• Structural Engineering and Mechanics
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• v.4 no.5
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• pp.513-527
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• 1996

In this paper, both an approximate expression and an exact expression for the contribution factor of an element to the natural frequency of the finite element discretized system of a structure in general and a membrane in particular have been derived from the energy conservation principle and the finite element formulation of structural eigenvalue problems. The approximate expression for the contribution factor of an element is used to predict and determine the elements to be removed in an iteration since it depends only on the quantities associated with the old system in the iteration. The exact expression for the contribution factor of an element makes it possible to check whether the element is correctly removed at the end of an iteration because it depends on both the old system and the new system in the iteration. Thus, the combined use of the approximate expression and the exact expression allows a considerable number of elements to be removed in a single iteration so that the efficiency of the evolutionary structural optimization method can be greatly improved for solving the natural frequency optimization problem of a structure. A square membrane with different boundary supports has been chosen to investigate the general evolutionary path for the fundamental natural frequency of the structure. The related results indicated that if the objective of a structural optimization is to raise the fundamental natural frequency of the structure to an optimal value, the general evolutionary path during its optimization is that the elements are gradually removed along the direction from the area surrounded by the contour of the highest value to that surrounded by the contour of the lowest value.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.401-410
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• 2008

The natural frequency of a beam plays an important role in not only vibration analysis but also understanding its dynamic characteristics. It is complicated to analyse the natural frequency of a stepped beam with discontinuously varying section. Approximate analysis methods such as Rayleigh-Ritz method, FEM, etc. are frequently used for the vibration analysis of stepped beams. In such a case, accuracy of these methods depends upon the number of partitioned elements, the number of the iterations in calculation and the assumed mode shape. This study presents an approximate analysis method for the fundamental natural frequency analysis of stepped cantilever beam, using equivalent beam transformation technique. Validity and usefulness are verified by comparing the proposed method with FEM for several example problems.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.1
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• pp.25-33
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• 2015

Following the previous works on the natural frequency of heaving circular cylinder, i.e. Lee and Lee (2013) and Kim and Lee (2013), an investigation of the same spirit on the 2-dimensional cylinder of Lewis form has been conducted. As before, the natural frequency is defined as that corresponding to the local maximum of the MCFR (Modulus of Complex Frequency Response), which is given by the equation of motion in the frequency domain analysis. Hydrodynamic coefficients were found by using the Ursell-Tasai method, and numerical results for them were obtained up to much higher frequencies than before, for which the method was known as numerically unstable in the past. For a wide range of H, the beam-draft ratio, and ${\sigma}$, the sectional area coefficient, including their practical ranges for a ship, results for the natural frequency were computed and presented in this work. Two approximate values for the natural frequency, one proposed by Lee (2008) and another one by the damped harmonic oscillator, were also compared with the current results, and for most cases it was observed that the current result is between the two values. Our numerical results showed that the values of the local maximum of MCFR as well as the natural frequencye increase as ${\sigma}$ increases while H decreases. At present, extension of the present finding to the 3-dimensional ship via the approximate theory like the strip method looks promising.

• Journal of Korean Association for Spatial Structures
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• v.15 no.4
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• pp.99-105
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• 2015

The serviceability design of the high-rise building is affected by the wind response vibration such as the acceleration, at this time it is important to calculate the natural frequency correctly. Since the suggestion equation of the natural frequency being used in the design phase is not the regression equation obtained from the vibration measurement of the high-rise building, the verification to use for the serviceability design of the high-rise building is necessary. This thesis conducted an ambient vibration measuring on the high-rise building through the mobile-phone application to calculate the natural frequency and suggested a natural frequency approximate expression following the building's height, and compared with the domestic/foreign standard and the result of the eigen-value analysis.

• Journal of Korean Association for Spatial Structures
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• v.16 no.2
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• pp.47-54
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• 2016

It is very important to calculate natural frequency of the observatory tower correctly because it is keenly affected by wind response vibration due to its large slenderness ratio, weight and small damping ratio. Additionally, suggestion equation of natural frequency being used in the design phase has considerable difference between actual measured value thereby making it inappropriate to be used in the serviceability design of the observatory tower. Therefore, this paper conducted an ambient vibration measuring on 10 observatory towers through mobile-phone application thereby calculating the natural frequency and comparing the result with the domestic and foreign standards and that of the eigen-value analysis. This paper suggested approximate equation of the natural frequency of the observatory tower; T=0.0266H. The square of the corelation coefficient is 0.940, which is high.

• Journal of KSNVE
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• v.11 no.2
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• pp.323-328
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• 2001

The paper describes a theoretical study on the flexural vibration of an elastic rectangular plate with periodically nonuniform material properties. The approximate solution of the natural frequency and mode shape has been obtained using the perturbation technique for sinusoidal modulation of the flexural rigidity and mass density. It has been shown that distributed modes exist in the plate which Is a two-dimensional model of the flat panel speaker.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.2
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• pp.72-77
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• 2002

In this paper, a simple method to measure the residual stress in microstructure is presented. In order to find the residual stress in micro-machined beam, the first natural frequency of the beam that has the residual stress inside is analyzed using Rayleigh's energy method. Micro gold electroplated structure is fabricated by surface micro-machining process including electroplating. The made structure is an approximate shape of clamped-clamped beam and its 1 st natural frequency is measured by resonance method. For the better estimation of the residual stress, an equivalent length of micro-fabricated beam to ideal beam is calculated by FEM. The residual stress was estimated from the equivalent length and the measured natural frequency. It was found that a tensile stress was residue in the micro beam structure.

• Journal of Korean Association for Spatial Structures
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• v.20 no.4
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• pp.177-184
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• 2020

This study evaluates safety assessment before and after repair of Seonamsa temple seungseon bridge, which refer to the representative Hongye bridge in Korea. In this approach natural frequency of the structure were considered in the modeling procedure. Trial & error method is applied to obtain the approximate natural frequency before and after retrofit construction. Stiffness of the actual structure was examined to account for the dynamic characteristics of Hongye bridge measured in the field and adjusting parameters in computer modeling. The safety and usability of the stone structure in terms of load bearing capacity and displacement were examined.

• Ocean Systems Engineering
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• v.7 no.1
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• pp.53-74
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• 2017

Ship shaped FPSO (Floating Production, Storage and Offloading) units are the most commonly used floating production units to extract hydrocarbons from reservoirs under the seabed. These structures are usually much larger than general cargo ships and have their natural frequency outside the wave frequency range. This results in the response to first order wave forces acting on the hull to be negligible. However, second order difference frequency forces start to significantly impact the motions of the structure. When the difference frequency between wave components matches the roll natural frequency, the structure experiences a significant roll motion which is also termed as second order roll. This paper describes the theory and numerical implementation behind the calculation of second order forces and motions of any general floating structure subjected to waves. The numerical implementation is validated in zero speed case against the commercial code OrcaFlex. The paper also describes in detail the popular approximations used to simplify the computation of second order forces and provides a discussion on the limitations of each approximation.

• Journal of the Korea institute for structural maintenance and inspection
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• v.18 no.6
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• pp.147-154
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• 2014

The cable damages of the bridge structures induce very important impact on the structural safety, which implies the close monitoring of the cable damage is required to secure sustained safety of the bridges. Most usual available maintenance techniques are based on the monitoring the change of the natural frequency of the structures by damages. However, existing method are based on vibration method to calculate lateral vibration and system identification can calculate the axial stiffness using sensitivity equation by trial error method. But the frequency study by the longitudinal movement need because of the sag effect in system identification. This study proposes a new method to investigate the damage magnitudes and status. The method improves the accuracies in the magnitudes and status of damages by adopting the natural frequency of longitudinal movement. The study results have been validated by comparing them with the approximate solution of FEM. Thus, the relationship of cable damage and frequency appear with relation that the severe damage has the little frequency. If we know the real frequency we can estimate the cable damage severity using this relationship. This method can be possible the efficient management of the cable damage.