• Magazine of the Korean Society of Agricultural Engineers
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• v.38 no.3
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• pp.50-57
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• 1996

A numerical method is presented to obtain the natural frequencies and mode shapes of the arbitrary tapered beams with static deflection due to arbitrary distributed dead loads. The differential equation governing free vibration of such beams is derived and solved numerically. The double integration method using the trapezoidal rule is used to solve the static behaviour of beams loaded arbitrary distributed dead load. Also, the Improved Euler method and the determinant search method are used to integrate the differential equation subjected to the boundary conditions and to determine the natural frequencies of the beams, respectively. In the numerical examples, the various geometries of the beams are considered : (1) linearly tapered beams as the arbitrary variable cross-section, (2) the triangular, sinusoidal and uniform loads as the arbitrary distributed dead loads and (3) the hinged-hinged, clamped-clamped and hinged-clamped ends as the end constraints. All numerical results are shown as the non-dimensional forms of the system parameters. The lowest three natural frequencies versus load parameter, slenderness ratio and section ratio are reported in figures. And for the comparison purpose, the typical mode shapes with and without the effects of static deflection are presented in the figure. According to the numerical results obtained in this analysis, the following conclusions may be drawn : (1) the natural frequencies increase when the effects of static deflections are included, (2) the effects are larger at the lower modes than the higher ones and (3) it should be betteF to include the effect of static deflection for calculating the frequencies when the beams are supported by both hinged ends or one hinged end.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.45-54
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• 1991

The closed forms of mass matrix with rotational inertia matrix are developed for free vibration analysis in space structures containing linearing tapered members with cross section of thin-walled tube. The exact displacement functions are used for formulating mass matrix. The very small slopes of the tapered member are used in usual practice, such that the series expansion forms of these are also developed to avoid numerical failure in vibration analysis. Significant improvements of accuracy and efficiency of free vibration analysis are achieved by using the mass matrices developed in this study. Frequencies of free vibration of tapered members are compared with solutions based upon stepped representation of beam element.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.7 no.2
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• pp.167-177
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• 1996

The cutoff frequencies of a double ridged rectangular waveguide are calculated by applying the modal analysis to its cross-section. And the characteristic impedance of its $TE_{10}$ mode is evaluated in a frequency range of 6 to 18 GHz. When both ends of a linearly tapered rectangular wa- veguide consists of single and double ridged rectangular cross-sections, the equivalent nonuniform transmission line of its $TE_{10}$ mode is solved numerically. It is shown that the input impedance at its single ridged terminal becomes nearly constant in the wide bandwidth.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.5
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• pp.40-45
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• 2008

In this paper, a microstrip linear tapered slot antenna is designed. A tapered slot antenna(TSA) has many advantages such as low profile, low weight, easy fabrication, and compatibility with monolithic microwave integrated circuits(MMIC). In addition, it has demonstrated multi octave bandwidth, moderately high gain, and symmetrical E- and H-plane beam patterns. A feed network is implemented with transition between a microstrip and a slot line for the microstrip linear tapered slot antenna. The transition is consist of two sides. One side has a microstrip line, the other side has a slot line. The dimensions of the microstrip and slot line are ${\lambda}_m/4$ and ${\lambda}_s/4$ at the center of the cross section of the microstrip and slot line. In order to get broad bandwidth antenna characteristics, the tapered length is chosen as $4{\lambda}_o$ and termination width is chosen as $1.75{\lambda}_o$. Experimental results show that the microstrip tapered slot antenna has symmetrical E- and H-plane beam patterns with around 5GHz of bandwidth at center frequency of 5.0GHz.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.17-26
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• 1991

Numerical methods are developed to obtain the critical loads and to analyze the post-buckling behaviour of the linearly varying tapered columns. The non-dimensional differential equations governing the elastica of post buckled column are derived by third order and solved numerically using the Runge-Kutta method and Regula-Falsi method. Three kinds of cross-sectional shape with simply supported end constraint are applied in unmerical examples. As the numerical results, the equlibrium paths. the typical elastica of post buckled columns and the critical load vs. section ratio curves are presented in figures. Also, the effects of cross-sectional shape factor on critical loads and postbuckling behaviour are presented in tables.

• Journal of Korean Society of Steel Construction
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• v.13 no.6
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• pp.683-691
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• 2001

Numerical methods are developed for solving the elastica and buckling load of tapered columns with shear deformation, subjected to a compressive end load. The linear, parabolic and sinusoidal tapers with the regular polygon cross-sections are considered, whose material volume and span length are always held constant. The differential equations governing the elastica of buckled column are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine the rotation at left end and the buckling load, respectively. The numerical methods developed herein for computing the elastica and the buckling loads of the columns are found to be efficient and reliable.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2A
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• pp.155-162
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• 2009

This paper deals with the strongest beams with the solid regular polygon cross-section, whose volumes are always held constant. The differential equation of the elastic deflection curve of such beam subjected to the concentrated and trapezoidal distributed loads are derived and solved numerically. The Runge-Kutta method and shooting method are used to integrate the differential equation and to determine the unknown initial boundary condition of the given beam. In the numerical examples, the simple beams are considered as the end constraint and also, the linear, parabolic and sinusoidal tapers are considered as the shape function of cross sectional depth. As the numerical results, the configurations, i.e. section ratios, of the strongest beams are determined by reading the section ratios from the numerical data related with the static behaviors, under which static maximum behaviors become to be minimum.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.3A
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• pp.251-258
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• 2009

This paper deals with the strongest beams with the solid regular polygon cross-section, whose volumes are always held constant. The differential equation of the elastic deflection curve of such beam subjected to the concentrated and trapezoidal distributed loads are derived and solved by using the double integration method. The Simpson's formula was used to numerically integrate the differential equation. In the numerical examples, the clamped-clamped and clamped-hinged ends are considered as the end constraints and the linear, parabolic and sinusoidal tapers are considered as the shape function of cross sectional depth. As the numerical results, the configurations, i.e. section ratios, of the strongest beams are determined by reading the section ratios from the numerical data obtained in this study, under which static maximum behaviors become to be minimum.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.703-711
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• 2018

In this paper is studied the effect of considering the theory of Timoshenko in the vibration of AFG beams that support ground masses. As it is known, Timoshenko theory takes into account the shear deformation and the rotational inertia, provides more accurate results in the general study of beams and is mandatory in the case of high frequencies or non-slender beams. The Rayleigh-Ritz Method is employed to obtain approximated solutions of the problem. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study. The incidence of the Timoshenko theory is analyzed for different cases of beam slenderness, variation of its cross section and compositions of its constituent material, as well as different amounts and positions of the attached masses.

• Proceedings of the Korea Concrete Institute Conference
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• 2010.05a
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• pp.459-460
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• 2010

For the application of slip form method to the pylon of Yi Sun-shin bridge which has much variation in its cross section, the change of setting properties of concrete due to changing weather and long pumping distance has to be taken into consideration. Different setting properties of several types of cement according to the amount of compound and ambient temperature were observed in this paper.