Search results for: wave propagation time

Authors: N. Fusun Oyman Serteller

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In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations

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Authors: Abdelghani Leghouchi

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This study aims to predict the consequences associated with the propagation of the flood wave that may occur after the failure of the Taksebt dam and suggest an efficient emergency action plan (EAP) for mitigation purposes. To achieve the objectives of this study, the hydrodynamic model HEC-RAS 2D was used for the flood routing of the dam break wave, which gave an estimate of the hydraulic characteristics downstream the Taksebt dam. Geospatial analysis of the simulation results conducted in a Geographic information system (GIS) environment showed that many residential areas are considered to be in danger in case of the Taksebt dam break event. Based on the obtained results, an emergency actions plan was suggested to moderate the causalities in the downstream area at risk. Overall, the present study showed that the integration of 2D hydraulic modeling and GIS provides great capabilities in providing realistic view of the dam break wave propagation that enhances assessing the associated risks and proposing appropriate mitigation measures.

Keywords: taksebt dam, dam break, wave propagation time, HEC-RAS 2D

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Authors: Edip Kemal, Sheshov Vlatko, Bojadjieva Julijana, Bogdanovic ALeksandra, Gjorgjeska Irena

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The wave propagation phenomenon in porous domains is of great importance in the field of geotechnical earthquake engineering. In these kinds of problems, the elastic waves propagate from the interior to the exterior domain and require special treatment at the computational level since apart from displacement in the solid-state there is a p-wave that takes place in the pore water phase. In this paper, a study on the implementation of multiphase finite elements is presented. The proposed algorithm is implemented in the ANSYS finite element software and tested on one-dimensional wave propagation considering both pore pressure wave propagation and displacement fields. In the simulation of porous media such as soils, the behavior is governed largely by the interaction of the solid skeleton with water and/or air in the pores. Therefore, coupled problems of fluid flow and deformation of the solid skeleton are considered in a detailed way.

Keywords: wave propagation, multiphase model, numerical methods, finite element method

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Authors: Fathi Alwafie

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In this paper we present the simulation of the propagation characteristics of the picocellular propagation channel environment. The first aim has been to find a correct description of the environment for received wave. The result of the first investigations is that the environment of the indoor wave significantly changes as we change the electric parameters of material constructions. A modified 3D ray tracing image method tool has been utilized for the coverage prediction. A detailed analysis of the dependence of the indoor wave on the wide-band characteristics of the channel: Root Mean Square (RMS) delay spread characteristics and mean excess delay, is also investigated.

Keywords: propagation, ray tracing, network, mobile computing

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Authors: Rohit Shrivastava, Stefan Luding

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A mechanical wave is propagation of vibration with transfer of energy and momentum. Studying the energy as well as spectral energy characteristics of a propagating wave through disordered granular media can assist in understanding the overall properties of wave propagation through inhomogeneous materials like soil. The study of these properties is aimed at modeling wave propagation for oil, mineral or gas exploration (seismic prospecting) or non-destructive testing for the study of internal structure of solids. The study of Energy content (Kinetic, Potential and Total Energy) of a pulse propagating through an idealized one-dimensional discrete particle system like a mass disordered granular chain can assist in understanding the energy attenuation due to disorder as a function of propagation distance. The spectral analysis of the energy signal can assist in understanding dispersion as well as attenuation due to scattering in different frequencies (scattering attenuation). The selection of one-dimensional granular chain also helps in studying only the P-wave attributes of the wave and removing the influence of shear or rotational waves. Granular chains with different mass distributions have been studied, by randomly selecting masses from normal, binary and uniform distributions and the standard deviation of the distribution is considered as the disorder parameter, higher standard deviation means higher disorder and lower standard deviation means lower disorder. For obtaining macroscopic/continuum properties, ensemble averaging has been used. Interpreting information from a Total Energy signal turned out to be much easier in comparison to displacement, velocity or acceleration signals of the wave, hence, indicating a better analysis method for wave propagation through granular materials. Increasing disorder leads to faster attenuation of the signal and decreases the Energy of higher frequency signals transmitted, but at the same time the energy of spatially localized high frequencies also increases. An ordered granular chain exhibits ballistic propagation of energy whereas, a disordered granular chain exhibits diffusive like propagation, which eventually becomes localized at long periods of time.

Keywords: discrete elements, energy attenuation, mass disorder, granular chain, spectral energy, wave propagation

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Authors: Sumit Kumar Vishawakarma, Tapas Ranjan Panihari

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The article investigates the propagation behavior of SV-wave, SH-wave, and P-wave in a continuously inhomogeneous cross-anisotropic material, where the material properties such as Young's moduli, shear modulus, and density vary as an arbitrary continuous function of depth. In the considered model, Hook's law, strain-displacement relations along with equilibrium equations have been used to derive the governing equation. The mathematical formulation of this physical problem gives rise to an eigenvalue problem with displacement components as fundamental variables. This leads to achieving the closed-form expressions for quasi-wave velocities of SV-wave, SH-wave, and P-wave in the considered framework. These characteristics of wave propagation along with the above-stated variation have been scrutinized based on their numerical results. This parametric study reveals that wave velocity remarkably fluctuates as the magnitude of inhomogeneity parameters increases and decreases. The prominent effect has been shown depicting the dependence of wave velocity on the degree of material anisotropy. The influence of phase angle and depth of the medium has been remarkably established. The present study may facilitate the theoretical foundation and practical application in the field of earthquake source mechanisms.

Keywords: cross-anisotropic, inhomogeneity, P-wave, SH-wave, SV-wave, shear modulus, Young’s modulus

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Authors: Soniya Chaudhary

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The present study analyses the propagation of Love wave in rotating piezoelectric layer lying over an elastic substrate with corrugated boundaries. The appropriate solutions in the considered medium satisfy the required boundary conditions to obtain the dispersion relation of Love wave for charge free as well as electrically shorted cases. The effects of rotation are shown by graphically on the non-dimensional speed of the Love wave. In addition to classical case, some existing results have been deduced as particular case of the present study. The present study may be useful in rotation sensor and SAW devices.

Keywords: corrugation, dispersion relation, love wave, piezoelectric

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Authors: Arash Ghahraman, Gyula Bene

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The object of this study is to investigate the effect of viscosity on the propagation of free-surface waves in an incompressible viscous fluid layer of arbitrary depth. While we provide a more detailed study of properties of linear surface waves, the description of fully nonlinear waves in terms of KdV-like (Korteweg-de Vries) equations is discussed. In the linear case, we find that in shallow enough fluids, no surface waves can propagate. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for any given horizontal wave number. The numerical results show that there can be two types of non-propagating modes. One type is always present, and there exist still infinitely many of such modes at the same parameters. In contrast, there can be zero, one or two modes belonging to the other type. Another significant feature is that KdV-like equations. They describe propagating nonlinear viscous surface waves. Since viscosity gives rise to a new wavenumber that cannot be small at the same time as the original one, these equations may not exist. Nonetheless, we propose a reasonable nonlinear description in terms of 1+1 variate functions that make possible successive approximations.

Keywords: free surface wave, water waves, KdV equation, viscosity

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Authors: Tukeaban Hasanova, Jamila Imamalieva

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By the operational method, the problem on two-dimensional wave propagation in elastic medium excited by the round cylinder is solved. An analytical solution responding to instantaneous application of speed to the inclusion at its subsequent change is constructed. The two-dimensional problem on wave propagation in an elastic medium is considered.

Keywords: cylinder, inclusion, wave, elastic medium, speed

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Authors: Ding Yu, Ge Yang, Wang Hong-Tao

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Aiming at the detonation performance and detonation wave propagation distance of liquid fuel detonation engine, the kerosene/oxygen-enriched air mixture is chosen as the research object; its detonation initiation and detonation wave propagation process by mild energy input are numerically studied by using Euler-Lagrange method in the present study. The effects of a semicircular obstacle, rectangular obstacle, and triangular obstacle on the detonation characteristic parameters in the detonation tube are compared and analyzed, and the effect of the angle between obstacle and flame propagation direction on flame propagation characteristics and detonation process when the blocking ratio is constant are studied. The results show that the flame propagation velocity decreases with the increase of the angle in the range of 0-90°, and when the angle is 0° which corresponds to the semicircle obstacle gets the highest detonation wave propagation velocity. With the increase of the angle in the range of 0-90°, DDT (Deflagration to detonation transition) distance decreases first and then increases.

Keywords: deflagration to detonation transition, numerical simulation, obstacle structure, turbulent flame

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Authors: H. Samadiyeh, R. Khajavi

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A new FD-based procedure, modal finite difference method (MFDM), is proposed for seismic wave propagation modeling, in which simulation is dealt with in the modal space. The method employs eigenvalues of a characteristic matrix formed by appropriate time-space FD stencils. Since MFD runs for different modes are totally independent of each other, MFDM can easily be parallelized while considerable simplicity in parallel-algorithm is also achieved. There is no requirement to any domain-decomposition procedure and inter-core data exchange. More important is the possibility to skip processing of less-significant modes, which enables one to adjust the procedure up to the level of accuracy needed. Thus, in addition to considerable ease of parallel programming, computation and storage costs are significantly reduced. The method is qualified for its efficiency by some numerical examples.

Keywords: Finite Difference Method, Graphics Processing Unit (GPU), Message Passing Interface (MPI), Modal, Wave propagation

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Authors: Soniya Chaudhary, Sanjeev Sahu

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Propagation of Rayleigh-type waves in a rotating piezoelectric plate is investigated. The materials are assumed to be transversely isotropic crystals. The frequency equation have been derived for electrically open and short cases. Effect of rotation and piezoelectricity have been shown. It is also found that piezoelectric material properties have an important effect on Rayleigh wave propagation. The result is relevant to the analysis and design of various acoustic surface wave devices constructed from piezoelectric materials also in SAW devices.

Keywords: rotation, frequency equation, piezoelectricity, rayleigh-type wave

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Authors: Abhinav Singhal, Sanjeev A. Sahu

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Propagation of Rayleigh-type surface waves in an initially stressed piezomagnetic half- space with irregular boundary is investigated. The materials are assumed to be transversely isotropic crystals. The dispersion relations have been derived for electrically open and short cases. Effect of initial stress and corrugation have been shown graphically. It is also found that piezomagnetic material properties have an important effect on wave propagation. The result is relevant to the analysis and design of various acoustic surface wave devices constructed from piezomagnetic materials.

Keywords: corrugation, frequency equation, piezomagnetic, rayleigh-type wave

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Authors: Nan Tang, Bin Wu, Cunfu He

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The trapezoid rods are widely used in civil engineering as load –carrying members. Ultrasonic guided wave is one of the most popular techniques in analyzing the propagation of elastic guided wave. The goal of this paper is to investigate the propagation of elastic waves in the isotropic bar with trapezoid cross-section. Dispersion curves that describe the relationship between the frequency and velocity provide the fundamental information to describe the propagation of elastic waves through a structure. Based on the SAFE (semi-analytical finite element) a linear algebraic system of equations is obtained. By using numerical methods, dispersion curves solved for the rods with the trapezoid cross-section. These fundamental information plays an important role in applying ultrasonic guided waves to NTD for structures with trapezoid cross section.

Keywords: guided wave, dispersion, finite element method, trapezoid rod

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Authors: R. K. Apalowo, D. Chronopoulos, V. Thierry

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A wave finite element (WFE) and finite element (FE) based computational method is presented by which the dispersion properties as well as the wave interaction coefficients for one-dimensional structural system can be predicted. The structural system is discretized as a system comprising a number of waveguides connected by a coupling joint. Uniform nodes are ensured at the interfaces of the coupling element with each waveguide. Then, equilibrium and continuity conditions are enforced at the interfaces. Wave propagation properties of each waveguide are calculated using the WFE method and the coupling element is modelled using the FE method. The scattering of waves through the coupling element, on which damage is modelled, is determined by coupling the FE and WFE models. Furthermore, the central aim is to evaluate the effect of pressurization on the wave dispersion and scattering characteristics of the prestressed structural system compared to that which is not prestressed. Numerical case studies are exhibited for two waveguides coupled through a coupling joint.

Keywords: Finite Element, Prestressed Structures, Wave Finite Element, Wave Propagation Properties, Wave Scattering Coefficients.

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Authors: Fatemeh Nemati, Lucinda Leonard, Gwyn Lintern, Richard Thomson

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In this study, we will use modern numerical modeling approaches to estimate tsunami risks to the southern coast of British Columbia from landslides. Wave generation is to be simulated using the NHWAVE model, which solves the Navier-Stokes equations due to the more complex behavior of flow near the landslide source; far-field wave propagation will be simulated using the simpler model FUNWAVE_TVD with high-order Boussinesq-type wave equations, with a focus on the accurate simulation of wave propagation and regional- or coastal-scale inundation predictions.

Keywords: FUNWAVE-TVD, landslide-generated tsunami, NHWAVE, tsunami risk

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Authors: Chih-Hua Chang

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This study uses a three-dimensional (3D) fully nonlinear model to simulate the wave generation problem caused by the movement of the seabed. The numerical model is first simplified into two dimensions and then compared with the existing two-dimensional (2D) experimental data and the 2D numerical results of other shallow-water wave models. Results show that this model is different from the earlier shallow-water wave models, with the phase being closer to the experimental results of wave propagation. The results of this study are also compared with those of the 3D experimental results of other researchers. Satisfactory results can be obtained in both the waveform and the flow field. This study assesses the application of the model to simulate the wave caused by the circular (radius r0) terrain rising or falling (moving distance bm). The influence of wave-making parameters r0 and bm are discussed. This study determines that small-range (e.g., r0 = 2, normalized by the static water depth), rising, or sinking terrain will produce significant wave groups in the far field. For large-scale moving terrain (e.g., r0 = 10), uplift and deformation will potentially generate the leading solitary-like waves in the far field.

Keywords: seismic wave, wave generation, far-field waves, seabed deformation

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Authors: Kyoungjin Kim

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Nanoscale thermites such as the composite mixture of nano-sized aluminum and molybdenum trioxide powders possess several technical advantages such as much higher reaction rate and shorter ignition delay, when compared to the conventional energetic formulations made of micron-sized metal and oxidizer particles. In this study, the self-propagation of combustion wave in compacted pellets of nanoscale thermite composites is modeled and computationally investigated by utilizing the activation energy reduction of aluminum particles due to nanoscale particle sizes. The present computational model predicts the speed of combustion wave propagation which is good agreement with the corresponding experiments of thermite reaction. Also, several characteristics of thermite reaction in nanoscale composites are discussed including the ignition delay and combustion wave structures.

Keywords: nanoparticles, thermite reaction, combustion wave, numerical modeling

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Authors: M. Eskandarighadi, C. R. McGann

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It is observed from past experiences of earthquakes that local site conditions can significantly affect the strong ground motion characteristicssuch as frequency content, amplitude, and duration of seismic waves. The most common method for investigating site response is one-dimensional seismic site response analysis. The infinite horizontal length of the model and the homogeneous characteristic of the soil are crucial assumptions of this method. One boundary condition that can be used in the sides is tying the sides horizontally for vertical 1D wave propagation. However, 1D analysis cannot account for the 2D nature of wave propagation in the condition where the soil profile is not fully horizontal or has heterogeneity within layers. Therefore, 2D seismic site response analysis can be used to take all of these limitations into account for a better understanding of local site conditions. Different types of boundary conditions can be appliedin 2D site response models, such as tied boundary condition, massive columns, and free-field boundary condition. The tied boundary condition has been used in 1D analysis, which is useful for 1D wave propagation. Employing two massive columns at the sides is another approach for capturing the 2D nature of wave propagation. Free-field boundary condition can simulate the free-field motion that would exist far from the domain of interest. The goal for free-field boundary condition is to minimize the unwanted reflection from sides. This research focuses on the comparison between these methods with examples and discusses the details and limitations of each of these boundary conditions.

Keywords: boundary condition, free-field, massive columns, opensees, site response analysis, wave propagation

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Authors: Kshitish Ch. Mistri, Abhishek Kumar Singh

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The effect of undulatory boundary surface of a medium as well as the degree of bonding between two consecutive mediums, on the propagation of surface waves is an unavoidable matter of fact. Therefore, this paper investigates the propagation of Rayleigh-type wave in a corrugated fibre-reinforced layer overlying an initially stressed orthotropic half-space under gravity. Also, the two mediums are assumed to be loosely (or imperfectly) bonded. Numerical computation of the obtained frequency equation has been carried out which aids to analyze the influence of corrugation, loose bonding, initial stress and gravity on the phase velocity of Rayleigh-type wave. Moreover, the presence and absence of corrugation, loose bonding and initial stress are also discussed in a comparative manner.

Keywords: corrugated boundary surface, fibre-reinforced layer, initial stress, loose bonding, orthotropic half-space, Rayleigh-type wave

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Authors: A. Keshavarz

Abstract:

A physical model for guiding the wave in photorefractive media is studied. Propagation of cos-Gaussian beam as the special cases of sinusoidal-Gaussian beams in photorefractive crystal is simulated numerically by the Crank-Nicolson method in one dimension. Results show that the beam profile deforms as the energy transfers from the center to the tails under propagation. This simulation approach is of significant interest for application in optical telecommunication. The results are presented graphically and discussed.

Keywords: beam propagation, cos-Gaussian beam, numerical simulation, photorefractive crystal

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Authors: Mahmood Heshmati, Farhang Daneshmand

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Material scientists and engineers have introduced novel materials with complex geometries due to the recent technological advances and promotion of manufacturing methods. Among them, lattice structures with graded architectures denoted by functionally graded porous materials (FGPMs) have been developed to optimize the structural response. FGPMs are achieved by tailoring the size and density of the internal pores in one or more directions that lead to the desired mechanical properties and structural responses. Also, FGPMs provide more flexible transition and the possibility of designing and fabricating structural elements with complex and variable properties. In this paper, wave propagation in lattice structures with functionally graded (FG) porosity is investigated in order to examine the ability of shock absorbing effect. The behavior of FG porous beams with different porosity distributions under impact load and the effects of porosity distribution and porosity content on the wave speed are studied. Important conclusions are made, along with a discussion of the future scope of studies on FGPMs structures.

Keywords: functionally graded, porous materials, wave propagation, impact load, finite element

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Authors: Yi Wang, Xun Liang

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This paper introduces a model of internet public opinion waves, which describes the message propagation and measures the influence of a detected event. We collect data on public opinion propagation from different platforms on the internet, including micro-blogs and news. Then, we compare the spread of public opinion to the seismic waves and correspondently define the P-wave and S-wave and other essential attributes and characteristics in the process. Further, a model is established to evaluate the magnitude scale of the events. In the end, a practical example is used to analyze the influence of network public opinion and test the reasonability and effectiveness of the proposed model.

Keywords: internet public opinion waves (IPOW), magnitude scale, cross-platform, information propagation

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Authors: Amrita Das, Abhishek Kumar Singh

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The present paper calibrates the efficacy of corrugated and loosely bonded common interface of a viscoelastic layer and a dry sandy Gibson half-space on the propagation of torsional surface wave. Using suitable boundary conditions, the dispersion relation for the concerned problem is deduced in complex form. Numerical computation of the real part of the obtained dispersion relation gives the dispersion curve whereas the imaginary part bestows the damping curves. The use of Whittaker’s function and Bessel’s functions are among the major concerns of the paper. The investigation of the influence of the affecting parameters viz. heterogeneities, sandiness, Biot’s gravity parameter, initial stresses, loosely bonded interface, corrugation and internal friction on the phase velocity as well as damped velocity of torsional wave, through numerical discussion and graphical illustration, is among the major highlights of the current study.

Keywords: corrugation, dry sandy Gibson half-space, loosely bonded interface, torsional wave, viscoelastic layer

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Authors: Yingchen Yang

Abstract:

Ocean waves are a rich renewable energy source that is nearly untapped to date, even though many wave energy conversion (WEC) technologies are currently under development. The present work discusses a vertical-axis WEC rotor for power generation. The rotor was specially designed to allow easy rearrangement of the same blades to achieve different rotor configurations and result in different wave-rotor interaction behaviors. These rotor configurations were tested in a wave tank under various wave conditions. The testing results indicate that all the rotor configurations perform unidirectional rotation about the vertical axis in waves, but the response characteristics are somewhat different. The rotor's unidirectional rotation about its vertical axis is essential in wave energy harvesting since it makes the rotor respond well in a wide range of the wave frequency and in any wave propagation directions. Result comparison among different configurations leads to a preferred rotor design for further hydrodynamic optimization.

Keywords: unidirectional rotation, vertical axis rotor, wave energy conversion, wave-rotor interaction

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Authors: Abhigna Bhatt, Arnab Banerjee

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A periodic system with only a single coupling degree of freedom is called a monocoupled system. Monocoupled systems with mechanisms like mass in the mass system generates effective negative mass, mass connected with rigid links generates inertial amplification, and spring-mass connected with a rigid link generateseffective negative stiffness. In this paper, the representative unit cell is introduced, considering all three mechanisms combined. Further, the dynamic stiffness matrix of the unit cell is constructed, and the dispersion relation is obtained by applying the Bloch theorem. The frequency response function is also calculated for the finite length of periodic unit cells. Moreover, the input displacement signal is given to the finite length of periodic structure and using inverse Fourier transform to visualize the wave propagation in the time domain. This visualization explains the sudden attenuation in metamaterial due to energy dissipation by an embedded resonator at the resonance frequency. The visualization created for wave propagation is found necessary to understand the insights of physics behind the attenuation characteristics of the system.

Keywords: mono coupled system, negative effective mass, negative effective stiffness, inertial amplifier, fourier transform

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Authors: Alireza Abdikian

Abstract:

By assuming a quantum relativistic degenerate electron-positron (e-p) plasma media, the nonlinear acoustic solitary propagation in the presence of the stationary ions for neutralizing the plasma background of bounded cylindrical geometry was investigated. By using the standard reductive perturbation technique with cooperation the quantum hydrodynamics model for the e-p fluid, the spherical Kadomtsev-Petviashvili equation was derived for small but finite amplitude waves and was given the solitary wave solution for the parameters relevant for dense astrophysical objects such as white dwarf stars. By using a suitable coordinate transformation and using improved F-expansion technique, the SKP equation can be solved analytically. The numerical results reveal that the relativistic effects lead to propagate the electrostatic bell shape structures and by increasing the relativistic effects, the amplitude and the width of the e-p acoustic solitary wave will decrease.

Keywords: Electron-positron plasma, Acoustic solitary wave, Relativistic plasmas, the spherical Kadomtsev-Petviashvili equation

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Authors: Benoit Rougier, Alexandre Lefrancois, Herve Aubert

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Microwave interrogation in the range 10-100 GHz is identified as an advanced technique to investigate simultaneously shock and particle velocity measurements. However, it requires the understanding of electromagnetic wave propagation in a multi-layered moving media. The existing models limit their approach to wave guides or evaluate the velocities with a fitting method, restricting therefore the domain of validity and the precision of the results. Moreover, few data of permittivity on high explosives at these frequencies under dynamic compression have been reported. In this paper, shock and particle velocities are computed concurrently for steady and unsteady shocks for various inert and reactive materials, via a propagation model based on Doppler shifts and signal amplitude. Refractive index of the material under compression is also calculated. From experimental data processing, it is demonstrated that Hugoniot curve can be evaluated. The comparison with published results proves the accuracy of the proposed method. This microwave interrogation technique seems promising for shock and detonation waves studies.

Keywords: electromagnetic propagation, experimental setup, Hugoniot measurement, shock propagation

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Authors: Kizito Ugochukwu Nwajeria

Abstract:

This paper presents a spectral quasi-linearization technique (SQLT) for solving time fractional diffusion wave equations in boundary value problems. The proposed method integrates spectral approximations for spatial derivatives with a quasi-linearization approach to address the nonlinearity introduced by fractional time derivatives. Time fractional differential equations typically formulated using Caputo or Riemann-Liouville derivatives, model complex phenomena such as anomalous diffusion and wave propagation, which are not captured by classical integer-order models. The SQLT method iteratively linearizes the nonlinear terms at each time step, transforming the original problem into a series of linear subproblems, which can be efficiently solved. Using high-order spectral methods such as Chebyshev or Legendre polynomials for spatial discretization, the technique achieves high accuracy in approximating the solution. A convergence analysis is provided, demonstrating the method's efficiency and establishing error bounds. Numerical experiments on a range of test problems confirm the effectiveness of SQLT in solving fractional diffusion wave equations with various boundary conditions. The method offers a robust framework for addressing time fractional differential equations in diverse fields, including materials science, bioengineering, and anomalous transport phenomena.

Keywords: spectral methods, quasilinearization, time-fractional diffusion-wave equations, boundary value problems, fractional calculus

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Authors: Tzong-Ying Hao, Mohammad T. Rahmani

Abstract:

The Torre Central building is a 9-story shear wall structure located in Santiago, Chile, and has been instrumented since 2009. Events of different intensity (ambient vibrations, weak and strong earthquake motions) have been recorded, and thus the building can serve as a full-scale benchmark to evaluate the structural health monitoring method developed. The first part of this article presents an analysis of inter-story drifts, and of changes in the first system frequencies (estimated from the relative displacement response of the 8th-floor with respect to the basement from recorded data) as baseline indicators of the occurrence of damage. During 2010 Chile earthquake the system frequencies were detected decreasing approximately 24% in the EW and 27% in NS motions. Near the end of shaking, an increase of about 17% in the EW motion was detected. The structural health monitoring (SHM) method based on changes in wave traveling time (wave method) within a layered shear beam model of structure is presented in the second part of this article. If structural damage occurs the velocity of wave propagated through the structure changes. The wave method measures the velocities of shear wave propagation from the impulse responses generated by recorded data at various locations inside the building. Our analysis and results show that the detected changes in wave velocities are consistent with the observed damages. On this basis, the wave method is proven for actual implementation in structural health monitoring systems.

Keywords: Chile earthquake, damage detection, earthquake response, impulse response, layered shear beam, structural health monitoring, Torre Central building, wave method, wave travel time

Procedia PDF Downloads 364