• Advances in nano research
• /
• 제9권2호
• /
• pp.91-104
• /
• 2020

The bending, stability (buckling) and vibration response of nano sized beams is presented in this study based on the Eringen's nonlocal elasticity theory in conjunction with the Euler-Bernoulli beam theory. For this purpose, the bending, buckling and vibration problem of Euler-Bernoulli nanobeams are developed and solved on the basis of nonlocal elasticity theory. The effects of various parameters such as nonlocal parameter e₀a, length of beam L, mode number n, distributed load q and cross-section on the bending, buckling and vibration behaviors of carbon nanotubes idealized as Euler-Bernoulli nanobeam is investigated. The transverse deflections, maximum transverse deflections, vibrational frequency and buckling load values of carbon nanotubes are given in tables and graphs.

• Advances in materials Research
• /
• 제7권3호
• /
• pp.163-174
• /
• 2018

This article studies the free and forced vibrations of the carbon nanotubes CNTs embedded in an elastic medium including thermal and dynamic load effects based on nonlocal Euler-Bernoulli beam. A Winkler type elastic foundation is employed to model the interaction of carbon nanotube and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, high temperature change, Winkler modulus parameter, vibration mode and aspect ratio of short carbon nanotubes on the vibration frequency are analyzed and discussed. The non-local Euler-Bernoulli beam model predicts lower resonance frequencies. The research work reveals the significance of the small-scale coefficient, the vibrational mode number, the elastic medium and the temperature change on the non-dimensional natural frequency.

• 한국건설순환자원학회논문집
• /
• 제11권4호
• /
• pp.467-475
• /
• 2023

본 논문에서는 내리기 시 파이프라인의 단면력 해석을 위한 합리적인 해석 모델을 제안했다. 본 해석 모델은 기하학적 특성과 경계조건을 고려하여 파이프라인을 분할한 후 two parameters Beam On Elastic Foundation과 Euler-Bernoulli 빔으로 모델링했다. 또한 파이프라인과 지반의 상호 작용 뿐만 아니라 파이프라인에 작용하는 축력을 했다. 기존 모델은 정형화된 하중 조건만 적용이 용이했으나 Segmented Pipeline Model로 정의된 제안 모델은 내리기 시 발생되는 대부분의 시공 조건에 대해 고려할 수 있다. 또한 가정을 최소화하고 요소를 세분화하여 모델링의 편의성과 적용성을 향상시켰다. 그럼에도 불구하고 이 모델은 FE 모델에 대비 높은 정확도를 갖고 있으므로 내리기 시 파이프라인의 안전성 평가는 물론 형상관리에도 효율적으로 활용될 수 있을 것으로 기대된다. 또한 시공 단계에서 파이프라인의 안전성을 확보함에 따라 운용 중 내구성 향상에 큰 도움이 될 것으로 판단된다.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
• /
• pp.138-143
• /
• 1989

In considering the singularities of robot, singularity avoidance control of robot wrist is very important. Because it is more difficult structurally to exclude the wrist singularity than the arm singularity. Since control policies with Jacobian may bring about mathematical singularities, control policies with Euler parameters that never cause mathematical singularities are necessary. In this research, singular status of robot wrist was analyzed and control algorithms for 3 and 4 axes robot wrist were proposed. Application results of the proposed control algorithms to the path including singularity showed us usefulness and validity.

• Kyungpook Mathematical Journal
• /
• 제49권4호
• /
• pp.731-742
• /
• 2009

In this paper, by introducing parameters ${\lambda}$, ${\alpha}$and two pairs of conjugate exponents (p, q), (r, s) and applying the improved Euler-Maclaurin's summation formula, we establish a reverse of the slightly sharper Hilbert-type inequality. As applications, the strengthened version and the equivalent form are given.

• Smart Structures and Systems
• /
• 제33권2호
• /
• pp.165-175
• /
• 2024

Rotating beams play a crucial role in representing complex mechanical components that are prevalent in vital sectors like energy and transportation industries. These components are susceptible to the initiation and propagation of cracks, posing a substantial risk to their structural integrity. This study presents a two-stage methodology for detecting the location and estimating the size of an open-edge transverse crack in a rotating Euler-Bernoulli beam with a uniform cross-section. Understanding the dynamic behavior of beams is vital for the effective design and evaluation of their operational performance. In this regard, modal parameters such as natural frequencies and eigenmodes are frequently employed to detect and identify damages in mechanical components. In this instance, the Frobenius method has been employed to determine the first two natural frequencies and corresponding eigenmodes associated with flapwise bending vibration. These calculations have been performed by solving the governing differential equation that describes the motion of the beam. Various parameters have been considered, such as rotational speed, beam slenderness, hub radius, and crack size and location. The effect of the crack has been replaced by a rotational spring whose stiffness represents the increase in local flexibility as a result of the damage presence. In the initial phase of the proposed methodology, a damage index utilizing the slope of the beam's eigenmode has been employed to estimate the location of the crack. After detecting the presence of damage, the size of the crack is determined using a Genetic Algorithm optimization technique. The ultimate goal of the proposed methodology is to enable the development of more suitable and reliable maintenance plans.

• 대한수학회논문집
• /
• 제26권4호
• /
• pp.709-720
• /
• 2011

We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
• /
• pp.175-177
• /
• 2003

The convergence characteristics of the LV scheme for the Euler equations have been investigated by using the Von Neumann stability analysis. The results indicated that the convergence rate is governed by a specific combination of CFD parameters. Based on this insight, it is shown that the convergence characteristics of the LV scheme is not deteriorated at any grid aspect-ratio as long as the local time step is defined based on the parameter combination. The numerical results demonstrated that this time step definition provide a uniform convergence for grid aspect-ratios between one to$1{\times}10^{4}$.

• 대한기계학회논문집
• /
• 제19권3호
• /
• pp.623-630
• /
• 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.

• Advances in concrete construction
• /
• 제12권6호
• /
• pp.491-497
• /
• 2021

Cell components play vital role within the cell when the cell under goes deformation. These components are microtubules, microfilaments and intermediate filaments. Intermediate filaments are like thread and are of different types. Like microtubules and microfilaments these components also undergo the deformation and their dynamics affected when change occurs within cell. In the present study, bending of intermediate filaments are studied keeping the nonlocal effects under consideration. It is observed that the nonlocal parameter has a great impact on the dynamics of intermediate filaments. This study is made by the application of Euler beam theory.