• Journal of Magnetics
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• v.21 no.3
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• pp.431-436
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• 2016

In the design of transformer winding, natural vibration frequency is an important parameter. This paper presents a 2D model to calculate axial vibration natural frequency of power transformer winding based on the elastic dynamics theory, and according to the elastic support equivalent principle of radial pressboards. The 3D model to calculate natural vibration frequency can be simplified as a 2D one as the support of pressboards on the winding is same. It is verified that results of the 2D model are consistent with those of 3D one, but the former can achieve much higher calculation efficiency. It shows that increasing the width and number of pressboards can improve axial natural frequency through formula analysis and simulation, and also the relations between the changes of axial pre-compression and axial natural vibration frequency on the windings are investigated. Finally, the proposed 2D model's effectiveness is proved when compared with tested ones.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.1
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• pp.26-32
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• 2003

The vibrational system of this study is consisted of a rotating cantilever pipe and the flow in the pipe. The equation of motion is derived by using Lagrange equation. The influences of the rotating angular velocity and the velocities of fluid flow in the pipe have been studied on the dynamic characteristics of a rotating cantilever pipe by numerical method. The tip-amplitude of axial vibration and maximum tip-deflection of axial direction of cantilever pipe are directly proportional to the velocity of fluid and rotating angular velocity of pipe In the steady state. respectively The bending tip-amplitude of cantilever pipe is inversely proportional to the velocity of fluid in the steady state. When the rotating angular velocity is 5 rad/s, the velocity of fluid increase with increasing the natural frequency of axial vibration at second mode and third mode, but the natural frequency axial direction of first mode is decreased. The natural frequency of lateral direction is decreased due to increase of the rotating angular velocity. It identifies that the Influence of velocity of fluid give much variation lower mode of vibration in lateral direction. And the Influence of velocity of fluid give much variation higher mode of vibration in axial direction.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.6
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• pp.163-168
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• 2001

Vibration problems occurred in an air cooled heat exchanger with axial flow fan for a petrochemical plant were investigated. Experimental field test and theoretical verification were performed. To find the main cause of the high vibration of the fan at the air inlet of the axial fan, the frequency spectrum was measured. The natural frequency of the driving support of the heat exchanger was numerically calculated. Both of the measured and the natural frequency were approximately equal to the blade passing frequency. Because it was difficult to modify the structure of the driving support during the normal operation of the plant, the blade number of the fan was increased, which greatly reduced the vibration level of the heat exchanger.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.75-81
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• 2000

Vibration problems induced by an air cooled heat exchanger with axial flow fan were investigated during the operation of a petrochemical plant. Two different studies were done; one was experimental field test and the other was theoretical verification. To find main cause of the blade passing frequency of the fan after installing additional blockage board at the air inlet of the axial fan, the frequency spectrum was measured. The vibrations of the blade passing frequency became higher. The natural frequency of driving support of the heat exchanger was theoretically calculated. It was approximately equal to the blade passing frequency. During the normal operation of the plant, it was impossible to modify the structure of the driving support. Instead, the blade number was increased to reduce vibration level. It increased the ratio of the forcing frequency to the natural frequency of the driving support over the resonance region.

• Earthquakes and Structures
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• v.9 no.6
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• pp.1181-1192
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• 2015

In this paper, an analytical method is proposed to study the effect of crack and axial load on vibration behavior and stability of the cracked columns. Using the local flexibility model, the crack has been simulated by a torsional spring with connecting two segments of column in crack location. By solving governing eigenvalue equation, the effects of crack parameters and axial load on the natural frequencies and buckling load as well as buckling load are investigated. The results show that the presents of crack cause to reduction in natural frequencies and buckling load whereas this reduction is affected by the location and depth of the crack. Furthermore, the tensile and compressive axial load increase and decrease the natural frequencies, respectively. In addition, as the compression load approaches to certain value, the fundamental natural frequency reaches zero and instability occurs. The accuracy of the model is validated through the experimental data reported in the literature.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.1340-1347
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• 2006

Dynamic response of buried pipelines both in the axial and the transverse directions on concrete pipe and steel pipe, FRP pipe were investigated through a free vibration analysis. End boundary conditions considered herein consist of free ends, fixed ends, and fixed-free ends in the axial and the transverse direction. Guided ends, simply supported ends, and supported-guided ends were added to the transverse direction. The buried pipeline was regarded as a beam on an elastic foundation and the ground displacement of sinusoidal wave was applied to it. Natural frequencies and mode shapes were determined according to end boundary conditions. In addition, the effects of parameters on the natural frequency were evaluated. The natural frequency is affected most significantly by the soil stiffness and the length of the buried pipelines. The natural frequency increases as the soil stiffness increases while it decreases as the length of the buried pipeline increases. Such behavior appears to be dominant in the axial direction rather than in the transverse direction of the buried pipelines.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.6
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• pp.580-586
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• 2011

This paper addresses the effect of transverse shear deformation and rotary inertia on the natural frequency of beams under axial loads. It has been reported in the author's paper using a finite element analysis that the Timoshenko effect in a rotating disk deceases and then increases again with increasing rotation speed. To validate the phenomenon, the simply-supported beams under uniform tension are selected in this study since they have exact solutions in vibration problem. The results show that the axial tension in beams would not make the Timoshenko effect decrease monotonically but could make the effect increase again unlike the results reported in the other studies for beams.

• Advances in nano research
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• v.9 no.3
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• pp.157-172
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• 2020

The aim of this present research is the effect of the higher-order terms of the governing equation on the forced longitudinal vibration of a nanorod model and making comparisons of the results with classical nonlocal elasticity theory. For this purpose, the free axial vibration along with forced one under the two various linear and harmonic axial concentrated forces in zigzag Single-Walled Carbon Nanotube (SWCNT) are analyzed dynamically. Three various theories containing the classical theory, which is called Eringen's nonlocal elasticity, along with Rayleigh and Bishop theories (higher-order theories) are established to justify the nonlocal behavior of constitutive relations. The governing equation and the related boundary conditions are derived from Hamilton's principle. The assumed modes method is adopted to solve the equation of motion. For the free axial vibration, the natural frequencies are calculated for the various values of the nonlocal parameter only based on Eringen's theory. The effects of the nonlocal parameter, thickness, length, and ratio of the excitation frequency to the natural frequency over time in dimensional and non-dimensional axial displacements are investigated for the first time.

• Structural Engineering and Mechanics
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• v.48 no.4
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• pp.519-545
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• 2013

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.