• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.621-631
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• 2018

In this paper, an exact analytical solution is developed for the analysis of the post-buckling non-linear response of simply supported deformable symmetric composite beams. For this, a new theory of higher order shear deformation is used for the analysis of composite beams in post-buckling. Unlike any other shear deformation beam theories, the number of functions unknown in the present theory is only two as the Euler-Bernoulli beam theory, while three unknowns are needed in the case of the other beam theories. The theory presents a parabolic distribution of transverse shear stresses, which satisfies the nullity conditions on both sides of the beam without a shear correction factor. The shear effect has a significant contribution to buckling and post-buckling behaviour. The results of this analysis show that classical and first-order theories underestimate the amplitude of the buckling whereas all the theories considered in this study give results very close to the static response of post-buckling. The numerical results obtained with the novel theory are not only much more accurate than those obtained using the Euler-Bernoulli theory but are almost comparable to those obtained using higher order theories, Accuracy and effectiveness of the current theory.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.11
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• pp.1157-1169
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• 2008

This paper presents spectral element formulation which approximates Lamb wave propagation by PZT transducers bonded on a thin plate. A two layer beam model under 2-D plane strain condition is introduced to simulate high-frequency dynamic responses induced by a piezoelectric (PZT) layer rigidly bonded on a base plate. Mindlin-Herrmann and Timoshenko beam theories are employed to represent the first symmetric and anti-symmetric Lamb wave modes on a base plate, respectively. The Euler-Bernoulli beam theory and 1-D linear piezoelectricity are used to model the electro-mechanical behavior of a PZT layer. The equations of motions of a two layer beam model are derived through Hamilton's principle. The necessary boundary conditions associated with the electro-mechanical properties of a PZT layer are formulated in the context of dual functions of a PZT layer as an actuator and a sensor. General spectral shape functions of response field and the associated boundary conditions are obtained through equations of motions converted into frequency domain. Detailed spectrum element formulation for composing the dynamic stiffness matrix of a two layer beam model is presented as well. The validity of the proposed spectral element is demonstrated through numerical examples.

• Advances in Computational Design
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• v.7 no.1
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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.

• Journal of Mechanical Science and Technology
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• v.19 no.9
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• pp.1731-1741
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• 2005

In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.11
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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.

• Advances in nano research
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• v.4 no.1
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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.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1999.10c
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• pp.206-211
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• 1999

The purpose of this study is to investigate the natural frequencies and mode shapes of beam-columns on the non-homogeneous foundaion. The beam model is based on the classical Bernoulli-Euler beam theory. The linear foundation modulus is chosen as the non-homogeneous foundation in this study . The differentidal equation goeverning free vibrations of such beam-columns subjected to axial load is derived and solved numerically for calculting the natural frquencies and mode shapes. In numerical fivekinds of end constraint are considered, and the lowest four natural frquencies and corresponding mode shape are obtained as the non-dimensional forms.

• Structural Engineering and Mechanics
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• v.41 no.2
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• pp.285-297
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• 2012

An inverse approach is presented for calculating the flexibility coefficient of open-side cracks in the cross sectional of beams. The cracked cross section is treated as a massless rotational spring which connects two segments of the beam. Based on the Euler-Bernoulli beam theory, the differential equation governing the forced vibration of each segment of the beam is written. By using a mathematical manipulation the time dependent differential equations are transformed into the static substitutes. The crack characteristics are then introduced to the solution of the differential equations via the boundary conditions. By having the time history of transverse response of an arbitrary location along the beam, the flexibility coefficient of crack is calculated. The method is applied for some cracked beams with solid rectangular cross sections and the results obtained are compared with the available data in literature. The comparison indicates that the predictions of the proposed method are in good agreement with the reported data. The procedure is quite general so as to it can be applicable for both single-side crack and double-side crack analogously. Hence, it is also applied for some test beams with double-side cracks.

• The Journal of the Acoustical Society of Korea
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• v.16 no.1
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• pp.16-23
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• 1997

As analysis of the forced dynamic response and vibrational mode for the cantilevered beam is described. Experimental results are compared with the natural frequencies and vibrational modes for the cantilevered beam using the theory of Bernoulli-Euler and finite element method. We have found 1st and 2nd resonance frequency of the cantilevered beam by means of the various external frequencies, $1{\sim}70Hz$, using magnetic transducer. And we have studied the vibrational displacement at obtained resonance frequency of the cantilevered beam. The experimental results for the nodes of cantilevered beam were 0 in 1st mode and 0,0.786 in 2nd mode. close agreement between the theoretically predicted results and experimental result was obtained for the vibrational mode.

• Wind and Structures
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• v.27 no.4
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• pp.247-254
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• 2018

In this paper, a simple first-order shear deformation theory is presented for dynamic behavior of functionally graded beams. Unlike the existing first-order shear deformation theory, the present one contains only three unknowns and has strong similarities with the classical beam theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions of simply supported FG beam are obtained and the results are compared with Euler-Bernoulli beam and the other shear deformation beam theory results. Comparison studies show that this new first-order shear deformation theory can achieve the same accuracy of the existing first-order shear deformation theory.