• 한국수학사학회지
• /
• 제17권1호
• /
• pp.43-52
• /
• 2004

In this paper we investigate the origin of the variational calculus with respect to the extremal principle. We also study the role the extremal principle has played in the development of the calculus of variations. We deal with Dido's isoperimetric problem, Maupertius's least action principle, brachistochrone problem, geodesics, Johann Bernoulli's principle of virtual work, Plateau's minimal surface and Dirichlet principle.

• Structural Engineering and Mechanics
• /
• 제63권2호
• /
• pp.161-169
• /
• 2017

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler-Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

• 한국철도학회:학술대회논문집
• /
• 한국철도학회 2011년도 춘계학술대회 논문집
• /
• pp.314-316
• /
• 2011

This paper develops a spectral element model for the composite beams with a surface-bonded piezoelectric layer from the governing equations of motion. The governing equations of motion are derived from Hamilton's principle by applying the Bernoulli-Euler beam theory for the bending vibration and the elementary rod theory for the longitudinal vibration of the composite beams. For the PZT layer, the Bernoulli-Euler beam theory and linear piezoelectricity theory are applied. The high accuracy of the present spectral element model is evaluated through the numerical examples by comparing with the finite element analysis results.

• 식품과학과 산업
• /
• 제51권2호
• /
• pp.114-126
• /
• 2018

The production of high quality oil to meet new standard needs a 'next generation' innovative oil refining tool in paradigm shift. 'Nanoneutralization' using controlled hydrodynamic cavitation-assisted Nanoreactor is successfully being introduced and commercialized into edible oil industry and it plays a key driver for sustainable development of food processing. This emerging technology using bubble dynamics as a consequence of Bernoulli's principle by hydrodynamic cavitation in Venturi-designed multi-flow through cell is radically changing the conventionally chemical-oriented neutralization. Nanoneutralization derived by the creation of nanometer-sized bubbles formed through scientifically structured geometric channels under high pressure has been proven to improve mass transfer and reaction rate so substantially reduce the chemicals required for refined vegetable oil and to increase oil yield while even improving oil quality. More researches on science behind this revolutionary technology will help usto better understand the principle and process hence makes its potential applications expandable in extraction, refining and modification of fats and oils processing.

• 한국음향학회지
• /
• 제37권6호
• /
• pp.422-427
• /
• 2018

본 연구에서는 소형 물체가 음파 정상파의 압력 마디 부근에 소형 물체가 부양하는 정상파 음파 공중부양(standing wave acoustic levitation) 현상에 대해 베르누이 원리를 이용하여 부양의 원인이 되는 음향 방사힘(acoustic radiation force)의 근원과 개형을 기존에 알려진 진동자에서 떨어진 거리에 따른 음향 방사힘의 그래프와 비교함을 통해 개념적으로 설명했다. 이러한 설명을 뒷받침하는 일련의 실험들을 BLT(Bolt-clamped Langevin Type) 초음파 진동자를 이용해서 수행하여, 물체들이 공기의 압력 마디 부근에 부양하고 있음을 확인했고, 물체가 부양하고 있는 상태에서 정상파가 형성되는 조건임을 확인했다. 더불어, 정상파 음파 공중부양 현상에서 부양하는 물체들이 수직하게 일렬로 정렬하는 현상 역시 설명할 수 있었다.

• 대한기계학회논문집B
• /
• 제37권7호
• /
• pp.629-636
• /
• 2013

공압 부상은 베르누이 원리에 기초한다. 그러나 공압 부상 방법은 제품의 원가 상승의 요인이 되는 대량의 유량을 소모하는 것으로 알려져 있다. 이 논문에서는 베르누이 부상 유동의 통찰력을 얻기 위해 수치 해석 연구를 수행하였다. 3차원 압축성 Navier-Stokes 방정식과 SST k-${\omega}$ 난류모델에 유한 체적법을 적용하여 계산하였다. 기체 유량, 공정 제품의 직경 그리고 원형실린더와 공정 제품사이의 간극을 다양하게 변화하여 공정 제품 주위의 유동 특성을 조사하였다. 그 결과 부상력을 위한 최적의 간극과 공급 기체 유량이 증가하면 큰 부상력이 발생한다는 것을 알았다.

• 한국전산구조공학회논문집
• /
• 제24권2호
• /
• pp.149-156
• /
• 2011

본 논문에서는 생브낭의 원리를 이용하여 보/판/쉘 등의 구조물에서 응력분포를 후처리함으로써 개선할 수 있는 방법을 개발하였다. 생브낭의 원리에 따르면, 주어진 탄성문제에 대해서 실제의 응력분포에 상관없이 합응력들로 문제를 기술할 수 있다. 현재까지 알려진 바에 따르면 유일하게 점근적으로 타당한 이론들은 Euler-Bernoulli(E-B) 보이론과 Kirchhoff-Love(K-L) 판이론 등이 있다. 많은 공학적 문제들이 이 두 이론들에 기초하여 해석되어 왔음은 주지의 사실이다. 하지만, 현대의 공학 문제들은 보다 정확한 해석기법을 요구한다. 본 연구에서는 자유도가 상대적으로 많은 고차이론 등을 사용하지 않고, 고전적인 E-B 또는 K-L 해석결과를 합응력 등가의 원리를 이용하여 후처리함으로써 변위 및 응력분포를 정확하게 예측할 수 있는 방법을 개발하였고, 이방성 보 수치예제를 통해 제안된 방법론을 탄성해석법과 비교 검증하였다.

• Structural Engineering and Mechanics
• /
• 제59권3호
• /
• pp.431-454
• /
• 2016

In this paper, the nonlinear static and free vibration analysis of Euler-Bernoulli composite beam model reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) with initial geometrical imperfection under uniformly distributed load using finite element method (FEM) is investigated. The governing equations of equilibrium are derived by the Hamilton's principle and von Karman type nonlinear strain-displacement relationships are employed. Also the influences of various loadings, amplitude of the waviness, UD, USFG, and SFG distributions of carbon nanotube (CNT) and different boundary conditions on the dimensionless transverse displacements and nonlinear frequency ratio are presented. It is seen that with increasing load, the displacement of USFG beam under force loads is more than for the other states. Moreover it can be seen that the nonlinear to linear natural frequency ratio decreases with increasing aspect ratio (h/L) for UD, USFG and SFG beam. Also, it is shown that at the specified value of (h/L), the natural frequency ratio increases with the increasing the values amplitude of waviness while the dimensionless nonlinear to linear maximum deflection decreases. Moreover, with considering the amplitude of waviness, the stiffness of Euler-Bernoulli beam model reinforced by FG-CNT increases. It is concluded that the R parameter increases with increasing of volume fraction while the rate of this parameter decreases. Thus one can be obtained the optimum value of FG-CNT volume fraction to prevent from resonance phenomenon.

• Steel and Composite Structures
• /
• 제21권5호
• /
• pp.999-1016
• /
• 2016

This study presents free vibration of beam made of porous material. The mechanical properties of the beam is variable in the thickness direction and the beam is investigated in three situations: poro/nonlinear nonsymmetric distribution, poro/nonlinear symmetric distribution, and poro/monotonous distribution. First, the governing equations of porous beam are derived using principle of virtual work based on Euler-Bernoulli theory. Then, the effect of pores compressibility on natural frequencies of the beam is studied by considering clamped-clamped, clamped-free and hinged-hinged boundary conditions. Moreover, the results are compared with homogeneous beam with the same boundary conditions. Finally, the effects of poroelastic parameters such as pores compressibility, coefficients of porosity and mass on natural frequencies has been considered separately and simultaneously.

• Structural Engineering and Mechanics
• /
• 제45권1호
• /
• pp.69-93
• /
• 2013

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.