• Title/Summary/Keyword: Bernoulli equation

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Determination of Elastic Modulus by Time Average ESPI and Euler-Bernoulli Equation (Time Average ESPI와 Euler-Bernoulli 방정식에 의한 탄성계수 측정)

  • Kim, Koung-Suk;Lee, Hang-Seo;Kang, Young-June;Kang, Ki-Soo
    • Journal of the Korean Society for Precision Engineering
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    • v.24 no.7 s.196
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    • pp.69-74
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    • 2007
  • The paper proposes a new sonic resonance test for a elastic modulus measurement which is based on time-average electronic speckle pattern interferometry(TA-ESPI) and Euler-Bernoulli equation. Previous measurement technique of elastic constant has the limitation of application for thin film or polymer material because contact to specimen affects the result. TA-ESPI has been developed as a non-contact optical measurement technique which can visualize resonance vibration mode shapes with whole-field. The maximum vibration amplitude at each vibration mode shape is a clue to find the resonance frequencies. The dynamic elastic constant of test material can be easily estimated from Euler-Bernoulli equation using the measured resonance frequencies. The proposed technique is able to give high accurate elastic modulus of materials through a simple experiment set up and analysis.

HARDY'S INEQUALITY RELATED TO A BERNOULLI EQUATION

  • Hyun, Jung-Soon;Kim, Sang-Dong
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.81-87
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    • 2002
  • The weighted Hardy's inequality is known as (equation omitted) where -$\infty$$\leq$a$\leq$b$\leq$$\infty$ and 1 < p < $\infty$. The purpose of this article is to provide a useful formula to express the weight r(x) in terms of s(x) or vice versa employing a Bernoulli equation having the other weight as coefficients.

GLOBAL EXISTENCE AND STABILITY FOR EULER-BERNOULLI BEAM EQUATION WITH MEMORY CONDITION AT THE BOUNDARY

  • Park, Jong-Yeoul;Kim, Joung-Ae
    • Journal of the Korean Mathematical Society
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    • v.42 no.6
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    • pp.1137-1152
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    • 2005
  • In this article we prove the existence of the solution to the mixed problem for Euler-Bernoulli beam equation with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.

DETERMINATION OF THE FLEXURAL RIGIDITY OF A BEAM FROM LIMITED BOUNDARY MEASUREMENTS

  • LESNIC DANIEL
    • Journal of applied mathematics & informatics
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    • v.20 no.1_2
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    • pp.17-34
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    • 2006
  • Inverse coefficient identification problems associated with the fourth-order Sturm-Liouville operator in the steady state Euler-Bernoulli beam equation are investigated. Unlike previous studies in which spectral data are used as additional information, in this paper only boundary information is used, hence non-destructive tests can be employed in practical applications.

Series Solution of High Order Abel, Bernoulli, Chini and Riccati Equations

  • Henk, Koppelaar;Peyman, Nasehpour
    • Kyungpook Mathematical Journal
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    • v.62 no.4
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    • pp.729-736
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    • 2022
  • To help solving intractable nonlinear evolution equations (NLEEs) of waves in the field of fluid dynamics we develop an algorithm to find new high order solutions of the class of Abel, Bernoulli, Chini and Riccati equations of the form y' = ayn + by + c, n > 1, with constant coefficients a, b, c. The role of this class of equations in NLEEs is explained in the introduction below. The basic algorithm to compute the coefficients of the power series solutions of the class, emerged long ago and is further developed in this paper. Practical application for hitherto unknown solutions is exemplified.

OME PROPERTIES OF THE BERNOULLI NUMBERS OF THE SECOND KIND AND THEIR GENERATING FUNCTION

  • Qi, Feng;Zhao, Jiao-Lian
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1909-1920
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    • 2018
  • In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

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.

Gemetrical Non-Linear Behavior of Simply Supported Tapered Beams (단순지지 변단면 보의 기하학적 비선형 거동)

  • 이병구
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.41 no.1
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    • pp.106-114
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    • 1999
  • This paper explores the geometrical non-linear behavior of the simply supported tapered beams subject to the trapezoidal distributed load and end moments. In order to apply the Bernoulli -Euler beam theory to this tapered beam, the bending moment equation on any point of the elastical is obtained by the redistribution of trapezoidal distributed load. On the basis of the bending moment equation and the BErnoulli-Euler beam theory, the differential equations governging the elastical of such beams are derived and solved numerically by using the Runge-Jutta method and the trial and error method. The three kinds of tapered beams (i.e. width, depth and square tapers) are analyzed in this study. The numerical results of non-linear behavior obtained in this study from the simply supported tapered beams are appeared to be quite well according to the results from the reference . As the numerical results, the elastica, the stress resultants and the load-displacement curves are given in the figures.

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