• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.1
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• pp.1-7
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• 1990

A method is developed for solving the elastica of cantilever beam subjected to a tip point load and uniform load. The Bernoulli-Euler differential equation of deflected beam is used. The Runge-Kutta method and the Regula Falsi method are used to perform the integration of the differential eqution and to determine the horizontal deflection, respectively. The horizontal and vertical deflections of the free end, and the free-end rotations are calculated for a range of parameters representing variations in tip point load and uniform load. All results are presented in nondimensional forms. And some typical elastic are also presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.188-193
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• 2013

The large mass method for dynamic analysis of statically determinate beams subjected to in-phase support motions is justified by showing that the equation of motion of the beams under consideration is equivalent to that of large mass model of the beam when an appropriate large mass ratio is employed. The accuracy of the stress responses based on the beam large mass method is investigated through careful numerical tests. The numerical results are compared to analytic solutions and the comparison shows that the large mass method yields not only the time history of motion but also the distributions of bending moment and shear force accurately.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.201-208
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• 2000

This paper explores the non-linear behavior of tapered beam subjected to a floating concentrated load. For applying the Bernoulli-Euler beam theory to this beam, the bending moment at any point of elastica is obtained from the final equilibrium state. By using the bending moment equation and the Bernoulli-Euler beam theory, the differential equations governing the elastica of clamped-roller beam are derived, and solved numerically. Three kinds of tapered beam types are considered. The numerical results of the non-linear behavior obtained in this study are agreed quite well to the results obtained from the laboratory-scale experiments.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.2 s.257
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• pp.231-236
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• 2007

This paper presents the effect of the center of the series on convergence in solving vibration problems by Differential Transformation Method(DTM) to the transverse vibration of the Euler-Bernoulli beam under varying axial force. The governing differential equation of the transverse vibration of the Euler-Bernoulli beam under varying axial force is derived. The concepts of DTM were briefly introduced. Numerical calculations are carried out and compared with previously published results. The effect of the center of the series on convergence in solving the problem by DTM is discussed.

• Steel and Composite Structures
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• v.32 no.5
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• pp.643-655
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• 2019

Perforation and cutouts of structures are compulsory in some modern applications such as in heat exchangers, nuclear power plants, filtration and microeletromicanical system (MEMS). This perforation complicates dynamic analyses of these structures. Thus, this work tends to introduce semi-analytical model capable of investigating the dynamic performance of perforated beam structure under free and forced conditions, for the first time. Closed forms for the equivalent geometrical and material characteristics of the regular square perforated beam regular square, are presented. The governing dynamical equation of motion is derived based on Euler-Bernoulli kinematic displacement. Closed forms for resonant frequencies, corresponding Eigen-mode functions and forced vibration time responses are derived. The proposed analytical procedure is proved and compared with both analytical and numerical analyses and good agreement is noticed. Parametric studies are conducted to illustrate effects of filling ratio and the number of holes on the free vibration characteristic, and forced vibration response of perforated beams. The obtained results are supportive in mechanical design of large devices and small systems (MEMS) based on perforated structure.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.4
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• pp.315-324
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• 2011

This paper presents a historical study on the derivation of the differential equation of motion for the single-degree-of-freedom m-k system with the harmonic excitation. It was Euler for the first time in the history of vibration theory who tackled the equation of motion for that system analytically, then gave the solution of the free vibration and described the resonance phenomena of the forced vibration in his famous paper E126 of 1739. As a result of the chronological progress in mechanics like pendulum condition from Galileo to Euler, the author asserts two conjectures that Euler could apply to obtain the equation of motion at that time.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.6
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• pp.553-561
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• 2011

A theoretical approach is carried out to predict the quality factors of flexible modes of a microcantilever on a squeeze-film. The frequency response function of an inertially-excited microcantilever beam is derived using an Euler-Bernoulli beam theory. The external force due to squeeze-film phenomenon is developed from the Reynolds equation. Slip boundary conditions are employed at the interfaces between the fluid and the structure to consider the gas rarefaction effect, and pressure boundary condition at both ends of fluid analysis region is enhanced to increase the exactness of predicted quality factors. To the end, an approximate equation is derived for the first bending mode of the microcantilever. Using the approximate equation, the quality factors of the second and third bending modes are calculated and compared with experimental results of previously reported work. The comparison shows the feasibility of the current approach.

• Journal of the Society of Naval Architects of Korea
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• v.59 no.6
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• pp.400-412
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• 2022

This paper provides the results of numerical and theoretical predictions of oil outflows from damaged single-hull and double-hull ships.Theoretical equations derived from the unsteady Bernoulli equation and a CFD method for multi-phase flow analysis were used to estimate the oil outflow rate from cargo tank. The predicted oil outflow rate from a single-hull cargo tank damaged due to grounding and collision accidents showed a good agreement with the available experimental results in both numerical and theoretical analyses. However, in the case of the double-hull conditions, the time variation of the amount of water and oil mixture inside the ballast tank predicted by the theoretical equation showed some different behavior from the numerical results. The reason was that the interaction of the oil flow with the water inflow in the ballast tank was not reflected in the theoretical equations. In the problems of the initial pressure condition in the cargo and ballast tanks, the oil outflow and water inflow were delayed at the pressure condition that the tanks were sealed. When the flow interaction between the oil and water in the ballast tank was less complicated, the theoretical and the numerical results showed a good agreement with each other.

• Journal of Advanced Marine Engineering and Technology
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• v.22 no.3
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• pp.275-284
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• 1998

Standard on the carbon dioxide extinguishing system was prepared by the committed of the national fire protection assocition(NFPA)in USA on 1980. And this code is also applied to the design of a marine fire extinguishing system The most important problem in design is the uniform discharge of $CO_2$ through each nozzle from the high pressure $CO_2$ storage facility. The purpose of this paper is to develop the computer software to design the marine fire protection piping system. By solving the continuity equation energy equation and Bernoulli's equation simulataneously the flowrate in branch pipelines and discharge nozzles can be calculated.

• Steel and Composite Structures
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• v.46 no.5
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• pp.637-647
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• 2023

Nonlinear free vibration and stability responses of a carbon nanotube reinforced composite beam under temperature rising are investigated in this paper. The material of the beam is considered as a polymeric matrix by reinforced the single-walled carbon nanotubes according to different distributions with temperature-dependent physical properties. With using the Hamilton's principle, the governing nonlinear partial differential equation is derived based on the Euler-Bernoulli beam theory. In the nonlinear kinematic assumption, the Von Kármán nonlinearity is used. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The critical buckling temperatures, the nonlinear natural frequencies and the nonlinear free response of the system is obtained. The effect of different patterns of reinforcement on the critical buckling temperature, nonlinear natural frequency, nonlinear free response and phase plane trajectory of the carbon nanotube reinforced composite beam investigated with temperature-dependent physical property.