• Title/Summary/Keyword: dispersion equations

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Active Dispersion-Correction Scheme of 2-D Finite Element Model for Simulation of Tsunami Propagation (지진해일 전파 수치모의를 위한 2차원 유한요소모형의 능동적 분산보정기법)

  • Yoon Sung Bum;Lim Chae Ho
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.17 no.1
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    • pp.1-8
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    • 2005
  • For the simulation of tsunami propagation an active dispersion-correction two-dimensional finite element model has been developed based on a shallow-water wave equation. This model employs an arbitrary triangular mesh and an explicit time integration scheme. However, the physical dispersion effects as included in the Boussinesq equations can be taken into account in the computation. The validity of the dispersion-correction scheme developed in this study is verified through the comparison of numerical solutions calculated using the new scheme with analytical ones considering dispersion effect of waves. As a result, the present model is shown to be considerably accurate.

Effective time-frequency characterization of Lamb wave dispersion in plate-like structures with non-reflecting boundaries

  • Wang, Zijian;Qiao, Pizhong;Shi, Binkai
    • Smart Structures and Systems
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    • v.21 no.2
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    • pp.195-205
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    • 2018
  • Research on Lamb wave-based damage identification in plate-like structures depends on precise knowledge of dispersive wave velocity. However, boundary reflections with the same frequency of interest and greater amplitude contaminate direct waves and thus compromise measurement of Lamb wave dispersion in different materials. In this study, non-reflecting boundaries were proposed in both numerical and experimental cases to facilitate time-frequency characterization of Lamb wave dispersion. First, the Lamb wave equations in isotropic and laminated materials were analytically solved. Second, the non-reflecting boundaries were used as a series of frames with gradually increased damping coefficients in finite element models to absorb waves at boundaries while avoiding wave reflections due to abrupt property changes of each frame. Third, damping clay was sealed at plate edges to reduce the boundary reflection in experimental test. Finally, the direct waves were subjected to the slant-stack and short-time Fourier transformations to calculate the dispersion curves of phase and group velocities, respectively. Both the numerical and experimental results suggest that the boundary reflections are effectively alleviated, and the dispersion curves generated by the time-frequency analysis are consistent with the analytical solutions, demonstrating that the combination of non-reflecting boundary and time-frequency analysis is a feasible and reliable scheme for characterizing Lamb wave dispersion in plate-like structures.

Simulation of the Dispersion of Air Pollutants in the Shihwa Area (시화지구의 대기오염물질 확산에 관한 전산모사)

  • Song, Eun-Seok;Yoo, Jin-Bog;Kim, Byoung-Su;Yi, Sung-Chul;Hong, Min-Sun;Jang, Young-Kee
    • Journal of Environmental Impact Assessment
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    • v.7 no.1
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    • pp.35-48
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    • 1998
  • Gaussian type models have limitations on predicting a detailed description of the near flow and pollution leads over complex terrains under neutral atmospheric conditions. Also, most models used recently have lack of ability to include atmospheric reactions. The model based on the numerical solution of the time-averaged Navier-Stokes equations and conservation equations needs to be developed to improve the limitations mentioned above. When the model was applied to the Shihwa area where the tracer experiment had been carried out, the simulation results have a great difference from the experimental results. There are two reasons that make the difference between the results by the model and the experiment. First, the Shihwa area is not a complex terrain. Second, meteorological data is insufficient. Therefore, the model should be applied to predict the dispersion of air pollutants over complex terrain rather than flat terrain in order that the model could be verified because the model was developed for the prediction of the dispersion over a complex terrain.

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Longitudinal Thermal Dispersion Enhancement by Oscillating Flow in a Grooved Channel (그루브 채널에서 왕복 유동에 의한 열확산 촉진에 관한 연구)

  • Kim, Seo-Young;Kim, Su-Hyeon;Kang, Byung-Ha
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.29 no.10 s.241
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    • pp.1075-1082
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    • 2005
  • The characteristics of longitudinal dispersion enhancement by the flow oscillation are numerically studied according to various groove geometries in a 2-D channel in the present study. The length of expanded section l$_{1}$/h$_{1}$ is varied from 0 to 8.75. The oscillating flow condition is given at both side ends, i.e., u = Asin ($2{\pi}ft$) The non-dimensional temperatures at both side ends are set to zero. The bottom and top walls are adiabatic. The local heat sources are located at the middle of the groove wall. In order to solve the governing equations, the SIMPIER algorithm is employed. The present results indicate that maximum longitudinal thermal dispersion can be achieved when the area ratio of the expanded section to the contracted section in the grooved channel becomes 1.

Finite difference TVD scheme for modeling two-dimensional advection-dispersion

  • Guan, Y.;Zhang, D.
    • Proceedings of the Korea Water Resources Association Conference
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    • 2006.05a
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    • pp.22-27
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    • 2006
  • This paper describes the development of the stream-tube based dispersion model for modeling contaminant transport in open channels. The operator-splitting technique is employed to separate the 2D contaminant transport equation into the pure advection and pure dispersion equations. Then the total variation diminishing (TVD) schemes are combined with the second-order Lax-Wendroff and third-order QUICKEST explicit finite difference schemes respectively to solve the pure advection equation in order to prevent the occurrence of numerical oscillations. Due to various limiters owning different features, the numerical tests for 1D pure advection and 2D dispersion are conducted to evaluate the performance of different TVD schemes firstly, then the TVD schemes are applied to experimental data for simulating the 2D mixing in a straight trapezoidal channel to test the model capability. Both the numerical tests and model application show that the TVD schemes are very competent for solving the advection-dominated transport problems.

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Analytical wave dispersion modeling in advanced piezoelectric double-layered nanobeam systems

  • Ebrahimi, F.;Haghi, P.;Dabbagh, A.
    • Structural Engineering and Mechanics
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    • v.67 no.2
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    • pp.175-183
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    • 2018
  • This research deals with the wave dispersion analysis of functionally graded double-layered nanobeam systems (FG-DNBSs) considering the piezoelectric effect based on nonlocal strain gradient theory. The nanobeam is modeled via Euler-Bernoulli beam theory. Material properties are considered to change gradually along the nanobeams' thickness on the basis of the rule of mixture. By implementing a Hamiltonian approach, the Euler-Lagrange equations of piezoelectric FG-DNBSs are obtained. Furthermore, applying an analytical solution, the dispersion relations of smart FG-DNBSs are derived by solving an eigenvalue problem. The effects of various parameters such as nonlocality, length scale parameter, interlayer stiffness, applied electric voltage, relative motions and gradient index on the wave dispersion characteristics of nanoscale beam have been investigated. Also, validity of reported results is proven in the framework of a diagram showing the convergence of this model's curve with that of a previous published attempt.

TM and TE Modes in Multiple-Ridged Circular Waveguides (다중 Ridge 원형 도파관의 TM과 TE 모우드 해석)

  • 유종원;명노훈
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.7 no.5
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    • pp.440-446
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    • 1996
  • The multiple-ridged circular waveguides is analyzed using Fourier series and the mode matching technique. The enforcement of the boundary conditions yields the simultaneous equations for the field coefficient inside the waveguides. The simultaneous equations are solved to represent a dispersion relation in an analytic series form. The numerical computation is performed to illustrate the behavior of the cutoff wavenumbers in terms of number, length and angle of ridges. The presented series solution is exact and rapidly-convergent so that it is efficient for numerical computation. A simple dispersion relation based on the dominant mode analysis is obtained and is shown to be very accurate for most practical applications.

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Torsional surface waves in a non-homogeneous isotropic layer over viscoelastic half-space

  • Kakar, Rajneesh;Gupta, Kishan Chand
    • Interaction and multiscale mechanics
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    • v.6 no.1
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    • pp.1-14
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    • 2013
  • The aim of this paper is to study the propagation of torsional surface waves in non-homogeneous isotropic layer of finite thickness placed over a homogeneous viscoelastic half-space, when both density and rigidity of the non-homogeneous medium are assumed to vary exponentially with depth. The frequency equations are obtained by using simple method of separation of variables. Further, it is seen that when viscoelastic parameter and non-homogeneity parameter is neglected, the dispersion equation gives the dispersion equations of Love waves in homogeneous, elastic and isotropic layer placed over homogeneous viscoelastic medium. The problem has been solved numerically and the effects of various inhomogeneities of the medium on torsional waves have been illustrated graphically.

Wave dispersion characteristics of porous graphene platelet-reinforced composite shells

  • Ebrahimi, Farzad;Seyfi, Ali;Dabbagh, Ali;Tornabene, Francesco
    • Structural Engineering and Mechanics
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    • v.71 no.1
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    • pp.99-107
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    • 2019
  • Wave propagation analysis of a porous graphene platelet reinforced (GPLR) nanocomposite shell is investigated for the first time. The homogenization of the utilized material is procured by extending the Halpin-Tsai relations for the porous nanocomposite. Both symmetric and asymmetric porosity distributions are regarded in this analysis. The equations of the shell's motion are derived according to Hamilton's principle coupled with the kinematic relations of the first-order shear deformation theory of the shells. The obtained governing equations are considered to be solved via an analytical solution which includes two longitudinal and circumferential wave numbers. The accuracy of the presented formulations is examined by comparing the results of this method with those reported by former authors. The simulations reveal a stiffness decrease in the cases which porosity influences are regarded. Also, one must pay attention to the effects of longitudinal wave number on the wave dispersion curves of the nanocomposite structure.

On propagation of elastic waves in an embedded sigmoid functionally graded curved beam

  • Zhou, Linyun;Moradi, Zohre;Al-Tamimi, Haneen M.;Ali, H. Elhosiny
    • Steel and Composite Structures
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    • v.44 no.1
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    • pp.17-31
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    • 2022
  • This investigation studies the characteristics of wave dispersion in sigmoid functionally graded (SFG) curved beams lying on an elastic substrate for the first time. Homogenization process was performed with the help of sigmoid function and two power laws. Moreover, various materials such as Zirconia, Alumina, Monel and Nickel steel were explored as curved beams materials. In addition, curved beams were rested on an elastic substrate which was modelled based on Winkler-Pasternak foundation. The SFG curved beams' governing equations were derived according to Euler-Bernoulli curved beam theory which is known as classic beam theory and Hamilton's principle. The resulted governing equations were solved via an analytical method. In order to validate the utilized method, the obtained outcomes were compared with other researches. Finally, the influences of various parameters, including wave number, opening angle, gradient index, Winkler coefficient and Pasternak coefficient were evaluated and indicated in the form of diagrams.