermi plasma system with three components, two temperature electrons, and ions. The hot electrons are mobile and produce restoring force to the system while cold electrons are immobile and produce inertia to the system. We have studied the dispersion behavior of electron acoustic waves in Fermi plasma with two temperature electrons and investigated its dependence with various plasma parameters. We have investigated KdV-B equation for the solitary profile of Fermi plasma with two temperature electrons and investigated its dependence with various plasma parameters.

Flexoelectric effects on wave propagation responses of piezoelectric nanobeams via nonlocal strain gradient higher order beam model

This paper is devoted to investigate the effects of the flexoelectric phenomenon on wave dispersion characteristics of piezoelectric nanobeams. Modified constitutive relations containing the flexoelectric effects are taken into account. The problem is formulated utilizing Reddy’s higher order shear deformation beam theory in conjunction with the nonlocal strain gradient theory (NSGT). Additionally, Hamilton’s principle is employed to derive the governing equations of the problem. Thereafter, considering harmonic wave dispersion, the solution of equations of motion is expressed as complex form. Applying this solution to the governing equations gives rise to the eigenvalue problem. Afterwards, the eigenvalue problem is solved analytically to achieve the wave frequencies and phase velocities of the system. Totally, the role of various involved parameters namely the flexoelectric effects and applied electric voltage on the wave dispersion curves is studied in detail. In addition, the size-dependency of the flexoelectric phenomenon on wave dispersion behavior of the nanobeam is explored. Due to the fact that adequate knowledge about wave dispersion characteristics of structures is of great value especially in nanotechnology field, it is hoped that the results presented here may be helpful for exact behavior determination of piezoelectric nano-structures.

Polarization effects on wave propagation characteristics of piezoelectric coupled laminated fiber-reinforced composite cylindrical shells

Wave characteristics are investigated in piezoelectric-coupled laminated fiber-reinforced composite cylindrical shells by considering the transverse shear effects, rotary inertia, and different polarizations of the piezoelectricity for the first time. The novelty of this study is to present a complete mathematical model to evaluate wave behavior in a laminated fiber-reinforced composite cylindrical shell coupled by the piezoelectric layer with different polarizations and considering the transverse shear effects and rotary inertia. Dispersion solutions for different wave modes are obtained by solving an eigenvalue problem. The effects of the piezoelectricity and its polarization on the wave dispersion behavior in different composites are studied. For different piezoelectric poling directions, the influences of laminate stacking sequence and fiber orientation on dispersion curves are investigated. The results of this study can be used for solving a wave propagation problem in smart composite shell structures considering different piezoelectric effects for dynamic stability evaluation and health monitoring.

Tunability of the Brewster angle and dispersion type of the asymmetric graphene-based hyperbolic metamaterials

In this paper, the reflection and transmission properties of the plane electromagnetic waves are investigated at the interface of an asymmetric graphene-based hyperbolic metamaterial composed of alternating stacks of graphene monolayers and dielectric layers. It is shown that the Brewster angle can be changed by tailoring the orientation of the optical axis of the considered structure as well as the chemical potential of the graphene. Furthermore, the propagation of the wave vectors and Poynting vectors are studied in the given structure. Such structures have singlet dispersion behavior for the transverse electric wave and triplet dispersion behavior for the transverse magnetic wave. These types of dispersion can be switched by modifying the orientation of the optical axis, the chemical potential of the graphene, and the frequency of the impinging wave. Such tunability characteristics of the graphene-based metamaterials may be practical to design optical devices such as hyperlenses and tunable optical filters.

Wave dispersion characteristics of heterogeneous nanoscale beams via a novel porosity-based homogenization scheme

The important effect of porosity on the mechanical behaviors of a continuum, makes it necessary to be accounted for while analyzing the structure. Motivated by this fact, a new porosity-dependent homogenization scheme is presented in this article to investigate the wave propagation responses of functionally graded (FG) nanobeams by considering the coupling effects between density and Young’s moduli in porous materials. In the introduced homogenization method, which is a modified form of the power-law model, dependency of effective Young’s modulus to the mass density is covered. Based on the Hamilton principle, the Navier equations are developed using the Euler-Bernoulli beam model. Thereafter, the constitutive equations are obtained employing the nonlocal elasticity theory of Eringen. Next, the governing equations are solved in order to reach the wave frequency. Once the validity of presented methodology is proved, a set of parametric studies are adopted to emphasize the role of each variant on the wave dispersion behaviors of porous FG nanobeams.

Measured power law attenuation of shear waves in swine liver

To characterize the attenuation and dispersion behavior of shear waves in excised swine liver samples, the complex shear modulus was measured with a Rheospectris C500 + from 10 Hz to 2000 Hz. The shear wave attenuation and shear wave speed were calculated from the complex modulus measurements. A power law fit was evaluated for the shear wave attenuation, and a power law fit with and without a constant offset was evaluated for the shear wave speed. The power law closely matches the measured shear wave attenuation over most of the frequency range evaluated, although some differences are observed in several of the samples below 400 Hz. The power law without the constant offset closely matches the measured shear wave speed above 200 Hz in all measurements, where the addition of the constant offset achieves a much closer fit in all measurements that contain discrepancies below 200 Hz. The results demonstrate that shear wave attenuation in swine liver follows a power law and that a power law with a constant offset is an effective model for the shear wave speed in swine liver. [Work supported in part by NIH Grants DK092255, EB023051, and EB012079.]

Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams

In this article, the wave dispersion analysis of heterogeneous functionally graded (FG) nanosize beams is undertaken in the framework of a nonlocal strain gradient higher-order beam theory. Shear deformation effects are completely included free from any additional shear correction coefficient by the means of a refined sinusoidal beam theorem. Furthermore, the small scale effects are covered based on the nonlocal strain gradient elasticity theory. This is proven that the aforementioned theory is powerful enough to guesstimate the behavior of the nanostructures better than formerly presented ones. In fact, both stiffness-softening and -hardening characteristics of nanosize elements are coupled together in this theory. On the other hand, the equivalent material properties are achieved utilizing the rule of mixture. The motion equations are derived extending the dynamic version of the principle of virtual work. Thereafter, the size-dependent partial differential equations of the problem are solved based on an exponential solution function to reach the circular wave frequency. Next, some graphical examples are presented to investigate the influences of various parameters on the wave propagation behaviors of FG nanobeams.

Wave propagation in piezoelectric cylindrical composite shells reinforced with angled and randomly oriented carbon nanotubes

Wave propagation behavior in piezoelectric cylindrical composite shells reinforced with angled and randomly oriented, straight carbon nanotubes (CNTs) is analytically investigated for the first time via the first-order shear deformation shell theory including the transverse shear effects and rotary inertia. The Mori-Tanaka method is used for micromechanical modeling. Dispersion solutions are computed by solving an eigenvalue problem. The effects of CNT orientation, CNT volume fraction, and shell geometry on the dispersion solutions are examined. Various orientations of CNTs lead to different dispersion behaviors; the variation of wave phase velocities is more significant at lower axial wave numbers; and the effects of CNT volume fraction and shell geometry on wave dispersion behaviors are more obvious at higher circumferential wave numbers. The presented model and analytical results of this study can be utilized in the wave propagation analysis of piezoelectric shells reinforced with CNTs for the design of new smart structures used in structural health monitoring and/or energy harvesting applications.

Experimental demonstration of a dissipative multi-resonator metamaterial for broadband elastic wave attenuation

Elastic metamaterials (EMMs) encompass a relatively new class of composite materials that exhibit unique dynamic effective material properties and possess the ability to mitigate or even completely inhibit the propagation of acoustic/elastic waves over specific frequency spectrums (band gaps). However, it is extremely difficult to achieve broadband energy absorption with single resonance based EMMs. Dissipative EMMs with multiple resonators have recently been suggested for the attenuation of elastic wave energy spanning broad frequency spectrums. In this study, we fabricate a dissipative EMM with multiple resonators comprised from layered spherical inclusions embedded in an epoxy matrix and experimentally demonstrate broadband elastic wave mitigation. An analytical solution combined with numerical simulations is used to validate the accuracy of the fabrication based on a single unit cell test. We also numerically investigate the dynamic wave dispersion behavior of the fabricated dissipative EMM and find that the two strong attenuation regions induced by the two internal resonators can be effectively combined into a broadband wave attenuation region by the intrinsic damping properties of the constitutive materials used in the design. This broadband wave attenuation is finally demonstrated through an impact test performed on finite EMM samples where the frequency spectrum of the transmitted amplitude is in very good agreement with the numerical results. This design can be easily scaled and implemented into different length scales, which will benefit a range of applications requiring broadband vibration, elastic wave, and/or seismic wave mitigation.