• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.690-695
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• 2003

The main purpose of this paper is to apply differential transformation method to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. The governing equation of motion of beam with open cracks on elastic foundation is derived. The concept of differential transformation is briefly introduced. The cracks are modeled by massless substitute spring. The effects of the crack location, size and the foundation constants, on the natural frequencies of the beam, are investigated.

• Structural Engineering and Mechanics
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• v.42 no.1
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• pp.95-119
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• 2012

In this paper, forced vibration differential equations of motion of Euler-Bernoulli beams with different boundary conditions and dynamic loads are solved using differential transform method (DTM), analytical solutions. Then, the modal deflections of these beams are obtained. The calculated modal deflections using DTM are represented in tables and depicted in graphs and compared with the results of the analytical solutions where a very good agreement is observed.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.315-326
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• 2021

Korobov type polynomials are introduced and extensively investigated many mathematicians ([1, 8-10, 12-14]). In this work, we define unified Apostol Korobov type polynomials and give some recurrences relations for these polynomials. Further, we consider the q-poly Korobov polynomials and the q-poly-Korobov type Changhee polynomials. We give some explicit relations and identities above mentioned functions.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.1
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• pp.13-22
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• 2013

This paper deals with a novel method for numerical analyses of the tapered geometrical non-linear beam with three unknown parameters, subjected a floating point load. The beams with hinged-movable end constraint are chosen as the objective beam. Cross sections of the beam whose flexural rigidities are functionally varied with the axial coordinate. The first order simultaneous differential equations governing the elastica of such beam are derived on the basis of the Bernoulli-Euler beam theory. A novel numerical method for solving these equations is developed by using the iteration technique. The processes of the solution method are extensively discussed through a typical numerical example. For validating theories developed herein, laboratory scaled experiments are conducted.

• Structural Engineering and Mechanics
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• v.59 no.6
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• pp.1139-1153
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• 2016

Elastic constraints are usually simplified as "spring forces" exerted on beam ends without considering the "spring deformation". The partial differential equation governing the free vibrations of a cantilever Bernoulli-Euler beam considering the deformation of elastic constraints is firstly established, and is nondimensionalized to obtain two dimensionless factors, $k_v$ and $k_r$, describing the effects of elastically vertical and rotational end constraints, respectively. Then the frequency equation for the above Bernoulli-Euler beam model is derived using the method of separation of variables. A numerical analysis method is proposed to solve the transcendental frequency equation for the continuous change of the frequency with $k_v$ and $k_r$. Then the mode shape functions are given. Finally, effects of $k_v$ and $k_r$ on free vibration characteristics of the beam with different slenderness ratios are calculated and analyzed. The results indicate that the effects of $k_v$ are larger on higher-order free vibration characteristics than on lower-order ones, and the impact strength decreases with slenderness ratio. Under a relatively larger slenderness ratio, the effects of $k_v$ can be neglected for the fundamental frequency characteristics, while cannot for higher-order ones. However, the effects of $k_r$ are large on both higher- and lower-order free vibration characteristics, and cannot be neglected no matter the slenderness ratio is large or small.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.2
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• pp.129-138
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• 2012

This paper deals with geometrical non-linear analyses of the tapered variable-arc-length beam, subjected to the combined load with an end moment and a point load. The beam is supported by a hinged end and a frictionless sliding support so that the axial length of the deformed beam can be increased by its load. Cross sections of the beam whose flexural rigidities are functionally varied with the axial coordinate. The simultaneous differential equations governing the elastica of such beam are derived on the basis of the Bernoulli-Euler beam theory. These differential equations are numerically solved by the iteration technique for obtaining the elastica of the deformed beam. For validating theories developed herein, laboratory scaled experiments are conducted.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.5
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• pp.477-483
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• 2015

In this paper, Euler-Bernoulli beam theories(EB-beam) are used, and Fast Fourier Transformation(FFT) analysis is then employed to extract their natural frequencies using both analytical approach and Co-rotational plane beam(CR-beam) EDISON program. EB-beam is used to analyze a spring-mass system with a single degree of freedom. Sinusoidal force with various frequencies and constant magnitude are applied to tip of each beam. After the oscillatory tip response is observed in EB-beam, it decreases and finally converges to the so-called 'steady-state.' The decreasing rate of the tip deflection with respect to time is reduced when the forcing frequency is increased. Although the tip deflection is found to be independent of the excitation frequency, it turns out that time to reach the steady state response is dependent on the forcing frequency.

• Journal of the Korean Recycled Construction Resources Institute
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• v.11 no.4
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• pp.467-475
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• 2023

To ensure the safety of the pipeline against large deformation of the pipeline during lowering construction, the analysis for pipeline becomes emphasized. The FE analysis has a lower efficiency at calculating time, while it could be obtained high accuracy. In this paper, a reasonable analytical model for analysis of pipeline is proposed during lowering-in. This analytical model is partitioned considering the geometrical characteristics and modeled as two parameters Beam On Elastic Foundation and Euler-Bernoulli beam considering the boundary condition. This takes into account the pipeline-soil interaction and the axial forces acting on the pipeline. Previous model can only be applied to standardized conditions, whereas the proposed model defined as Segmented Pipeline Model can be considered for the majority of construction conditions occurred during lowering-in. In addition, minimized assumptions and segmented elements lead to improve the convenience and applicability of modeling. Nevertheless, the model shows accurate results compared to the FE model. Accordingly, it is expected that it will be used efficiently for configuration management as well as safety assessment of pipeline during lowering-in.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.463-469
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• 2014

In this paper, we construct new q-extension of Euler polynomials with weight 0. These modified q-Euler polynomials are useful to study various identities of Carlitz's q-Bernoulli numbers.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.3
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• pp.223-229
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• 2014

In this paper, the natural frequency and damping ratio are analyzed with the acceleration signal of an Euler-Bernoulli beam using the impact hammer test. The results are presented according to crack depth and position using the recursive least squares method. The results are compared and investigated with FEM analysis of CATIA. Both methods agree well with each other regarding the natural mode characteristics. The captured acceleration can be used for the calculation of the natural frequency and damping ratio using time series methods that are based on the measured acceleration. Using these data, a recursive time series model with the acceleration signal was configured and the behaviors of the natural frequency and damping ratio were investigated and analyzed. Finally, the results can be used for the prediction of crack position and depth under different crack conditions for an Euler-Bernoulli beam.