• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.693-710
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• 2015

This paper presents a nonlocal shear deformation beam theory for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The developed theory account for higher-order variation of transverse shear strain through the depth of the nanobeam, and satisfy the stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. In addition, this nonlocal nanobeam model incorporates the length scale parameter which can capture the small scale effect and it has strong similarities with Euler-Bernoulli beam model in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

• Wind and Structures
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• v.27 no.6
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• pp.431-438
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• 2018

This paper presents a free vibration analysis of size-dependent functionally graded (FG) nanobeams with all surface effects considerations on the basis of modified couple stress theory. The material properties of FG nanobeam are assumed to vary according to power law distribution. Based on the Euler-Bernoulli beam theory, the modeled nanobeam and its equations of motion are derived using Hamilton's principle. An analytical method is used to discretize the model and the equation of motion. The model is validated by comparing the benchmark results with the obtained results. Results show that the vibration behavior of a nanobeam is significantly influenced by surface density, surface tension and surface elasticity. Also, it is shown that by increasing the beam size, influence of surface effect reduces to zero, and the natural frequency tends to its classical value.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.713-716
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• 2004

In this paper a dynamic behavior of a double-cracked cnatilver beam with a tip mass and the moving mass is presented. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using Lagrange's equation. The influences of the moving mass, a tip mass and double cracks have been studied on the dynamic behavior of a cantilever beam system by numerical method. The cracks section are represented by the local flexibility matrix connecting two undamaged beam segments. ,Therefore, the cracks are modelled as a rotational spring. Totally, as a tip mass is increased, the natural frequency of cantilever beam is decreased. The position of the crack is located in front of the cantilever beam, the frequencies of a double-cracked cantilever beam presents minimum frequency.

• Coupled systems mechanics
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• v.6 no.3
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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.

• Advanced Composite Materials
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• v.18 no.2
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• pp.105-119
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• 2009

In this work, the structural response of thin-walled composite beams with pretwist angle is investigated by using a mixed beam approach that combines the stiffness and flexibility methods in a unified manner. The Reissner's semi-complimentary energy functional is used to derive the stiffness matrix that approximates the beam in an Euler-Bernoulli level for extension and bending and Vlasov level for torsion. The bending and torsion-related warpings induced by the pretwist effects are derived in a closed form. The developed theory is validated with available literature and detailed finite element structural analysis results using the MSC/NASTRAN. Pretwisted composite beams with rectangular solid and thin-walled box sections are illustrated to validate the current approach. Acceptable correlation has been achieved for cases considered in this study. The effects of pretwist and fiber orientation angles on the static behavior of pretwisted composite beams are also studied.

• Structural Engineering and Mechanics
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• v.71 no.3
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• pp.223-232
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• 2019

Since the actuators with small- scale structures may be exposed to external reciprocal actions lead to create undesirable loads causing instability, the buckling behaviors of them are interested to make reliable or accurate actions. Therefore, the purpose of this paper is to analyze plastic buckling behavior of the micro beam structures by adopting a Conventional Mechanism-based Strain Gradient plasticity (CMSG) theory. The effect of length scale on critical force is considered for three types of boundary conditions, i.e. the simply supported, cantilever and clamped - simply supported micro beams. For each case, the stability equations of the buckling are calculated to obtain related critical forces. The constitutive equation involves work hardening phenomenon through defining an index of multiple plastic hardening exponent. In addition, the Euler-Bernoulli hypothesis is used for kinematic of deflection. Corresponding to each length scale and index of the plastic work hardening, the critical forces are determined to compare them together.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.707-710
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• 2005

In this paper, we studied about the dynamic behavior of a cracked rotating cantilever beam. The influences of a rotating angular velocity, the crack depth and the crack position on the dynamic behavior of a cracked cantilever beam have been studied by the numerical method. The cracked cantilever beam is modeled by the Euler-Bernoulli beam theory. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The lateral tip displacement and the axial tip deflection of a rotating cantilever beam is more sensitive to the rotating angular velocity than the depth and position of crack. Totally, as the crack depth is increased, the natural frequency of a rotating cantilever beam is decreased in the first and second mode of vibration.

• Steel and Composite Structures
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• v.19 no.6
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• pp.1421-1447
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• 2015

In this paper, the effect of material-temperature dependent on the wave propagation of a cantilever beam composed of functionally graded material (FGM) under the effect of an impact force is investigated. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. Material properties of the beam are temperature-dependent and change in the thickness direction. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Euler-Bernoulli beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain and frequency domain by using Newmark average acceleration method. In order to establish the accuracy of the present formulation and results, the comparison study is performed with the published results available in the literature. Good agreement is observed. In the study, the effects of material distributions and temperature rising on the wave propagation of the FGM beam are investigated in detail.

• Advances in concrete construction
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• v.17 no.4
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• pp.187-210
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• 2024

Cantilever structures demonstrate diverse nonlocal effects, resulting in either stiffness hardening or dynamic softening behaviors, as various studies have indicated. This research delves into the free and forced vibration analysis of rotating nanoscale cylindrical beams and tubes under external dynamic stress, aiming to thoroughly explore the nonlocal impact from both angles. Utilizing Euler-Bernoulli and Reddy beam theories, in conjunction with higher-order tube theory and Hamilton's principle, nonlocal governing equations are derived with precise boundary conditions for both local and nonlocal behaviors. The study specifically examines two-dimensional functionally graded materials (2D-FGM), characterized by axially functionally graded (AFG) and radial porosity distributions. The resulting partial differential equations are solved using the generalized differential quadrature element method (GDQEM) and Newmark-beta procedures to acquire time-dependent results. This investigation underscores the significant influence of boundary conditions when nonlocal forces act on cantilever structures.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.547-551
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• 1996

In this paper, robust vibration control of a one-link flexible robot arm based on variable structure system is discussed. We derive dynamic equations of it using a Lagrangian assumed modes method based on Bernoulli-Euler Beam theory. The optimal sliding surface is designed and the problem of chattering is also solved by the adoption of a continuous control law within a small neighborhood of the switching hyperplane.