• Coupled systems mechanics
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• v.9 no.4
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• pp.381-396
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• 2020

Analytical investigation of the fracture of inhomogeneous beam with two parallel lengthwise cracks is performed. The thickness of the beam varies continuously along the beam length. The beam is loaded in three-point bending. Two beam configurations with different lengths of the cracks are analyzed. The two cracks are located arbitrary along the thickness of the beam. Solutions to the strain energy release rate are derived assuming that the material has non-linear elastic mechanical behavior. Besides, the beam exhibits continuous material inhomogeneity along its thickness. The balance of the energy is analyzed in order to derive the strain energy release rate. Verifications of the solutions are carried-out by considering the complementary strain energy stored in the beam configurations. The influence of the continuous variation of the thickness along the beam length on the lengthwise fracture behavior is investigated. The dependence of the lengthwise fracture on the lengths of the two parallel cracks is also studied.

• Coupled systems mechanics
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• v.12 no.1
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• pp.69-81
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• 2023

This paper considers a delamination analysis of a statically undetermined inhomogeneous beam structure of rectangular section with viscoelastic behavior under torsion. The beam is built in at its two ends. The beam has two longitudinal inhomogeneous layers with a delamination crack between them. A notch is made in the upper crack arm. The external torsion moment applied on the beam is a function of time. Under these conditions, the beam has one degree of indeterminacy. In order to derive the strain energy release rate, first, the static indeterminacy is resolved. Then the strain energy release rate is obtained by analyzing the balance of the energy with considering the viscoelastic behavior. The strain energy release rate is found also by analyzing the compliance of the beam for checkup. Solution of the strain energy release rate in a beam without a notch in the upper crack arm is derived too. In this case, the beam has two degrees of static indeterminacy (the torsion moment in the upper crack arm is treated as an additional internal redundant unknown). A parametric investigation of the strain energy release rate is carried-out.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.10
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• pp.936-945
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• 2007

We studied the influences of open cracks in free vibrating beam with rectangular section using a numerical model. The crack was assumed to be single and always open during the free vibration and equivalent bending stiffness of a cracked beam was calculated based on the strain energy balance. By Galerkin's method, the frequencies of cantilever beam could be obtained with respect to various crack depths and locations. Also, the experiments on the cracked beams were carried out to find natural frequencies. The cracks were initiated at five locations and the crack depths were increased by five steps at each location. The experimental results were compared with the numerical results and the comparison results were discussed.

• Proceedings of the KSR Conference
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• 2006.11b
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• pp.1430-1435
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• 2006

This study deals with the problem of balance beam system to stabilize about static and sinusoidal disturbance. wherein the design objectives are to keep the gap deviation from static and sinusoidal disturbance. In this paper propose the 2-Degree of Freedom(DOF) structure and a simple first-order controller which is designed by Characteristic ratio assignment (CRA) method. Matlab simulation result verify stabilization of balance beam system despite of disturbance. Hybrid simulation between digital controller and analog plant is presented by Matlab Simulink.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.9
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• pp.526-537
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• 2000

This paper deals with a sliding mode controller with integral compensation in a magnetic suspension system The control scheme comprises an integral controller which is designed for achieving zero steady-steate error under step disturbance input and a sliding mode controller which is designed for enhancing robustness under plant parametric variations. A procedure is developed for determining the coefficients of the switching plane and integral control gain such that the overall closed-loop system has stable eigenvalues. A proper continuous design signal is introduced to overcome the chattering problem. The performance of a magnetically suspended balance beam using the proposed integral sliding mode controller is illustrated. Simulation and experimental results also show that the proposed method is effective under the external step disturbance and input channel parametric variations.

• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.1-14
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• 2016

In this paper, an alternative analytical method is presented to evaluate the nonlinear vibration behavior of single and double tapered cantilever beams. The admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Based on the Lagrange method and the Newton Harmonic Balance (NHB) method, analytical approximate solutions in closed and explicit form are obtained. These approximate solutions show excellent agreement with those of numeric method for small as well as large amplitude. Moreover, due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large amplitude vibration response of tapered beams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.396-400
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• 2006

We studied the influences of open cracks in free vibrating beam with rectangular section using a numerical model. The crack was assumed to be single and always open during the free vibration and equivalent bending stiffness of a cracked beam was calculated based on the strain energy balance. By Galerkin's method, the frequencies of cantilever beam could he obtained with respect to various crack depths and locations. Also, the experiments on the cracked beams were carried out to find natural frequencies. The cracks were initiated at five locations and the crack depths were increased by five steps at each location. The experimental results were compared with the numerical results and the comparison results were discussed.

• Journal of the Korean Vacuum Society
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• v.8 no.4B
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• pp.548-555
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• 1999

The NBI (Neutral BGeam Injection) System for the Korea Superconducting Tokamak Advanced Research (KSTAR) is composed of ion sources, neutralizers, bending magnets, ion dumps, and calorimeter. The vacuum chamber, in which all of the beam line components are enclosed, is composed of differential pumping system for the effective transfer of the neutral beams. The needed pumping speeds of each of the divided vacuum chamber and the optimized gas flow rate ot the neutralizer were calculated with the help of the particle balance equations. The minimum gas flow rate to the ion sources for producing needed beam current (120kV, 65A, 78MW), the pressure distributions in the vacuum chamber for minimizing re-ionization loss, and the beam loss rate on the beam line components were used as the input in the calculation. Also the scenario for short pulse operation was determined by analysing the time dependent equations. It showed that beam extraction during less than 0.5 sec could be made only with TMP.

• Advances in aircraft and spacecraft science
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• v.2 no.2
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• pp.199-215
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• 2015

This study focuses on the limit cycle oscillations (LCOs) of cantilever swept-back wings containing a cubic nonlinearity in an incompressible flow. The governing aeroelastic equations of two degrees-of-freedom swept wings are derived through applying the strip theory and unsteady aerodynamics. In order to apply strip theory, mode shapes of the cantilever beam are used. The harmonic balance method is used to calculate the frequencies of LCOs. Linear flutter analysis is conducted for several values of sweep angles to obtain the flutter boundaries.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.7
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• pp.339-345
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• 2000

This paper deals with the displacement estimation of magnetically suspended simple 1 DOF(degree of freedom) system without the displacement sensor. Inherently electro-magnet for control has two natural feedback loops. One is the transfer function which represents the dependance of the amount of the magnetic flux on the gap displace-ments. The other is the transfer function expressing the properties that the back electromotive force is derived from the time derivative of the magnetic flux. Through these two feedback loops, information about the gap length can be represented by the magnetic flux and the coil current. This means that the gap length can be detected from these two states variables of the electromagnet without a displacements sensor(self-sensing). The displacement can be estimated with the magnetic flux subtracted by the coil current. In this paper we use a balance beam in order to deal with the displacement sensorless estimation of the magnetic bearing system. For the stable estimation of the gap displacements by using the method of self-sensing simple PD controller is used. We first show the mathematical model of the balance beam, and then we show the effectiveness of the current and flux feedback for making stable estimation of the gap displacements for the balance beam. Simulation results show the effectiveness of the current and flux feedback for good estimation of the displacement without using displacement sensor.