• Water for future
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• v.28 no.3
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• pp.205-216
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• 1995

Existing equations for dispersion coefficient are analyzed in depth to select proper dispersion coefficient which can represent dispersion characteristics of natural streams. Several equations are tested with measured data which were collected in 26 streams in the United States. Findings of this study are as follows. Elder's equation should not be used to estimate dispersion coefficient of the one-dimensional dispersion model because it underestimates significantly. McQuivey and Keefer's equation is overestimating, whereas Magazine et al.'s equation is underestimating. However, Iwasa and Aya's equation predicts relatively well. Fischer's equation is generally overestimating. Liu's equation predicts quite well. The performance of Liu's equation is the best of all especially in terms of accuracy. However, Liu's equation is generally overestimating in case of large river because the square of channel width is included in the equation. Therefore, it is recommended not to use Liu's equation in case of large rivers, especially rivers of which channel width is larger than 200m.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.4
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• pp.197-200
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• 1999

An extension of the modified leap-frog scheme is made to solve the nonlinear shallow-water equations. In the extended model. the physical dispersion of the Boussinesq equations is replaced by the numerical dispersion resulted from the leap-frog finite difference scheme. The model is used to simulate propagations of a solitary wave over a constant water depth and a linearly varying water depth. Obtained numerical results are compared with available analytical and other numerical solutions. A reasonable agreement is observed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.5B
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• pp.551-555
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• 2006

In this study, new dispersion-correction terms are added to a leap-frog finite difference scheme for the linear shallow-water equations with the purpose of considering dispersion effects of the linear Boussinesq equations for propagation of tsunamis. The numerical model developed in this study is tested to the problem that the initial free surface displacement is a Gaussian hump over a constant water depth, and the predicted numerical results are compared with analytical solutions. The results of the present numerical model are accurate in comparison with those of existing models.

• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.701-711
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• 2018

Herein, the thermo-magneto-elastic wave dispersion answers of functionally graded (FG) double-nanobeam systems (DNBSs) are surveyed implementing a nonlocal strain gradient theory (NSGT). The kinematic relations are derived employing the classical beam theory. Also, scale influences are covered precisely in the framework of NSGT. Moreover, Mori-Tanaka homogenization model is introduced in order to obtain the effective material properties of FG nanobeams. Meanwhile, effects of external forces such as thermal and Lorentz forces are included in this research. Also, based upon the Hamilton's principle, the Euler-Lagrange equations are developed; afterwards, these equations are incorporated with those of NSGT to reach the nonlocal governing equations of FG-DNBSs. Furthermore, according to an analytical approach, the governing equations are solved to obtain the wave frequencies and phase velocities of FG-DNBSs. At the end, some illustrations are rendered to clarify the influences of a wide range of involved parameters.

• Coupled systems mechanics
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• v.13 no.3
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• pp.247-275
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• 2024

The paper studies the influence of the fluid flow velocity and flow direction in the initial state on the dispersion of the axisymmetric waves propagating in the inhomogeneously pre-stressed hollow cylinder containing this fluid. The corresponding eigenvalue problem is formulated within the scope of the three-dimensional linearized theory of elastic waves in bodies with initial stresses, and with linearized Euler equations for the inviscid compressible fluid. The discrete-analytical solution method is employed, and analytical expressions of the sought values are derived from the solution to the corresponding field equations by employing the discrete-analytical method. The dispersion equation is obtained using these expressions and boundary and related compatibility conditions. Numerical results related to the action of the fluid flow velocity and flow direction on the influence of the inhomogeneous initial stresses on the dispersion curves in the zeroth and first modes are presented and discussed. As a result of the analyses of the numerical results, it is established how the fluid flow velocity and flow direction act on the magnitude of the influence of the initial inhomogeneous stresses on the wave propagation velocity in the cylinder containing the fluid.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.5
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• pp.1785-1795
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• 2013

Most of the previous models for analysis of shallow water flow assumed the uniform velocity distributions over the flow depth so that they produced incorrect velocity prediction at meandering part due to the ignorance of secondary current. In this study, the vertical velocity profiles in longitudinal and transverse direction were decomposed as the mean and variation components, which resulted in additional dispersion stresses terms in momentum equations. The proposed model were applied at the channels with $30^{\circ}$, $90^{\circ}$, $270^{\circ}$ bends, and shallow water flow in curved channel was analyzed using dispersion stresses. The dispersion stresses acted as a sink or source in the momentum equations, which caused the transverse convection of momentum to shift from the inner bank to the outer bank.

• ETRI Journal
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• v.35 no.5
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• pp.827-837
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• 2013

In this paper, we present wideband common-mode (CM) noise suppression using a vertical stepped impedance electromagnetic bandgap (VSI-EBG) structure for high-speed differential signals in multilayer printed circuit boards. This technique is an original design that enables us to apply the VSI-EBG structure to differential signals without sacrificing the differential characteristics. In addition, the analytical dispersion equations for the bandgap prediction of the CM propagation in the VSIEBG structure are extracted, and the closed-form expressions for the bandgap cutoff frequencies are derived. Based on the dispersion equations, the effects of the impedance ratio, the EBG patch length, and via inductances on the bandgap of the VSI-EBG structure for differential signals are thoroughly examined. The proposed dispersion equations are verified through agreement with the full-wave simulation results. It is experimentally demonstrated that the proposed VSI-EBG structure for differential signaling suppresses the CM noise in the wideband frequency range without degrading the differential characteristics.

• Structural Engineering and Mechanics
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• v.39 no.6
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• pp.861-875
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• 2011

The aim of the present article is to study the micropolar thermoelastic interactions in an infinite Kelvin-Voigt type viscoelastic thermally conducting plate. The coupled dynamic thermoelasticity and generalized theories of thermoelasticity, namely, Lord and Shulman's and Green and Lindsay's are employed by assuming the mechanical behaviour as dynamic to study the problem. The model has been simplified by using Helmholtz decomposition technique and the resulting equations have been solved by using variable separable method to obtain the secular equations in isolated mathematical conditions for homogeneous isotropic micropolar thermo-viscoelastic plate for symmetric and skew-symmetric wave modes. The dispersion curves, attenuation coefficients, amplitudes of stresses and temperature distribution for symmetric and skew-symmetric modes are computed numerically and presented graphically for a magnesium crystal.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.30 no.9
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• pp.589-595
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• 2017

MOS-FET structured gas sensors were manufactured using MWCNTs for application as NOx gas sensors. As the gas sensors need to be heated to facilitate desorption of the gas molecules, heat dispersion plays a key role in boosting the degree of uniformity of molecular desorption. We report the desorption of gas molecules from the sensor at $150^{\circ}C$ for different sensor electrode gaps (30, 60, and $90{\mu}m$). The COMSOL analysis program was used to verify the process of heat dispersion. For heat analysis, structure of FET gas sensor modeling was proceeded. In addition, a property value of the material was used for two-dimensional modeling. To ascertain the degree of heat dispersion by FEM, the governing equations were presented as partial differential equations. The heat analysis revealed that although a large electrode gap is advantageous for effective gas adsorption, consideration of the heat dispersion gradient indicated that the optimal electrode gap for the sensor is $60{\mu}m$.

• Structural Engineering and Mechanics
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• v.58 no.2
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• pp.347-378
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• 2016

Within the scope of the plane-strain state, by utilizing the three-dimensional linearized theory of elastic waves in initially stressed piezoelectric and elastic materials, Lamb wave propagation and the influence of the initial stresses on this propagation in a sandwich plate with pre-stressed piezoelectric face and pre-stressed metal elastic core layers are investigated. Dispersion equations are derived for the extensional and flexural Lamb waves and, as a result of numerical solution to these equations, the corresponding dispersion curves for the first (fundamental) and second modes are constructed. Concrete numerical results are obtained for the cases where the face layers' materials are PZT-2 or PZT-6B, but the material of the middle layer is Steel (St) or Aluminum (Al). Sandwich plates PZT-2/St/PZT-2, PZT-2/Al/PZT-2, PZT-6B/St/PZT-6B and PZT-6B/Al/PZT-6B are examined and the influence of the problem parameters such as piezoelectric and dielectric constants, layer thickness ratios and third order elastic constants of the St and Al on the effects of the initial stresses on the wave propagation velocity is studied.