• Title/Summary/Keyword: Differential Transformation

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Buckling of fully and partially embedded non-prismatic columns using differential quadrature and differential transformation methods

  • Rajasekaran, S.
    • Structural Engineering and Mechanics
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    • v.28 no.2
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    • pp.221-238
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    • 2008
  • Numerical solution to buckling analysis of beams and columns are obtained by the method of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for various support conditions considering the variation of flexural rigidity. The solution technique is applied to find the buckling load of fully or partially embedded columns such as piles. A simple semi- inverse method of DQ or HDQ is proposed for determining the flexural rigidities at various sections of non-prismatic column ( pile) partially and fully embedded given the buckling load, buckled shape and sub-grade reaction of the soil. The obtained results are compared with the existing solutions available from other numerical methods and analytical results. In addition, this paper also uses a recently developed technique, known as the differential transformation (DT) to determine the critical buckling load of fully or partially supported heavy prismatic piles as well as fully supported non-prismatic piles. In solving the problem, governing differential equation is converted to algebraic equations using differential transformation methods (DT) which must be solved together with applied boundary conditions. The symbolic programming package, Mathematica is ideally suitable to solve such recursive equations by considering fairly large number of terms.

Free Vibration Analysis of Solid and Annular Circular Membranes with Continuously Varying Density Using The Differential Transformation Method

  • Shin, Young-Jae;Yun, Jong-Hak;Jaun, Su-Ju;You, Young-chan
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.988-993
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    • 2003
  • This paper presents the application of the technique of differential transformation of free vibration of membrane. Numerical calculations are carried out and compared with previously published results. The results obtained by the present method agree very well with those reported in the previous works. The present analysis shows the usefulness and validity of differential transformation in solving a solid and annular circular membranes problem of the responses of the free vibration.

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Kinematic Modeling for a Type of Mobile Robot using Differential Motion Transformation (미소운동 변환방법을 이용한 몇가지 이동로봇의 기구학 모델)

  • Park, Jae-Han;Kim, Soon-Chul;Yi, Soo-Yeong
    • Journal of Institute of Control, Robotics and Systems
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    • v.19 no.12
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    • pp.1145-1151
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    • 2013
  • Kinematic modeling is a prerequisite for motion planning and the control of mobile robots. In this paper, we proposed a new method of kinematic modeling for a type of mobile robot based on differential motion transformation. The differential motion implies a small translation and rotation in three-dimensional space in a small time interval. Thus, transformation of the differential motion gives the velocity relationship, i.e., Jacobian between two coordinate frames. Since the theory of the differential motion transformation is well-developed, it is useful for the systematic velocity kinematic modeling of mobile robots. In order to show the validity for application of the differential motion transformation, we obtained velocity kinematic models for a type of exemplar mobile robot including spherical ballbots.

Application of differential transformation method for free vibration analysis of wind turbine

  • Bozdogan, Kanat Burak;Maleki, Farshid Khosravi
    • Wind and Structures
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    • v.32 no.1
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    • pp.11-17
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    • 2021
  • In recent years, there has been a tendency towards renewable energy sources considering the damages caused by non-renewable energy resources to nature and humans. One of the renewable energy sources is wind and energy is obtained with the help of wind turbines. To determine the behavior of wind turbines under earthquake loads, dynamic characteristics are required. In this study, the differential transformation method is proposed to determine the free vibration analysis of wind turbines with a variable cross-section. The wind turbine is modeled as an equivalent variable continuous flexural beam and blade weight is considered as a point mass at the top of the structures. The differential equation representing the free vibration of the wind turbine is transformed into an algebraic equation with the help of differential transformation method and the angular frequencies and the mode shapes of the wind turbine are obtained by the help of the differential transformation method. In the study, a sample taken from the literature was solved with the presented method and the suitability of the method was investigated. The same wind turbine example also modeled by finite element modelling software, ABAQUS. Results of the finite element model and differential transformation method are compared with each other and the results are in good agreement.

Kinematic Modeling for Autonomous Bicycle Using Differential Motion Transformation (미소운동 변환을 이용한 자율주행 자전거의 기구학 모델)

  • Yi, Soo-Yeong
    • The Journal of Korea Robotics Society
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    • v.8 no.4
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    • pp.292-297
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    • 2013
  • This paper presents a new method of kinematic modeling for autonomous bicycle by using the differential motion transformation. Kinematic model is indispensable to trajectory planning and control for an autonomous mobile robot. The conventional methods of kinematic modeling for an autonomous bicycle depend on intuition by geometry. On the contrary, the proposed method in this paper is based on the systematic differential motion transformation, thus applicable to various types of autonomous bicycles. The differential motion transformation gives Jacobian between two coordinate frames and the velocity kinematics as a result.

Post-buckling Behavior of Tapered Columns under a Combined Load using Differential Transformation

  • Yoo, Yeong Chan
    • Architectural research
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    • v.8 no.1
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    • pp.47-56
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    • 2006
  • In this research, the analysis of post-buckling behavior of tapered columns has been performed under a combined load of uniformly distributed axial load along the length and concentric axial load at free end by solving the nonlinear differential equation with the differential transformation technique. The buckling load at various slopes at free end of column is calculated and the results of the analysis using the differential transformation technique is verified with those of previous studies. It is also shown through the results that the buckling load of sinusoidal tapered columns is largest, the linear is second largest, and the parabolic is small in the all ranges of slopes at free end and the deflection of parabolic tapered columns in the x coordinates is largest, the sinusoidal is second largest, and the linear is smallest in the range of slope 0 to 140 degrees at free end. However, when the range of the slope is 160 to 176 degrees at the free end, the deflection of sinusoidal tapered columns in the x coordinates is largest, the linear is second largest, and the parabolic is smallest. In addition, for the linear tapered column, the buckling load increases along with the flexural stiffness ratio. Also, for the parabolic and the sinusoidal tapered column, the buckling loads increase and decrease as the flexural ratios increase in the range of flexural stiffness ratio n = 1.0 to n = 2.0. Through this research, it is verified that the differential transformation technique can be applied to solve the nonlinear differential equation problems, such as analysis of post-buckling behavior of tapered columns. It is also expected that the differential transformation technique apply to various more complicated problems in future.

Vibration Analysis for Beams on Variable Two-Parameter Elastic Foundations Using Differetial Transformation (Differential Transformation에 의한 가변 2 파라미터 탄성기초에 설치된 보의 진동해석)

  • 신영재;김재호;황정기
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.11 no.8
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    • pp.357-363
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    • 2001
  • This paper presents the application of the technique Q( differential transformation to the vibration analysis of beams resting on variable two-parameter elastic foundations. The closed form series solutions for beams are obtained for various boundary conditions. Numerical calculations are carried out and compared with previously published results. The results obtained by the present method agree very well with those reported in the previous works. The present analysis shows the usefulness and validity of differential transformation in solving nonlinear problem of the free vibration.

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Vibration Analysis of Euler-Bernoulli Beam with Open Cracks on Elastic foundations Using Differential Transformation Method and Generalized Differential Quadrature Method (미분변환법과 일반화 미분구적법을 이용한 탄성 지반상의 열림 균열을 가진 Euler-Bernoulli 보의 진동 해석)

  • Hwang Ki-Sup;Yun Jong-Hak;Shin Young-Jae
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.30 no.3 s.246
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    • pp.279-286
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    • 2006
  • The main purpose of this paper is to apply differential transformation method(DTM) and generalized differential quadrature method(GDQM) to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. In this paper the concepts of DTM and GDQM were briefly introduced. The governing equation of motion of the beam with open cracks on elastic foundation is derived. 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. Numerical calculations are carried out and compared with previous published results.

Analysis of Beam Resting on Hyperbolic Winkler Elastic Foundation by Differential Transformation (미분 변환법에 의한 쌍곡선형태 Winkler 탄성 지반상의 보 해석)

  • Shin, Yung-Jae;Yun, Jong-Hak;Jaun, Su-Ju
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.11b
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    • pp.1060-1065
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    • 2002
  • In this paper, the numerical analysis of beam rest ing on hyperbolic Winkler elastic foundation by differential transformation is performed. Accordig to the change of parameter of hyperbolic Winkler elastic foundation, beam deformation is computed when the boundary conditions are clamped-clamped, pined-pined and clamped-free.

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Analysis of Beam Resting on Hyperbolic Winkler Elastic Foundation by Differential Transformation (미분 변환법에 의한 쌍곡선형태 Winkler 탄성 지반상의 보 해석)

  • Shin, Young-Jae;Yun, Jong-Hak;Jaun, Su-Ju
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.11a
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    • pp.402.2-402
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    • 2002
  • In this paper, the numerical analysis of beam resting on hyperbolic Winkler elastic foundation by differential transformation is performed. Accordig to the change of parameter of hyperbolic Winkler elastic foundation, beam deformation is computed when the boundary conditions are clamped-clamped, pined-pined and clamped-free.

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