Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

A COUNTER PROPAGATING WAVE STATE WITH A PERIODICALLY HORIZONTAL MOTION OF DEFECTS

Convection in a horizontal fluid layer heated from below is one of models for studying patterns of convection in binary fluid mixtures and has been extensively studied. In this article, the convection structures in a rectangular cell were investigated for the aspect-ratio Г= 12 and the separation ratio ψ = -0.47. Simulations were preformed by solving the hydrodynamic equations using the SIMPLE method. A Counter Propagating Wave （CPW） state was found in binary fluid convection with a periodically horizontal motion of defects, and the pattern dynamics was further discuss.

Optical properties of the electromagnetic waves propagating in an elliptical cylinder multilayer structure

Theoretical description of the wave propagation in an elliptical cylinder multilayer structure under the conditions of H polarization and E polarization is presented. A transfer matrix method has been developed for elliptical cylinder waves. The formulas of reflection and transmission coefficients for an elliptical cylinder multilayer structure are driven. Reflection and transmission coefficients of elliptical cylinder waves by a single elliptical cylinder interface is presented. The obtained formulas can be generalized to the cold plasma filled structures and thus the obtained results in the limit of circular cylinder structures are investigated.

Parametric Instabilities of Parallel Propagating Circularly Polarized Alfven Waves:One-Dimensional Hybrid Simulations

By performing one-dimensional （l-D） hybrid simulations, we analyze in detail the parametric instabilities of the Alfv^n waves with a spectrum in a low beta plasma. The parametric instabilities experience two stages. In the first stage, the density modes are excited and immediately couple with the pump Alfv6n waves. In the second stage, each pump Alfv^n wave decays into a density mode and a daughter Alfv6n mode similar to the monochromatic cases. Ftlrthermore, the proton velocity beam will also be formed after the saturation of the parametric instabilities. When the plasma beta is high, the parametric decay in the second stage will be strongly suppressed.

Study on the Propagation and Focusing Mechanism of Long Waves over A Submerged Atoll

An analytical solution for long waves propagating over a submerged atoll is established. The atolls involved in this study are annular coral reefs with large lagoons in the middle, and the expression of the cross section is a trinomial function of the radial distance, i.e., h=ar(2s)-br~s+h_0, where s is the positive rational number. This analytical solution extends the theory by Wang et al.(2018) as s is no longer limited to s=2/m, where m is the positive integer. In addition, by adjusting the terrain parameters properly, the analytic solution can be degenerated to describe the wave propagation over topography with a hump or pit. According to the relationship between wave rays and wave energy, the distribution characteristics and formation mechanism of energy over the topography are expounded. When the lagoon is non-existent, all wave rays converge at the x-axis, which results in an abrupt amplification of the wave amplitude around the convergence point. When a lagoon is mounted on the top of the atoll, the rays are scattered due to the refraction of the lagoon, and only some rays converge at the symmetrical axis and the ridges on both sides,which results in the amplification of wave amplitudes in these areas.

Effect of porous surface layer on wave propagation in elastic cylinder immersed in fluid

To study the damage to an elastic cylinder immersed in fluid, a model of an elastic cylinder wrapped with a porous medium immersed in fluid is designed. This structure can both identify the properties of guided waves in a more practical model and address the relationship between the cylinder damage degree and the surface and surrounding medium. The principal motivation is to perform a detailed quantitative analysis of the longitudinal mode and flexural mode in an elastic cylinder wrapped with a porous medium immersed in fluid. The frequency equations for the propagation of waves are derived each for a pervious surface and an impervious surface by employing Biot theory. The influences of the various parameters of the porous medium wrapping layer on the phase velocity and attenuation are discussed. The results show that the influences of porosity on the dispersion curves of guided waves are much more significant than those of thickness,whereas the phase velocity is independent of the static permeability. There is an apparent “mode switching” between the two low-order modes. The characteristics of attenuation are in good agreement with the results from the dispersion curves.This work can support future studies for optimizing the theory on detecting the damage to cylinder or pipeline.

On wave dispersion of rotating viscoelastic nanobeam based on general nonlocal elasticity in thermal environment

The present research focuses on the analysis of wave propagation on a rotating viscoelastic nanobeam supported on the viscoelastic foundation which is subject to thermal gradient effects.A comprehensive and accurate model of a viscoelastic nanobeam is constructed by using a novel nonclassical mechanical model.Based on the general nonlocal theory(GNT),Kelvin-Voigt model,and Timoshenko beam theory,the motion equations for the nanobeam are obtained.Through the GNT,material hardening and softening behaviors are simultaneously taken into account during wave propagation.An analytical solution is utilized to generate the results for torsional(TO),longitudinal(LA),and transverse(TA)types of wave dispersion.Moreover,the effects of nonlocal parameters,Kelvin-Voigt damping,foundation damping,Winkler-Pasternak coefficients,rotating speed,and thermal gradient are illustrated and discussed in detail.

Wave propagation responses of porous bi-directional functionally graded magneto-electro-elastic nanoshells via nonlocal strain gradient theory

This study examines the wave propagation characteristics for a bi-directional functional grading of barium titanate(BaTiO_(3)) and cobalt ferrite(CoFe_(2)O_(4)) porous nanoshells,the porosity distribution of which is simulated by the honeycomb-shaped symmetrical and asymmetrical distribution functions.The nonlocal strain gradient theory(NSGT) and first-order shear deformation theory are used to determine the size effect and shear deformation,respectively.Nonlocal governing equations are derived for the nanoshells by Hamilton's principle.The resulting dimensionless differential equations are solved by means of an analytical solution of the combined exponential function after dimensionless treatment.Finally,extensive parametric surveys are conducted to investigate the influence of diverse parameters,such as dimensionless scale parameters,radiusto-thickness ratios,bi-directional functionally graded(FG) indices,porosity coefficients,and dimensionless electromagnetic potentials on the wave propagation characteristics.Based on the analysis results,the effect of the dimensionless scale parameters on the dispersion relationship is found to be related to the ratio of the scale parameters.The wave propagation characteristics of nanoshells in the presence of a magnetoelectric field depend on the bi-directional FG indices.

Multi-axial unsplit frequency-shifted perfectly matched layer for displacement-based anisotropic wave simulation in infinite domain

Multi-axial perfectly matched layer(M-PML),known to have lost the perfect-matching property owing to multi-axial coordinate stretching,has been numerically validated to be long-time stable and it is thus used extensively in linear anisotropic wave simulation and in isotropic cases where the PML becomes unstable.We are concerned with the construction of the M-PML for anisotropic wave simulation based on a second order wave equation implemented with the displacement-based numerical method.We address the benefit of the incorrect chain rule,which is implicitly adopted in the previous derivation of the M-PML.We show that using the frequency-shifted stretching function improves the absorbing efficiency of the M-PML for near-grazing incident waves.Then,through multi-axial complex-coordinate stretching the second order anisotropic wave equation in a weak form,we derive a time-domain multi-axial unsplit frequency-shifted PML(M-UFSPML)using the frequency-shifted stretching function and the incorrect chain rule.A new approach is provided to reduce the number of memory variables needed for computing convolution terms in the M-UFSPML.The obtained M-UFSPML is well suited for implementation with a finite element or the spectral element method.By providing several typical examples,we numerically verify the accuracy and long-time stability of the implementation of our M-UFSPML by utilizing the Legendre spectral element method.

Intrinsic Wave Velocity Propagation:A Novel Parameter for Assessing the Effect of Anthracycline Chemotherapy Agents on Cardiac Diastolic Function in Breast Cancer Patients

Objective Anthracycline chemotherapeutic agents have significant cardiotoxicity.The present study emphasized the effect of anthracycline chemotherapy drugs on left ventricular(LV)myocardial stiffness in breast cancer patients by measuring the intrinsic wave velocity propagation(IVP),and evaluating the potential clinical value of IVP in detecting early LV diastolic function impairment.Methods A total of 68 newly diagnosed breast cancer patients,who were treated with anthracycline-based chemotherapy,were analyzed.Transthoracic echocardiography was performed at baseline(T0),and after 1,2,3,4 and 8 chemotherapeutic cycles(T1,T2,T3,T4 and T5,respectively).Then,the IVP,LV strain parameters[global longitudinal strain(GLS),longitudinal peak strain rate at systole(LSRs),longitudinal peak strain rate at early diastole(LSRe),longitudinal peak strain rate at late diastole(LSRa),and the E/LSRe ratio],and conventional echocardiographic parameters were obtained and further analyzed.A relative reduction of>15%in GLS was considered a marker of early LV subclinical dysfunction.Results Compared to the T0 stage,IVP significantly increased at the T1 stage.However,there were no significant changes in GLS,LSRs,or LSRe between the T0 and T1 stages.These parameters significantly decreased from the T2 stage.LSRa started to significantly decrease at the T5 stage,and the E/LSRe ratio started to significantly increase at the T3 stage(all P<0.05).At the T0 stage,IVP(AUC=0.752,P<0.001)had a good predictive value for LV subclinical dysfunction after chemotherapy.Conclusions IVP is a potentially sensitive parameter for the early clinical assessment of anthracycline-related cardiac diastolic impairment.

TRANSIENT-STATE RESPONSE OF WAVE PROPAGATION IN MAGNETO-ELECTRO-ELASTIC SQUARE COLUMN

This is a continued work in studying the wave propagation in a magneto-electroelastic square column （MEESC）. Based on the analytic dispersive equation, group velocity equation and steady-state response obtained in our previous paper ＇Steady-state response of the wave propagation in a magneto-electro-elastic square column＇ published in CME, the dynamical behavior of MEESC was studied in this paper. The unlimited column is an open system. The transientstate response in the open system subjected by arbitrary external fields was derived when the propagating wave pursuing method was introduced.

Disintegration of Linear Edge Waves

It is demonstrated that offshore wavenumbers of edge waves change from imaginary wavenumbers in deep water to real wavenumbers in shallow water. This finding indicates that edge waves in the offshore direction exist as evanescent waves in deep water and as propagating waves in shallow water. Since evanescent waves can stably exist in a limited region while propagating waves cannot, energy should be released from nearshore regions. In the present study, the instability region is predicted based on both the full water wave solution and the shallow-water wave approximation.

Numerical analysis of moving train induced vibrations on tunnel,surrounding ground and structure

This study is focused on the effect of vibration induced by moving trains in tunnels on the surrounding ground and structures.A three-dimensional finite element model is established for a one-track railway tunnel and an adjacent twelve-storey building frame by using commercial software Midas GTS-NX(2019)and Midas Gen.This study considered the moving load effect of a complete train,which varies with space as well as with time.The effect of factors such as train speed,overburden pressure on the tunnel and variation in soil properties are studied in the time domain.As a result,the variations in horizontal and vertical acceleration for two different sites,i.e.,the free ground surface(without structure)and the area containing the structure,are compared.Also,the displacement pattern of the raft foundation is plotted for different train velocities.At lower speeds,the heaving phenomenon is negligible,but as the speed increases,both the heaving and differential settlement increase in the foundation.This study demonstrates that the effect of moving train vibrations should be considered in the design of new nearby structures and proper ground improvement should be considered for existing structures.

Effect of intermittent joint distribution on the mechanical and acoustic behavior of rock masses

The mechanical characteristics and acoustic behavior of rock masses are greatly influenced by stochastic joints.In this study,numerical models of rock masses incorporating intermittent joints with different numbers and dip angles were produced using the finite element method(FEM)with the intrinsic cohesive zone model(ICZM).Then,the uniaxial compressive and wave propagation simulations were performed.The results indicate that the joint number and dip angle can affect the mechanical and acoustic properties of the models.The uniaxial compressive strength(UCS)and wave velocity of rock masses decrease monotonically as the joint number increases.However,the wave velocity grows monotonically as the joint dip angle increases.When the joint dip angle is 45°–60°,the UCS of the rock mass is lower than that of other dip angles.The wave velocity parallel to the joints is greater than that perpendicular to the joints.When the dip angle of joints remains unchanged,the UCS and wave velocity are positively related.When the joint dip angle increases,the variation amplitude of the UCS regarding the wave velocity increases.To reveal the effect of the joint distribution on the velocity,a theoretical model was also proposed.According to the theoretical wave velocity,the change in wave velocity of models with various joint numbers and dip angles was consistent with the simulation results.Furthermore,a theoretical indicator(i.e.fabric tensor)was adopted to analyze the variation of the wave velocity and UCS.

Study of the propagation direction of the internal waves in the South China Sea using satellite images

Internal wave propagation carries considerable vertical shear which can lead to turbulence and mixing. Based on the analysis of more than 2 500 synthetic aperture radar （SAR） and optical satellite images, the in- ternal wave propagation in the whole South China Sea was investigated systematically. The results show that （1） in the northeastern South China Sea, most internal waves propagate westward from the Luzon Strait and are diffracted by coral reefs near the Dongsha Islands. Some impinge onto the shelf and a few are reflected; （2） in the northwestern South China Sea, most internal waves are generated at the shelf and propagate northwestward or westward to the coast; （3） in the western South China Sea, most internal waves propagate westward to the Vietnamese coast, except a few propagate southward to the deep sea; and （4） in the southern South China Sea, most internal waves propagate southwestward to the coast. Some prop- agate southeastward to the coast of Kalimantan Island, and a few propagate southeastward because of the influence of the Mekon~ River.

Scattering of SH waves induced by a symmetrical V-shaped canyon: a unified analytical solution

This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.

Dynamic mechanical properties and wave propagation of composite rock-mortar specimens based on SHPB tests

Filled inclusions in rock discontinuities play a key role in the mechanical characteristics of the rock and thereby influence the stability of rock engineering. In this study, a series of impact tests were performed using a split Hopkinson pressure bar system with high-speed photography to investigate the effect of interlayer strength on the wave propagation and fracturing process in composite rock-mortar specimens.The results indicate that the transmission coefficient, nominal dynamic strength, interlayer closure, and specific normal stiffness generally increase linearly with increasing interlayer stiffness. The cement mortar layer can serve as a buffer during the deformation of composite specimens. The digital images show that tensile cracks are typically initiated at the rock-mortar interface, propagate along the loading direction, and eventually result in a tensile failure regardless of the interlayer properties. However, when a relatively weaker layer is sandwiched between the rock matrix, an increasing amount of cement mortar is violently ejected and slight slabbing occurs near the rock-mortar interface.

Experimental verification of effect of horizontal inhomogeneity of evaporation duct on electromagnetic wave propagation

The evaporation duct which forms above the ocean surface has a significant influence on electromagnetic wave propagation above 2 GHz over the ocean. The effects of horizontal inhomogeneity of evaporation duct on electromagnetic wave propagation are investigated, both in numerical simulation and experimental observation methods, in this paper. Firstly, the features of the horizontal inhomogeneity of the evaporation duct are discussed. Then, two typical inhomogeneous cases are simulated and compared with the homogeneous case. The result shows that path loss is significantly higher than that in the homogeneous case when the evaporation duct height （EDH） at the receiver is lower than that at the transmitter. It is also concluded that the horizontal inhomogeneity of the evaporation duct has a significant influence when the EDH is low or when the electromagnetic wave frequency is lower than 13 GHz. Finally, experimental data collected on a 149-km long propagation path in the South China Sea in 2013 are used to verify the conclusion. The experimental results are consis- tent with the simulation results. The horizontal inhomogeneity of evaporation duct should be considered when modeling electromagnetic wave propagation over the ocean.

Study on Far Field Wave Patterns and Their Characteristics of Havelock Form Green Function

A new mathematical integral representation including five integrals about the far field wave shape fimction of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase curves and propagation wave patterns are investigated by applying stationary phase analysis method to the new representation. Some findings are summarized as follows： （1） when 0〈r 〈0.25 （where r is the Strouhal number）, three types of stationary phase curves corresponding to three propagation wave patterns such as fan wave pattern, inner V and outer V wave patterns, are found in the integral representation. （2） When r 〉0.25, besides three types of wave patterns such as a ring-faning wave pattern, a fan wave pattern and an inner V wave pattern, a new one called parallel wave pattern is also found which not only exists in the integrals about the ring-fan wave and fan wave, but also in the integrals whose interval is [0, 7＇] ~ In addition, Characteristics about these parallel waves such as mathematical expressions, existence conditions, propagation directions and wave lengths are obtained, and cancellation relationships between these parallel waves are stated, which certificates the fact that there are no parallel waves existing in the far field.

A Predictive 6G Network with Environment Sensing Enhancement:From Radio Wave Propagation Perspective

In order to support the future digital society,sixth generation(6G)network faces the challenge to work efficiently and flexibly in a wider range of scenarios.The traditional way of system design is to sequentially get the electromagnetic wave propagation model of typical scenarios firstly and then do the network design by simulation offline,which obviously leads to a 6G network lacking of adaptation to dynamic environments.Recently,with the aid of sensing enhancement,more environment information can be obtained.Based on this,from radio wave propagation perspective,we propose a predictive 6G network with environment sensing enhancement,the electromagnetic wave propagation characteristics prediction enabled network(EWave Net),to further release the potential of 6G.To this end,a prediction plane is created to sense,predict and utilize the physical environment information in EWave Net to realize the electromagnetic wave propagation characteristics prediction timely.A two-level closed feedback workflow is also designed to enhance the sensing and prediction ability for EWave Net.Several promising application cases of EWave Net are analyzed and the open issues to achieve this goal are addressed finally.