• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.13 no.1
• /
• pp.63-69
• /
• 2003

The ordinary differential equations governing free vibrations of elastic horizontally curved beams are derived, in which the effects of rotatory inertia and shear deformation as well as the effects of both vertical and torsional inertias are included. Frequencies and mode shapes are computed numerically for parabolic curved beams with the hinged-hinged, hinged-clamped and clamped-clamped ends. Comparisons of natural frequencies between this study and ADINA are made to validate the theories and numerical methods developed herein. The lowest three natural frequency parameters are reported. with and without the effects of rotatory inertia and shear deformation. as functions of the three non-dimensional system parameters: the horizontal rise to span length ratio. the slenderness ratio and the stiffness parameter.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.17 no.12
• /
• pp.1201-1207
• /
• 2007

The Timoshenko beam theories are used to model the rotating shaft. The nondimensional equations of motion for the rotating shaft subjected to moving mass and compressive axial forces are derived by using Hamilton's principle. Influence of system parameters such as the speed ratio. the mass ratio and the Rayleigh coefficient is discussed on the response of the moving system. The effects of compressive axial forces are also included in the analysis. The results are presented and compared with the available solutions of a rotating shaft subject to a moving mass and a moving load.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2002.10a
• /
• pp.11-16
• /
• 2002

The differential equations governing free vibrations of the elastic, horizontally curved beams with unsymmetric axis are derived in Cartesian coordinates rather than in polar coordinates, in which the effect of torsional inertia is included. Frequencies are computed numerically for the sinusoidal curved beams with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters are reported, with and without torsional inertia, as functions of three non-dimensional system parameters: the horizontal rise to chord length ratio, the span length to chord length ratio, and the slenderness ratio.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.16 no.5
• /
• pp.435-440
• /
• 2003

The electron-atom collision studies have been essentially used for testing and developing suitable theories of the scattering and collision processes, and for providing a tool for obtaining detailed information on the structure of the target atoms and molecules and final collision products. And, the development of that has also been strongly motivated by the need for electron collision data in such fields as laser Physics and development, astrophysics, Plasma devices, upper atmospheric processes and radiation physics. The concept and the Principle of determination of the electron collision cross sections for atoms and molecules by using the present electron swarm method are explained.

• Steel and Composite Structures
• /
• v.33 no.1
• /
• pp.133-142
• /
• 2019

In the present study, microstructure-dependent static stability analysis of inhomogeneous tapered micro-columns is performed. It is considered that the micro column is made of functionally graded materials and has a variable cross-section. The material and geometrical properties of micro column vary continuously throughout the axial direction. Euler-Bernoulli beam and modified couple stress theories are used to model the nonhomogeneous micro column with variable cross section. Rayleigh-Ritz solution method is implemented to obtain the critical buckling loads for various parameters. A detailed parametric study is performed to examine the influences of taper ratio, material gradation, length scale parameter, and boundary conditions. The validity of the present results is demonstrated by comparing them with some related results available in the literature. It can be emphasized that the size-dependency on the critical buckling loads is more prominent for bigger length scale parameter-to-thickness ratio and changes in the material gradation and taper ratio affect significantly the values of critical buckling loads.

• Computers and Concrete
• /
• v.30 no.2
• /
• pp.85-97
• /
• 2022

Using a combination of nonlocal Eringen as well as classical beam theories, this research explores the thermal buckling of a bidirectional functionally graded nanobeam. The formulations of the presented problem are acquired by means on conserved energy as well as nonlocal theory. The results are obtained via generalized differential quadrature method (GDQM). The mechanical properties of the generated material vary in both axial and lateral directions, two-dimensional functionally graded material (2D-FGM). In nanostructures, porosity gaps are seen as a flaw. Finally, the information gained is used to the creation of small-scale sensors, providing an outstanding overview of nanostructure production history.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.16 no.3
• /
• pp.251-260
• /
• 2003

A three dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of deep, tapered rods and beams with circular cross section. Unlike conventional rod and beam theories, which are mathematically one-dimensional (1-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sup r/, u/sub θ/ and u/sub z/, in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in , and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the rods and beams are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rods and beams. Novel numerical results are tabulated for nine different tapered rods and beams with linear, quadratic, and cubic variations of radial thickness in the axial direction using the 3D theory. Comparisons are also made with results for linearly tapered beams from 1-D classical Euler-Bernoulli beam theory.

• Journal of Korean Society of Steel Construction
• /
• v.12 no.5 s.48
• /
• pp.595-604
• /
• 2000

Web openings of large beams provide space for wiring, piping, and duct work to provide for proper drainage, pipes and duct must be slightly sloped with the attendant result that all web openings can not be centered on the centroidal axes of the beams. Test specimens are made for opening-depth to beam-depth ratio of 0.5 and for eccentricities of the opening center line of 10% from middepth of the beam because of the proximity of the opening edge to the flange. In this paper, available test results and theories relating to the strength of composite beams having eccentric rectangular openings are surveyed and experiments were carried out to examine the structural behaviors. In all the tests in this paper good agreement is demonstrated with maximum loads measured in tests, and observed failure modes Furthermore, compared with analytical values and experimental values of interaction diagram between moment and shear capacity were safed as it is scattered with outer part of the analytical values.

• Steel and Composite Structures
• /
• v.26 no.1
• /
• pp.79-87
• /
• 2018

In order to study the natural vibration characteristics of steel-concrete composite truss beam (SCCTB), the influence of multiple factors such as interface slip, shear deformation and moment of inertia are considered. Afterwards, based on the Hamilton principle the vibration control differential equation and natural boundary conditions of SCCTB are deduced. By solving SCCTB differential equations of vibration control, an analytical calculation method is proposed for analyzing the natural vibration characteristics of SCCTB. The natural frequencies of SCCTBs with different degrees of shear connection and effective lengths are calculated by using the analytical method, and the results are compared against those obtained from ANSYS finite element numerical calculation method. The results show that the analytical method considering the influence factors such as interface slip, shear deformation and moment of inertia are in good agreement with those obtained from ANSYS finite element numerical calculation method. This evidences the correctness of the analytical method and show that the method proposed exhibits improvement over the previously developed theories for the natural vibration characteristics of SCCTB. Finally, based on the analytical method, the influence factors of SCCTB natural vibration characteristics are analyzed. The results indicate that the influence of interface slip stiffness on SCCTB's natural frequency is more than 10% and therefore cannot be neglected. Moreover, shear deformation has an effect of more than 35% on SCCTB's natural frequency and the effect cannot be ignored either in this case too.

• Advances in concrete construction
• /
• v.8 no.4
• /
• pp.285-294
• /
• 2019

In the present paper, the fiber theory has been employed to model the reinforced concrete (RC) deep beams (DBs) considering the reinforcing steel bar-concrete interaction. To simulate numerically the behavior of materials, the uniaxial materials' constitutive laws have been employed for reinforcements and concrete and the bond stress-slip between the reinforcing steel bars and surrounding concrete are taken into account. Because of the high sensitivity of DBs to shear deformations, the Timoshenko beam theory has been applied. The shear stress-strain (S-SS) relationship has been defined by the modified compression field theory (MCFT) model. By modeling about 300 RC panels and employing a produced numerical database, a study has been carried out to show the sensitivity of the MCFT model. This is performed based on the multiple linear regression (MLR) models. The results of this research also illustrate how different parameters such as characteristic compressive strength of concrete, yield strength of reinforcements and the percentages of reinforcements in different directions get involved in the shear behavior of RC panels without applying complex theories. Based on the results obtained from the analysis of the MCFT S-SS model, a relatively simplified numerical S-SS model has been proposed. Application of the proposed S-SS model in modeling and analyzing the considered samples indicates that there is a good agreement between the simulated and the experimental test results. The comparison between the proposed S-SS model and the MCFT model indicates that in addition to the advantage of better accuracy, the main advantage of the proposed method is simplicity in application.