블록형 베르누이 원리 탐구 실험장치 개발

박진호,박종호 한국물리학회 2019 새물리 Vol.69 No.12

본 연구에서는 다양한 변인을 직접 조작하여 베르누이 원리를 시각적으로 확인할 수 있는 블록형 실험장치를 개발하였다. 블록형 베르누이 실험 장치는 기본적으로 3 가지 실린더 (직경 ϕ25, ϕ50, ϕ80) 형태로 제작하여 실린더의 표면적을 학생들이 변형할 수 있도록 하였다. 3 가지의 기본 실린더는 I자, L 자, T자로 구성된 3 가지의 연결관을 사용하여 다양한 형태의 실험 장치를 구성할 수 있다. 또한 풍력과풍속을 조절하며 그에 대한 현상을 시각적으로 확인할 수 있는 보조 실험 장치들을 제작하여 수준별 실험이가능하게 하였다. 실린더의 직경이 다른 두 부분의 풍속과 압력을 측정한 실험값을 베르누이 정리 및연속방정식을 이용하여 비교한 결과, 두 지점의 오차가 10% 이내로 유사한 것으로 나타났다. 또한 탁구공및 비행물체, 향 등을 이용한 시각 장치를 통해 유체의 속도를 정성적으로 관찰할 수 있었다. 이 장치를통해 학생들이 관의 표면적에 따른 풍속의 변화와 압력의 변화를 알 수 있으며, 학생들이 직접 블록형으로구성된 실험장치를 다양한 형태로 변형하여 실험 활동을 통해 베르누이 원리를 이해하는데 도움이 될것이라 기대한다. A Device for a block-type Bernoulli’s principle inquiry experiment was designed to verify the principle of Bernoulli visually by directly manipulating various variables. That device was basically constructed using three tubes with diameters of ϕ25, ϕ50, and ϕ80 so that the surface area of the tube could be modified by the students. The three basic tubes can be constructed of various types of experimental devices by using three tubes consisting of I, L and T. The devices were designed in such a way that wind power and wind speed, could be controlled and phenomena related to them could be checked visually. When the experimental values for wind speed and pressure in two different parts of the tube were compared by means of the Bernoulli theorem and the continuous equation, the errors at the two points were found to be similar to within 10%. In addition, the speed of the fluid was observed qualitatively through visual devices using ping pong balls, flying objects, and scents. Thus, students should be able to understand various phenomena by applying Bernoulli’s principle and experimenting with various types of experimental block-type devices.

Some closed formulas for generalizations of Bernoulli and Euler numbers and polynomials

Z. Zhang,H. Yang 장전수학회 2008 Proceedings of the Jangjeon mathematical society Vol.11 No.2

The purpose of this paper is to give some recurrence relations and closed formulas of generalized Bernoulli-Euler numbers and polynomials.

CERTAIN COMBINATORIC CONVOLUTION SUMS AND THEIR RELATIONS TO BERNOULLI AND EULER POLYNOMIALS

Kim, Daeyeoul,Bayad, Abdelmejid,Ikikardes, Nazli Yildiz Korean Mathematical Society 2015 대한수학회지 Vol.52 No.3

In this paper, we give relationship between Bernoulli-Euler polynomials and convolution sums of divisor functions. First, we establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli and Euler polynomials. Second, as applications, we show five identities concerning the third and fourth-order convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli or Euler polynomials.

CERTAIN COMBINATORIC CONVOLUTION SUMS AND THEIR RELATIONS TO BERNOULLI AND EULER POLYNOMIALS

김대열,Abdelmejid Bayad,Nazli Yildiz Ikikardes 대한수학회 2015 대한수학회지 Vol.52 No.3

In this paper, we give relationship between Bernoulli-Euler polynomials and convolution sums of divisor functions. First, we establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli and Euler polynomials. Second, as ap- plications, we show five identities concerning the third and fourth-order convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli or Euler polynomials.

Formulas and relations for Bernoulli-type numbers and polynomials derive from Bessel function

Selin Selen Ozbek Simsek,Yilmaz Simsek 대한수학회 2023 대한수학회논문집 Vol.38 No.4

The main purpose of this paper is to give some new identities and properties related to Bernoulli type numbers and polynomials associated with the Bessel function of the first kind. We give symmetric properties of the Bernoulli type numbers and polynomials. Moreover, using generating functions and the Fa \`{a} di Bruno's formula, we derive some new formulas and relations related to not only these polynomials, but also the Bernoulli numbers and polynomials and the Euler numbers and polynomials.

Reconstruction of Displacement, Velocity and Acceleration from Measured Dynamic Strain for Bernoulli-Beam Type Girders of Bridges

박광연,전상범,박연철,이해성 대한토목학회 2023 KSCE Journal of Civil Engineering Vol.27 No.5

This paper presents a new approach for reconstructing displacement, velocity and acceleration from measured strain in Bernoulli-beam type girders of bridges. A minimization problem is defined using the L2-norm of the strain-displacement relation of the Bernoulli beam with a regularization function to form a low-cut, spatial filter converting measured strain into displacement. A standard finite element procedure is applied to discretize the minimization problem. Fundamental characteristics of the spatial filter are discussed using the spatial Fourier transform. A temporal filter is adopted to filter out temporal noise in the displacement reconstructed by the spatial filter and to reconstruct velocity. Acceleration is calculated by the 1st-order central finite difference of the reconstructed velocity by the temporal filter. The validity of the proposed approach is demonstrated through a numerical simulation and field measurement on two-span continuous Bernoulli beams. It is shown that the proposed approach yields a good estimation of displacement and its temporal derivatives even for sparsely measured strain in the spatial domain. Detailed results of the numerical study are presented and discussed.

PHENOMENA AND PROPERTIES OF ROOTS OF BERNOULLI-FIBONACCI POLYNOMIALS

CHEON SEOUNG RYOO The Korean Society for Computational and Applied M 2024 Journal of applied and pure mathematics Vol.6 No.1

In this paper, we investigate the distribution of the zeros of the Bernoulli-Fibonacci polynomials by using computer.

On the static and dynamic stability of beams with an axial piezoelectric actuation

Zehetner, C.,Irschik, H. Techno-Press 2008 Smart Structures and Systems, An International Jou Vol.4 No.1

The present contribution is concerned with the static and dynamic stability of a piezo-laminated Bernoulli-Euler beam subjected to an axial compressive force. Recently, an inconsistent derivation of the equations of motions of such a smart structural system has been presented in the literature, where it has been claimed, that an axial piezoelectric actuation can be used to control its stability. The main scope of the present paper is to show that this unfortunately is impossible. We present a consistent theory for composite beams in plane bending. Using an exact description of the kinematics of the beam axis, together with the Bernoulli-Euler assumptions, we obtain a single-layer theory capable of taking into account the effects of piezoelectric actuation and buckling. The assumption of an inextensible beam axis, which is frequently used in the literature, is discussed afterwards. We show that the cited inconsistent beam model is due to inadmissible mixing of the assumptions of an inextensible beam axis and a vanishing axial displacement, leading to the erroneous result that the stability might be enhanced by an axial piezoelectric actuation. Our analytical formulations for simply supported Bernoulli-Euler type beams are verified by means of three-dimensional finite element computations performed with ABAQUS.

선형 변단면 정확탄성곡선형 아치의 자유진동

이병구(Lee Byoung Koo),이태은(Lee Tae Eun),김권식(Kim Gwon Sik) 대한토목학회 2009 대한토목학회논문집 A Vol.29 No.6A

이 논문은 선형 변단면 정확탄성곡선형 아치의 자유진동에 관한 연구이다. 정확탄성곡선형 아치의 선형은 Bernoulli-Euler 보 이론을 이용하여 산정하였다. 이러한 선형을 갖는 아치의 자유진동을 지배하는 미분방정식을 유도하고 이를 수치해석하여 무차원 고유진동수를 산출하였다. 수치해석 예에서는 세 종류의 선형 변단면과 두 종류의 지점조건을 채택하였다. 이 연구의 결과를 검증하기 위하여 이 연구와 SAP 2000의 고유진동수를 비교하였다. 수치해석의 결과로 지점조건, 변단면 형상, 세장비 및 단면비가 최저차 4개의 무차원 고유진동수에 미치는 영향을 분석하였다. This study deals with the free vibrations of the elastica shaped arch with linear taper. The shape of elastica is obtained from the Bernoulli-Euler beam theory. Differential equations governing free vibrations of such arch are derived and numerically solved to determine natural frequencies, in which three kinds of taper type and two kinds of end constraint, respectively, are considered. For validating the theories presented herein, the frequency parameters obtained ill this study are compared to those of SAP 2000. As results of the numerical analyses, effects of end constraint, taper type, slenderness ratio and section ratio and the lowest four non-dimensional frequency parameters are extensively investigated.

On the static and dynamic stability of beams with an axial piezoelectric actuation

C. Zehetner,H. Irschik 국제구조공학회 2008 Smart Structures and Systems, An International Jou Vol.4 No.1

The present contribution is concerned with the static and dynamic stability of a piezo-laminated Bernoulli-Euler beam subjected to an axial compressive force. Recently, an inconsistent derivation of the equations of motions of such a smart structural system has been presented in the literature, where it has been claimed, that an axial piezoelectric actuation can be used to control its stability. The main scope of the present paper is to show that this unfortunately is impossible. We present a consistent theory for composite beams in plane bending. Using an exact description of the kinematics of the beam axis, together with the Bernoulli-Euler assumptions, we obtain a single-layer theory capable of taking into account the effects of piezoelectric actuation and buckling. The assumption of an inextensible beam axis, which is frequently used in the literature, is discussed afterwards. We show that the cited inconsistent beam model is due to inadmissible mixing of the assumptions of an inextensible beam axis and a vanishing axial displacement, leading to the erroneous result that the stability might be enhanced by an axial piezoelectric actuation. Our analytical formulations for simply supported Bernoulli-Euler type beams are verified by means of three-dimensional finite element computations performed with ABAQUS.