• Title/Summary/Keyword: Euler Bernoulli

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Nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation

  • Javanmard, Mehran;Bayat, Mahdi;Ardakani, Alireza
    • Steel and Composite Structures
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    • v.15 no.4
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    • pp.439-449
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    • 2013
  • In this study simply supported nonlinear Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads is investigated. A new kind of analytical technique for a non-linear problem called He's Energy Balance Method (EBM) is used to obtain the analytical solution for non-linear vibration behavior of the problem. Analytical expressions for geometrically non-linear vibration of Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads are provided. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. The variation of different parameter to the nonlinear frequency is considered completely in this study. The nonlinear vibration equation is analyzed numerically using Runge-Kutta $4^{th}$ technique. Comparison of Energy Balance Method (EBM) with Runge-Kutta $4^{th}$ leads to highly accurate solutions.

MORE EXPANSION FORMULAS FOR q, 𝜔-APOSTOL BERNOULLI AND EULER POLYNOMIALS

  • Ernst, Thomas
    • Communications of the Korean Mathematical Society
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    • v.35 no.2
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    • pp.417-445
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    • 2020
  • The purpose of this article is to continue the study of q, 𝜔-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, 𝜔-Apostol Bernoulli and Euler polynomials, Ward-𝜔 numbers and multiple q, 𝜔power sums. Like before, the q, 𝜔-module for the alphabet of q, 𝜔-real numbers plays a crucial role, as well as the q, 𝜔-rational numbers and the Ward-𝜔 numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.

Impact Force Roconstruction and Impact Model Identification Using Inverse Dynamics of an Impacted Beam (역동역학을 이용한 충격을 받는 보의 충격력 복원 및 충격모델의 변수 파악)

  • 박형순;박윤식
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.3
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    • pp.623-630
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    • 1995
  • The impulse response functions (force-strain relations) for Euler-Bernoulli and Timoshenko beams are considered. The response of a beam to a transverse impact force is numerically obtained with the convolution approach using the impulse response function obtained by Laplace transform. Using this relation, the impact force history is determined in the time domain and results are compared with those from Hertz's contact law. The parameters of timpact force model are identified using the recovered force and compared with the Hertz's contact model. In order to verify the proposed algorithm, measurements were done using an impact hammer and a steel ball drop test and these results are also compared with the simulated values.

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.

Design on the Controller of Flexible Robot using Sliding Sector Control (슬라이딩 섹터 제어를 이용한 유연한 로봇 팔에 대한 제어기 설계)

  • Han, Jong-Kil;Bae, Sung-Hwan;Yang, Keun-Ho
    • The Journal of the Korea institute of electronic communication sciences
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    • v.5 no.5
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    • pp.541-546
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    • 2010
  • When a flexible arm is rotated by a motor about an joint axis, transverse vibration may occur. The motor torque should be controlled in such a way that the moter rotates by a specified angle, while simultaneously stabilizing vibration of the flexible arm so that it is arrested at the end of rotation. In this paper, the dynamic model of flexible robot arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Nonlinear control with hysteresis deadzone using the sliding sector theory with continued input function in the sector is proposed.

Differential transform method for free vibration analysis of a moving beam

  • Yesilce, Yusuf
    • Structural Engineering and Mechanics
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    • v.35 no.5
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    • pp.645-658
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    • 2010
  • In this study, the Differential Transform Method (DTM) is employed in order to solve the governing differential equation of a moving Bernoulli-Euler beam with axial force effect and investigate its free flexural vibration characteristics. The free vibration analysis of a moving Bernoulli-Euler beam using DTM has not been investigated by any of the studies in open literature so far. At first, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Bernoulli-Euler beam theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equation of the motion. The calculated natural frequencies of the moving beams with various combinations of boundary conditions using DTM are tabulated in several tables and are compared with the results of the analytical solution where a very good agreement is observed.

Non-Linear Behavior of Tapered Simple Beam with a Floating Concentrated Load (변화위치 집중하중을 받는 변단면 단순보의 비선형 거동)

  • 이병구
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.42 no.2
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    • pp.108-114
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    • 2000
  • This paper explores the non-linear behavior of tapered beam subjected to a floating concentration load. For applying the Bernoulli-Euler beam theory to this beam, the bending moment at any point of elastical is obtained from the final equilibrium stage. By using the bending moment equation and the Bernoulli-Euler beam theory, the differential equations governing the elastica of simple beam are derived , and solved numberically . Three kinds of tapered beam types are considered . The numerical results of the non-linear behavior obtained in this study are agreed quite well to the results obtained from the laboratory-scale experiments.

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IDENTITIES AND RELATIONS ON THE q-APOSTOL TYPE FROBENIUS-EULER NUMBERS AND POLYNOMIALS

  • Kucukoglu, Irem;Simsek, Yilmaz
    • Journal of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.265-284
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    • 2019
  • The main purpose of this paper is to investigate the q-Apostol type Frobenius-Euler numbers and polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive q-integers. By using infinite series representation for q-Apostol type Frobenius-Euler numbers and polynomials including their interpolation functions, we not only give some identities and relations for these numbers and polynomials, but also define generating functions for new numbers and polynomials. Further we give remarks and observations on generating functions for these new numbers and polynomials. By using these generating functions, we derive recurrence relations and finite sums related to these numbers and polynomials. Moreover, by applying higher-order derivative to these generating functions, we derive some new formulas including the Hurwitz-Lerch zeta function, the Apostol-Bernoulli numbers and the Apostol-Euler numbers. Finally, for an application of the generating functions, we derive a multiplication formula, which is very important property in the theories of normalized polynomials and Dedekind type sums.