• Structural Engineering and Mechanics
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• v.18 no.3
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• pp.303-314
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• 2004

An artificial neural network (ANN) application is presented for flexural and axial vibration analysis of elastic beams with various support conditions. The first three natural frequencies of beams are obtained using multi layer neural network based back-propagation error learning algorithm. The natural frequencies of beams are calculated for six different boundary conditions via direct solution of governing differential equations of beams and Rayleigh's approximate method. The training of the network has been made using these data only flexural vibration case. The trained neural network, however, had been tested for cantilever beam (C-F), and both end free (F-F) in case the axial vibration, and clamped-clamped (C-C), and Guided-Pinned (G-P) support condition in case the flexural vibrations which were not included in the training set. The results found by using artificial neural network are sufficiently close to the theoretical results. It has been demonstrated that the artificial neural network approach applied in this study is highly successful for the purposes of free vibration analysis of elastic beams.

• Journal of the Korean Society for Precision Engineering
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• v.28 no.8
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• pp.959-965
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• 2011

This paper presents the dynamic modeling and vibration suppression methods for axially deploying beams subjected to gravity. A modal modeling method is employed to develop the lateral vibration model for axially deploying beams. Simulation is made to validate the proposed model as well as to investigate the dynamics of axially deploying beams. This paper rigorously investigates the gravity effect as a source of vibration for axially deploying beams. In order to suppress lateral vibration for deploying beams, the moving speed command is modified by using the input shaping method, Experiments are also performed to prove the proposed vibration suppression method. The simulations and experiments show that the proposed modeling and input shaping methods are effective for the dynamic analysis and vibration suppression of axially deploying beams subjected to gravity.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.175-180
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• 1993

A new method for the vibration analysis of arbitrarily-shaped beams is proposed on the assumption of imaginary seperation of the beams into prismatic beams and the remaining portions. The stiffness and mass of the beams are devided into two portions according to the seperation. Applying the mode shapes of prismatic beams and Lagrange's equations give new characteristics equation. This equation has a low dimension of matrix with the coupling terms showing the effect of remaining portions on the vibration of arbitrarily-shaped beams

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.468-473
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• 2004

The objective of this paper is to analyze the characteristics of wave transmission through various junctions in coupled beams. The in-plane vibration as veil as the out-of-plane vibration are generated due to the wave conversion at the junctions in the coupled beams. The out-of-plane vibration is associated with propagation of out-of-plane waves (flexural waves). The in-plane vibration is associated with propagation of in-plane waves (longitudinal and torsional waves). In order to effectively reduce vibration and structure-borne noise, it is necessary to understand the characteristics of wave conversion at various junctions in the coupled structures. The numerical results in this paper have showed the characteristics of wave transmission through various junctions in coupled beams. Those could be helpful to designer to develop the idea to reduce vibration and structure-borne noise.

• Structural Engineering and Mechanics
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• v.59 no.6
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• pp.1055-1070
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• 2016

The aim of this experimental study is to investigate the free vibration and buckling behaviors of hybrid composite beams having different span lengths and orientation angles subjected to different impact energy levels. The impact energies are applied in range from 10 J to 30 J. Free vibration and buckling behaviors of intact and impacted hybrid composite beams are compared with each other for different span lengths, orientation angles and impact levels. In free vibration analysis, the first three modes of hybrid beams are considered and natural frequencies are normalized. It is seen that first and second modes are mostly affected with increasing impact energy level. Also, the fundamental natural frequency is mostly affected with the usage of mold that have 40 mm span length (SP40). Moreover, as the impact energy increases, the normalized critical buckling loads decrease gradually for $0^{\circ}$ and $30^{\circ}$ oriented hybrid beams but they fluctuate for the other beams.

• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.689-703
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• 2011

A new perturbation method is introduced to study the undamped free vibration of a non-prismatic Timoshenko beam for its natural frequencies and vibration modes. For simplicity, the natural modes of vibration of its corresponding prismatic Euler-Bernoulli beam with the same length and boundary conditions are used as Ritz base functions with necessary modifications to account for shear strain in the Timoshenko beam. The new method can transform two coupled partial differential equations governing the transverse vibration of the non-prismatic Timoshenko beam into a set of nonlinear algebraic equations. It significantly simplifies the solution process and is applicable to non-prismatic beams with various boundary conditions. Three examples indicated that the new method is more accurate than the previous perturbation methods. It successfully takes into account the effect of shear deformation of Timoshenko beams particularly at the free end of cantilever structures.

• Steel and Composite Structures
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• v.11 no.6
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• pp.489-504
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• 2011

This paper presents a theoretical investigation in free vibration of sigmoid functionally graded beams with variable cross-section by using Bernoulli-Euler beam theory. The mechanical properties are assumed to vary continuously through the thickness of the beam, and obey a two power law of the volume fraction of the constituents. Governing equation is reduced to an ordinary differential equation in spatial coordinate for a family of cross-section geometries with exponentially varying width. Analytical solutions of the vibration of the S-FGM beam are obtained for three different types of boundary conditions associated with simply supported, clamped and free ends. Results show that, all other parameters remaining the same, the natural frequencies of S-FGM beams are always proportional to those of homogeneous isotropic beams. Therefore, one can predict the behaviour of S-FGM beams knowing that of similar homogeneous beams.

• Journal of KSNVE
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• v.9 no.4
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• pp.828-834
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• 1999

The paper describes the vibration and the stability of nonuniform tapered beams resting on two-layered elastic foundations. The two-layered elastic foundations are constructed by discributed Winkler springs and shearing layers as ofen used in oil models. Governing equations are derived from energy experssions using Hamilton's Principle. The associated eigenvalue problems are solved to obtain the free vibration frequencies or the buckling loads. Numerical results for the vibration and the stability of beams under an axial force are presented and compared with other available solutions. Finally, vibration frequencies and critical forces are investigated for various thickness ratios, shear foundation parameters, Winkler foundation parameters, and boundary conditions of tapered beams.

• Steel and Composite Structures
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• v.24 no.1
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• pp.65-77
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• 2017

The purpose of this research is to study the nonlinear free vibration and post-buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams resting on a nonlinear elastic foundation. Uniformly and functionally graded distributions of single walled carbon nanotubes as reinforcing phase are considered in the polymeric matrix. The modified form of rule of mixture is used to estimate the material properties of CNTRC beams. The governing equations are derived employing Euler-Bernoulli beam theory along with energy method and Hamilton's principle. Applying von $K\acute{a}rm\acute{a}n's$ strain-displacement assumptions, the geometric nonlinearity is taken into consideration. The developed governing equations with quadratic and cubic nonlinearities are solved using variational iteration method (VIM) and the analytical expressions and numerical results are obtained for vibration and stability analysis of nanocomposite beams. The presented comparative results are indicative for the reliability, accuracy and fast convergence rate of the solution. Eventually, the effects of different parameters, such as foundation stiffness, volume fraction and distributions of carbon nanotubes, slenderness ratio, vibration amplitude, coefficients of elastic foundation and boundary conditions on the nonlinear frequencies, vibration response and post-buckling loads of FG-CNTRC beams are examined. The developed analytical solution provides direct insight into parametric studies of particular parameters of the problem.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.47-55
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• 2003

Curved beams are one of the most important basic structural units as well as the beams, columns and plates. Most complicated structures consist of only these basic units and therefore it is very attractive research subject to analysis both the static and dynamic behavior of such units including the arches. The problems of free vibrations of curved beams have been the subject of much work due to their many practical applications.(an ellipsis)