• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.254-257
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• 2006

In this paper a dynamic behavior(natural frequency) of a cracked cantilever and simply supported pipe conveying fluid is presented. In addition, an analysis of the flutter and buckling instability of a cracked pipe conveying fluid subjected to a follower compressive load is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.281-298
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• 2015

In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.625-630
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• 2007

This paper accounts for derivations and formulations of the finite element dynamic equation of the rotor-bearing system to analyze its whirling speed. It turns out to be a different form from previous researcher's because of different successive sequences of Euler angles. Correspondingly the adoption of other rotation tensor will be needed for a consistent derivation of the dynamic equation. The process of its finite element formulation with consistent mass matrix and gyroscopic matrix involves a general definition of the modal analysis or the Eigen analysis for the damped system in the inertial frame and rotating frame, respectively.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.99-104
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• 2007

In this paper a dynamic behavior(natural frequency) of a cracked cantilever beam with tip mass and follower force is presented. In addition. an analysis of the flutter and buckling instability of a cracked cantilever beam subjected to a follower compressive load is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter ins stability based on the variation of the first two resonant frequencies of the beam. Besides. the effect of the crack's intensity and location on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.689-694
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported pipe conveying fluid subject to the moving mass. The equation of motion is derived by using Lagrange's equation. The influences of the velocity of moving mass and the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The presence of crack results in higher deflections of pipe. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. Totally, as the velocity of fluid flow and the crack severity are increased, the mid-span deflection of simply supported pipe conveying fluid is increased. The time which produce the maximum dynamic deflection of the simply supported pipe is delayed according to the increment of the crack severity.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.419-432
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• 2015

The free vibration of rotating Euler-Bernoulli beams with the thickness and/or width of the cross-section vary linearly along the length is investigated by using the Adomian modified decomposition method (AMDM). Based on the AMDM, the governing differential equation for the rotating tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and the closed form series solution of the corresponding mode shapes can be easily obtained simultaneously. The computed results for different taper ratios as well as different offset length and rotational speeds are presented in several tables and figures. The accuracy is assured from the convergence and comparison with the previous published results. It is shown that the AMDM provides an accurate and straightforward method of free vibration analysis of rotating tapered beams.

• Steel and Composite Structures
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• v.11 no.6
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• pp.489-504
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• 2011

This paper presents a theoretical investigation in free vibration of sigmoid functionally graded beams with variable cross-section by using Bernoulli-Euler beam theory. The mechanical properties are assumed to vary continuously through the thickness of the beam, and obey a two power law of the volume fraction of the constituents. Governing equation is reduced to an ordinary differential equation in spatial coordinate for a family of cross-section geometries with exponentially varying width. Analytical solutions of the vibration of the S-FGM beam are obtained for three different types of boundary conditions associated with simply supported, clamped and free ends. Results show that, all other parameters remaining the same, the natural frequencies of S-FGM beams are always proportional to those of homogeneous isotropic beams. Therefore, one can predict the behaviour of S-FGM beams knowing that of similar homogeneous beams.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.565-572
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• 2004

Numerical stability analysis of one-dimensional axial flow in solid rocket motors is performed based on the Euler equation coupled with an unsteady combustion equation of solid propellant. In order to check the numerical scheme, behavior of a standing wave in a closed tube is examined. A standing wave in solid rocket motor decays or grows depending on the total effect of propellant combustion, nozzle flow, and so on. The stability boundary of the fundamental mode standing wave is determined by changing one of the combustion parameters. In addition growth rates of the wave are calculated numerically in relatively low Mach number flow region for the motors with different port and nozzle throat diameters. The results obtained here agree well with the approximate solution. The same scheme is applied to a motor with shorter length and L＊-instability is observed.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.3B no.3
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• pp.115-121
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• 2003

This paper proposes a radiation model, which considers radiation transport as an important component in hot gas analysis. This radiation model is derived from combining the method of partial characteristics (MPC) with net emission coefficient (NEC), and it covers the drawbacks of existing models. Subsequently, using this proposed model, the arc-flow interaction in an arcing chamber can be efficiently computed. The arc is represented as an energy source term composed of ohmic heating and the radiation transport in the energy conservation equation. Ohmic heating term was computed by the electric field analysis within the conducting plasma region. Radiation transport was calculated by the proposed radiation model. Also, in this paper, radiation models were introduced and applied to the gas circuit breaker (GCB) model. Through simulation results, the efficiency of the proposed model was confirmed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.4
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• pp.419-426
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• 2004

In this paper, studied about the effect of open crack and the moving mass on the dynamic behavior of simply supported pipe conveying fluid. The equation of motion is derived by using Lagrange's equation. The influences of the velocity of moving mass, the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. Therefore, the crack is modelled as a rotational spring. Totally, as the velocity of fluid flow is increased, the mid-span deflection of simply supported pipe conveying fluid is increased. The position of the crack is located in the middle point of the pipe, the mid-span deflection of simply supported pipe presents maximum deflection.