• Structural Engineering and Mechanics
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• v.9 no.5
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• pp.449-467
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• 2000

The natural frequencies and the corresponding mode shapes of a non-uniform beam carrying multiple point masses are determined by using the analytical-and-numerical-combined method. To confirm the reliability of the last approach, all the presented results are compared with those obtained from the existing literature or the conventional finite element method and close agreement is achieved. For a "uniform" beam, the natural frequencies and mode shapes of the "clamped-hinged" beam are exactly equal to those of the "hinged-clamped" beam so that one eigenvalue equation is available for two boundary conditions, but this is not true for a "non-uniform" beam. To improve this drawback, a simple transformation function ${\varphi}({\xi})=(e+{\xi}{\alpha})^2$ is presented. Where ${\xi}=x/L$ is the ratio of the axial coordinate x to the beam length L, ${\alpha}$ is a taper constant for the non-uniform beam, e=1.0 for "positive" taper and e=1.0+$|{\alpha}|$ for "negative" taper (where $|{\alpha}|$ is the absolute value of ${\alpha}$). Based on the last function, the eigenvalue equation for a non-uniform beam with "positive" taper (with increasingly varying stiffness) is also available for that with "negative" taper (with decreasingly varying stiffness) so that half of the effort may be saved. For the purpose of comparison, the eigenvalue equations for a positively-tapered beam with five types of boundary conditions are derived. Besides, a general expression for the "normal" mode shapes of the non-uniform beam is also presented.

• Steel and Composite Structures
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• v.14 no.1
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• pp.73-83
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• 2013

In this paper Hamiltonian Approach (HA) have been used to analysis the nonlinear free vibration of Simply-Supported (S-S) and for the Clamped-Clamped (C-C) Euler-Bernoulli beams fixed at one end subjected to the axial loads. First we used Galerkin's method to obtain an ordinary differential equation from the governing nonlinear partial differential equation. The effect of different parameter such as variation of amplitude to the obtained on the non-linear frequency is considered. Comparison of HA with Runge-Kutta 4th leads to highly accurate solutions. It is predicted that Hamiltonian Approach can be applied easily for nonlinear problems in engineering.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.42-47
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• 2007

An analytical method for the free vibration of a flexible rectangular plate in contact with water is developed by the Rayleigh.Ritz method. The plate clamped along the edges is partially contacted with water at both sides. It is assumed that the water bounded by rigid walls is incompressible and inviscid. The wet mode shape of the plate is assumed as a combination of the dry mode shapes of a clamped beam. The liquid motion is described by using the liquid displacement potential and determined by using the compatibility conditions along the liquid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict excellently the fluid.coupled natural frequencies comparing with the finite element analysis result.

• Structural Engineering and Mechanics
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• v.64 no.6
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• pp.723-730
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• 2017

This paper studies on dynamic and stability behavior of a clamped-elastically restrained nanobeam under the action of a nonconservative force with an emphasis on the influence of surface properties on divergence and flutter instability. Using the Euler-Bernoulli beam theory incorporating surface effects, a governing equation for a clamped-elastically restrained nanobeam is derived according to Hamilton's principle. The characteristic equation is obtained explicitly and the force-frequency interaction curves are displayed to show the influence of the surface effects, spring stiffness of the elastic restraint end on critical loads including divergence and flutter loads. Divergence and flutter instability transition is analyzed. Euler buckling and stability of Beck's column are some special cases of the present at macroscale.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.3-10
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• 1996

Numerical methods are developed for solving the buckling loads and the elastica of clamped- free columns of circular cross-section with constant volume. The column model is based rut the Timoshenko beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to solve the governing differential equations and to compute the eigenvalues. Extensive numerical results, including buckling loads, elastica of buckled shapes and effects of shear de-formation, are presented in non-dimensional form for elastic columns whose radius of circular cross-section varies both linearly and parabolically with column length.

• Advances in materials Research
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• v.7 no.1
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• pp.1-16
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• 2018

Thermal bifurcation buckling behavior of fully clamped Euler-Bernoulli nanobeam built of a through thickness functionally graded material is explored for the first time in the present paper. The variation of material properties of the FG nanobeam are graded along the thickness by a power-law form. Temperature dependency of the material constituents is also taken into consideration. Eringen's nonlocal elasticity model is employed to define the small-scale effects and long-range connections between the particles. The stability equations of the thermally induced FG nanobeam are derived via the principal of the minimum total potential energy and solved analytically for clamped boundary conditions, which lead for more accurate results. Moreover, the obtained buckling loads of FG nanobeam are validated with those existing works. Parametric studies are performed to examine the influences of various parameters such as power-law exponent, small scale effects and beam thickness on the critical thermal buckling load of the temperature-dependent FG nanobeams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.706-711
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• 2000

This paper deals with the free vibrations of horizontally curved beams on an elastic foundation. Taking into account the effects of rotatory inertia and shear deformation, the differential equations governing free vibrations of noncircular curved beams resting on Pasternak-type foundations are derived and solved numerically. The lowest three natural frequencies for parabolic curved beams with hinged-hinged and clamped-clamped end restraints are calculated. Numerical results are presented to show the effects on the natural frequencies of the non-dimensional system parameters: the horizontal rise to span length ratio, the Winkler foundation parameter, the shear foundation parameter, and the width ratio of contact area between the beam and foundation.

• Journal of KSNVE
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• v.7 no.2
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• pp.331-345
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• 1997

A theoretical formulation for the analysis of free vibration of clamped-free cylindrical shells with plates attached at arbitrary axial position(s) was completed and it was programed to get the numerical results which yield natural frequencies and mode shape of the combined system of the plate and the shells. The frequencies and mode shapes from theoretical calculation were compared with those of commercial finite element code, ANSYS. In order to validate the theory, modal test was also performed by impact test and FFT analysis. The results shows good agreement with those of ANSYS and test results in frequencies and mode shapes. The method developed herein is likely to be used for the analysis of the free vibration of the clamped-free circular cylindrical shells with any kinds of lids such as hollow circular plates, conical shells, spherical shells, or semi-spherical shells.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.309-316
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• 1998

In this paper, a newly derived formulation of a crack detection model is presented and its feasibility to detect cracks in structures is verified experimentally. To meet this objective, the followig approach is utilized. Firstly, the crack detection scheme which consists of the damage localization model and the crack detection model is formulated. Secondly, the feasibility and practicality of the complete procedure of the crack detection model is evaluated by locating and sizing cracks in clamped-clamped beams for which a f3w modal parameters were measured for sixteen uncracked and cracked states. Major results observed from the crack detection exercises include that far most damage cases, the predicted crack locations falls within very close to the inflicted locations of cracks in the test beam and the size of crack values estimated at the predicted locations are very close to the inflicted magnitudes.