• Structural Engineering and Mechanics
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• 제65권1호
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• pp.9-17
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• 2018

This study concerns about calculating exact natural frequencies of frames using a single variable shear deformation theory (SVSDT) which considers the parabolic shear stress distribution across the cross section. Free vibration analyses are performed for multi-bay, multi-storey and multi-bay multi-storey type frame structures. Dynamic stiffness formulations are derived and used to obtain first five natural frequencies of frames. Different beam and column cross sections are considered to reveal their effects on free vibration analysis. The calculated natural frequencies are tabulated with the results obtained using Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT). Moreover, the effects of inner and outer columns on natural frequencies are compared for multi-bay frames. Several mode shapes are plotted.

• Advances in Computational Design
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• 제7권1호
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• pp.1-17
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• 2022

In this study, a new strategy is presented to transmit the fundamental elastic beam problem into the modern optimization platform and solve it by using artificial intelligence (AI) tools. As a practical example, deflection of Euler-Bernoulli beam is mathematically formulated by 2nd-order ordinary differential equations (ODEs) in accordance to the classical beam theory. This fundamental engineer problem is then transmitted from classic formulation to its artificial-intelligence presentation where the behavior of the beam is simulated by using neural networks (NNs). The supervised training strategy is employed in the developed NNs implemented in the heuristic optimization algorithms as the fitness function. Different evolutionary optimization tools such as genetic algorithm (GA) and particle swarm optimization (PSO) are used to solve this non-linear optimization problem. The step-by-step procedure of the proposed method is presented in the form of a practical flowchart. The results indicate that the proposed method of using AI toolsin solving beam ODEs can efficiently lead to accurate solutions with low computational costs, and should prove useful to solve more complex practical applications.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.826-831
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• 2005

In this paper the effect of moving mass on dynamic behavior of cracked cantilever beam on elastic foundations is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. That is, the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. The crack is assumed to be in the first mode of fracture. As the depth of the crack is increased, the tip displacement of the cantilever beam is increased. When the crack depth is constant the frequency of a cracked beam is proportional to the spring stiffness.

• 한국소음진동공학회논문집
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• 제25권12호
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• pp.874-880
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• 2015

This paper presents the vibration analysis of a deploying beam with spin when the beam has a time-dependent spinning speed. In the previous studies for the deploying beams with spin, the spinning speed was time-independent. However, it is more reasonable to consider the time-dependent spinning speed. The present study introduces the time-dependent spinning speed in the modeling. The Euler-Bernoulli beam theory and von Karman nonlinear strain theory are used together to derive the equations of motion. After the equations of motion are transformed into the weak forms, the weak forms are discretized. The natural frequency and dynamic response are obtained. The effect of the time-dependent spinning speed on the dynamic response is studied.

• 한국소음진동공학회논문집
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• 제15권10호
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• pp.1195-1201
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• 2005

In this paper, the effect of a moving mass on dynamic behavior of the cracked cantilever beam on elastic foundations is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. That is, the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory The crack is assumed to be in the first mode of fracture. As the depth of crack is increased, the tip displacement of the cantilever beam is Increased. When the depth of crack is constant, the frequency of a cracked beam is proportional to the spring stiffness.

• Smart Structures and Systems
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• 제22권6호
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• pp.689-697
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• 2018

This paper presents a model of the elastic curve for rectangular beams with straight haunches under uniformly distributed load and moments in the ends considering the bending and shear deformations (Timoshenko Theory) to obtain the deflections and rotations on the beam, which is the main part of this research. The traditional model of the elastic curve for rectangular beams under uniformly distributed load considers only the bending deformations (Euler-Bernoulli Theory). Also, a comparison is made between the proposed and traditional model of simply supported beams with respect to the rotations in two supports and the maximum deflection of the beam. Also, another comparison is made for beams fixed at both ends with respect to the moments and reactions in the support A, and the maximum deflection of the beam. Results show that the proposed model is greater for simply supported beams in the maximum deflection and the traditional model is greater for beams fixed at both ends in the maximum deflection. Then, the proposed model is more appropriate and safe with respect the traditional model for structural analysis, because the shear forces and bending moments are present in any type of structure and the bending and shear deformations appear.

• 한국정밀공학회지
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• 제17권11호
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• pp.165-175
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• 2000

In recent years, it becomes a very important issue to consider the mechanical systems such as high-speed vehicles and railway trains moving on elastic beam structures. In this paper, a general approach, which can predict the dynamic behavior of constrained mechanical system and elastic beam structure, is proposed. Also, various supporting conditions of a foundation support are considered for the elastic beam structures. The elastic structure is assumed to be a nonuniform and linear Bernoulli-Euler beam with proportional damping effect. Combined Differential-Algebraic Equations of motion are derived using multibody dynamics theory and Finite Element Method. The proposed equations of motion can be solved numerically using generalizd coordinate partitioning method and Predictor-Corrector algorithm, which is an implicit multi-step integration method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.321-321
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• 2000

This paper presents a sliding mode controller based on variable structure for the tip position control of a single-link flexible manipulator. Dynamic equations of a single-link flexible manipulator are derived from the Euler-Lagrange equation using a Lagrangian assumed modes method based on Bernoulli-Euler Beam theory. Simulation results are presented to show the validity of the system modeling, controller design.

• Advances in nano research
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• 제4권1호
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• pp.31-44
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• 2016

This article is concerned with the free vibration problem for chiral double-walled carbon nanotube (DWCNTs) modelled using the non-local elasticity theory and Euler Bernoulli beam model. According to the governing equations of non-local Euler Bernoulli beam theory and the boundary conditions, the analytical solution is derived and two branches of transverse wave propagating are obtained. The numerical results obtained provide better representations of the vibration behaviour of double-walled carbon nanotube, where the aspect ratio of the (DWCNTs), the vibrational mode number, the small-scale coefficient and chirality of double-walled carbon nanotube on the frequency ratio (${\chi}^N$) of the (DWCNTs) are significant. In this work, the numerical results obtained can be used to predict and prevent the phenomenon of resonance for the forced vibration analyses of double -walled carbon nanotubes.

• Coupled systems mechanics
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• 제6권3호
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• pp.251-272
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• 2017

In this paper, the thermo-mechanical vibration characteristics of functionally graded (FG) nanobeams subjected to three types of thermal loading including uniform, linear and non-linear temperature change are investigated in the framework of third-order shear deformation beam theory which captures both the microstructural and shear deformation effects without the need for any shear correction factors. Material properties of FG nanobeam are assumed to be temperature-dependent and vary gradually along the thickness according to the power-law form. Hence, applying a third-order shear deformation beam theory (TSDBT) with more rigorous kinetics of displacements to anticipate the behaviors of FG nanobeams is more appropriate than using other theories. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. The obtained results are compared with those predicted by the nonlocal Euler-Bernoulli beam theory and nonlocal Timoshenko beam theory and it is revealed that the proposed modeling can accurately predict the vibration responses of FG nanobeams. The obtained results are presented for the thermo-mechanical vibration analysis of the FG nanobeams such as the effects of material graduation, nonlocal parameter, mode number, slenderness ratio and thermal loading in detail. The present study is associated to aerospace, mechanical and nuclear engineering structures which are under thermal loads.