• Structural Engineering and Mechanics
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• v.76 no.1
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• pp.129-139
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• 2020

In this piece of work, carbon nanotubes motion equations are framed by Kelvin's method. Employment of the Kelvin's method procedure gives birth to the tube frequency equation. It is also exhibited that the effect of frequencies is investigated by varying the different index of polynomial function. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped, simply supported-simply supported and these frequency curves are higher than that of clamped-free curves. Computer software MATLAB is utilized for the frequencies of single-walled carbon nanotubes.

• Advances in concrete construction
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• v.9 no.3
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• pp.301-312
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• 2020

This research deals with the study of the orthotropic vibrational features of single-walled carbon nanotubes according to Kelvin's model and to check the accuracy of the models, the results have been compared with earlier modeling/simulations. Obtaining rough approximations of the natural frequencies of CNTs using continuum equations are still a common procedure, even at high harmonics. The effects of different physical and material parameters on the fundamental frequencies are investigated for zigzag and chiral single-walled carbon nanotubes invoking Kelvin's theory. By using nonlocal Kelvin's model, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes (SWCNTs) have been calculated. The influence of frequencies with nonlocal parameters and bending rigidity are investigated in detail for these tubes. Computer software MATLAB is utilized for the frequencies of SWCNTs and current results shows a good stability with comparison of other studies.

• Advances in nano research
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• v.8 no.3
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• pp.229-244
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• 2020

In this paper, modified Kelvin's model has been used to analyze the orthotropic vibration frequencies of single walled carbon nanotubes with clamped-clamped and clamped-free boundary conditions. For this system the governing equation is developed with wave propagation approach. Armchair, zigzag and chiral structures are considered for the vibrational analysis to investigate the effect of different modes, in-plane rigidity and mass density per unit lateral area. Throughout the computations, on decreasing the length-to-diameter ratios, the frequencies of said structure increases. In addition, by increasing three different value of in-plane rigidity resulting frequencies also increase and frequencies decrease on increasing mass density per unit lateral area. The results generated using computer software MATLAB to furnish the evidence regarding applicability of present model and also verified by available published literature.

• Journal of ILASS-Korea
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• v.2 no.1
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• pp.8-17
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• 1997

A study has been carried out on the instability of a conical liquid sheet by using the linear instability theory. Various analytical methods using the Kelvin-Helmholtz instability theory were tried to examine the wave growth on cylindrical liquid sheets. Cylinderical liquid sheets were extended to the case with the conical sheets. Perturbations due to tangential motion as well as longitudinal one were taken into account. And it was assumed the the breakup occurs when amplitude ratio exceeds exp(12), drop sizes were predicted only by theoretical approach. The predicted drop size agreed well with the measured Sauter mean diameter, $D_{32}$.

• Journal of ILASS-Korea
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• v.3 no.2
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• pp.1-13
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• 1998

A theoretical and experimental study was carried out to predict the drop size distribution of the pressure swirl atomizer. Various analytical methods using the Kelvin-Helmholtz instability theory were tried to examine the wave growth on cylindrical liquid sheets. Cylinderical liquid sheets were extended to the case with the conical sheets. Perturbations due to tangential motion as well as longitudinal one were taken into account. And it was assumed that the breakup occurs when amplitude ratio exceeds exp(12), drop sizes were predicted only by theoretical approach. Drop size distribution was obtained by using maximum entropy formalism. Seven constraints in the form of the definition of mean diameter were used in this formulation in order to avoid the difficulties of estimating source terms. In this study $D_{10}$ only was introduced into the formulation as a constraint. The predicted drop size and drop size distribution agreed well with the measured data.

• Coupled systems mechanics
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• v.5 no.2
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• pp.157-190
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• 2016

This paper deals with frequency analysis of Euler-Bernoulli beams carrying an arbitrary number of Kelvin-Voigt viscoelastic dampers, subjected to harmonic loads. Multiple external/internal dampers occurring at the same position along the beam axis, modeling external damping devices and internal damping due to damage or imperfect connections, are considered. The challenge is to handle simultaneous discontinuities of the response, in particular bending-moment/rotation discontinuities at the location of external/internal rotational dampers, shear-force/deflection discontinuities at the location of external/internal translational dampers. Following a generalized function approach, the paper will show that exact closed-form expressions of the frequency response under point/polynomial loads can readily be derived, for any number of dampers. Also, the exact dynamic stiffness matrix and load vector of the beam will be built in a closed analytical form, to be used in a standard assemblage procedure for exact frequency response analysis of frames.

• Journal of the Society of Naval Architects of Korea
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• v.37 no.4
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• pp.1-10
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• 2000

A panel method based on the raised panel approach is developed for the nonlinear ship wave problem of practical hull forms. For the validation of the present numerical scheme. the developed method is first applied to Series 60 hull for which the extensive experimental data are available. As practical applications. the developed method is applied to KRISO 3600 TEU container ship and KRISO 300K VLCC. With the primary emphasis on the nonlinear effects of the global wave pattern generated by the two commercial ships. the calculated wave patterns are compared and verified with the experiments of KRISO. It is found that the calculated results of the present method are quite satisfactory compared with the linear methods like Dawson's approach and Neumann-Kelvin solution.

• Nuclear Engineering and Technology
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• v.44 no.8
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• pp.871-888
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• 2012

This paper aims at presenting the state of the art, the recent progress, and the perspective for the future, in the modelling of two-phase flow in the horizontal legs of a PWR. All phenomena relevant for safety analysis are listed first. The selection of the modelling approach for system codes is then discussed, including the number of fluids or fields, the space and time resolution, and the use of flow regime maps. The classical two-fluid six-equation one-pressure model as it is implemented in the CATHARE code is then presented and its properties are described. It is shown that the axial effects of gravity forces may be correctly taken into account even in the case of change of the cross section area or of the pipe orientation. It is also shown that it can predict both fluvial and torrential flow with a possible hydraulic jump. Since phase stratification plays a dominant role, the Kelvin-Helmholtz instability and the stability of bubbly flow regime are discussed. A transition criterion based on a stability analysis of shallow water waves may be used to predict the Kelvin-Helmholtz instability. Recent experimental data obtained in the METERO test facility are analysed to model the transition from a bubbly to stratified flow regime. Finally, perspectives for further improvement of the modelling are drawn including dynamic modelling of turbulence and interfacial area and multi-field models.

• Coupled systems mechanics
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• v.2 no.4
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• pp.375-387
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• 2013

Soils consist of an assemblage of particles with different sizes and shapes which form a skeleton whose voids are filled with water and air. Hence, soil behaviour must be analyzed by incorporating the effects of the transient flow of the pore-fluid through the voids, and therefore requires a two-phase continuum formulation for saturated porous media. The present paper presents briefly the Biot's basic theory of dynamics of saturated porous media with u-P formulation to determine the responses of pore fluid and soil skeleton during cyclic loading. Kelvin elements are attached to transmitting boundary. The Pastor-Zienkiewicz-Chan model has been used to describe the inelastic behavior of soils under isotropic cyclic loadings. Newmark-Beta method is employed to discretize the time domain. The response of fluid-saturated porous media which are subjected to time dependent loads has been simulated numerically to predict the liquefaction potential of a semi-infinite saturated sandy layer using finite-infinite elements. A settlement of 17.1 cm is observed at top surface. It is also noticed that liquefaction occurs at shallow depth. The mathematical advantage of the coupled finite element analysis is that the excess pore pressure and displacement can be evaluated simultaneously without using any empirical relationship.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.4
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• pp.981-989
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• 1995

A new weight function approach to determine SIF(stress intensity factor) using single-layer potential has been presented. The crack surface displacement field was represented by one boundary integral term whose kernel was modified from Kelvin's fundamental solution. The proposed method enables the calculation of SIF using only one SIF solution without any modification for the crack geometries symmetric in two-dimensional plane such as a center crack in a plate with or without an internal hole, double edge cracks, circumferential crack or radial cracks in a pipe. The application procedure to those crack problems is very simple and straightforward with only one SIF solution. The necessary information in the analysis is two reference SIFs. The analysis results using present closed-form solution were in good agreement with those of the literature.