• Structural Engineering and Mechanics
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• v.40 no.4
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• pp.583-594
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• 2011

In the present study, free vibration of an axially functionally graded (AFG) pile embedded in Winkler-Pasternak elastic foundation is analyzed within the framework of the Euler-Bernoulli beam theory. The material properties of the pile vary continuously in the axial direction according to the power-law form. The frequency equation is obtained by using Lagrange's equations. The unknown functions denoting the transverse deflections of the AFG pile is expressed in modal form. In this study, the effects of material variations, the parameters of the elastic foundation on the fundamental frequencies are examined. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• Computers and Concrete
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• v.18 no.5
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• pp.1053-1063
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• 2016

As concrete is most usable material in construction industry it's been required to improve its quality. Nowadays, nanotechnology offers the possibility of great advances in construction. For the first time, the nonlinear buckling of straight concrete columns armed with single-walled carbon nanotubes (SWCNTs) resting on foundation is investigated in the present study. The column is modelled with Euler-Bernoulli beam theory. The characteristics of the equivalent composite being determined using the Mori-Tanaka model. The foundation around the column is simulated with spring and shear layer. Employing nonlinear strains-displacements, energy methods and Hamilton's principal, the governing equations are derived. Differential quadrature method (DQM) is used in order to obtain the buckling load of structure. The influences of volume percent of SWCNTs, geometrical parameters, elastic foundation and boundary conditions on the buckling of column are investigated. Numerical results indicate that reinforcing the concrete column with SWCNTs, the structure becomes stiffer and the buckling load increases with respect to concrete column armed with steel.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.11
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• pp.1119-1126
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• 2007

In this paper, the dynamic stability of a cracked cantilever pipe conveying fluid with tip mass is investigated. The pipe is modelled by the Euler-Bernoulli beam theory in which rotatory inertia and shear deformation effects are ignored. The equation of motion is derived by the energy expressions using extended Hamilton's Principle. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influence of the crack severity, the position of crack, the mass ratio, and a tip mass on the stability of a cantilever pipe conveying fluid are studied by the numerical method. Besides, the critical flow velocity and the stability maps of the pipe system as a function of mass ratios($\beta$) for the changing each parameter are obtained.

• Structural Engineering and Mechanics
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• v.61 no.3
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• pp.335-345
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• 2017

Free vibration analysis for continuous bridge under any number of vehicles is conducted in this paper. Calculation strategy for natural frequency and mode shape is proposed based on Euler-Bernoulli beam theory and numerical assembly method. Firstly, a half-car planar model is adopted; equations of motion and displacement functions for bridge and vehicle are established, respectively. Secondly, the undermined coefficient matrices for wheels, vehicles, intermediate support, left-end support and right-end support are derived. Then, the numerical assembly technique for conventional finite element method is adopted to construct the overall matrix of coefficients for whole system. Finally, natural frequencies and corresponding mode shapes are determined based on iterative method and overall matrix solution. Numerical simulation is presented to verify the effectiveness of the proposed method. The results reveal that the solutions of present method are exact ones. Natural frequencies and associate modal shapes of continuous bridge under different conditions of vehicles are investigated. The influences of vehicle parameters on natural frequencies are also demonstrated.

• 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 Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.949-954
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• 2006

The purpose of this paper is to investigate the stability of tapered columns with clamped one end and carrying a tip mass of rotatory inertia with translational elastic support at the other end. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck columns is derived using the Bernoulli-Euler beam theory. Both the divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter, mass ratio and spring stiffness.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.963-968
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• 2006

The main purpose of this paper is to investigate the stability of water tower with a relatively small footing. The water tower is modeled that the column carrying a container is supported by a rotational spring at the base and is of constant cross-section, with a weight per unit length of column axis. The column model is based on the Bernoulli-Euler beam theory. The Runge-Kutta method and Determinant Search method are used to perform the integration of the governing differential equation and to determine the critical values(critical own weight. and critical buckling load), respectively. The critical buckling loads are calculated over a range of system parameters: the rotational stiffness parameter, the dimensionless radius of container and the own weight parameter of the column. The relation between the rotational stiffness parameter and the critical own weight parameter of the column is analyzed.

• Journal of the Korean Society for Precision Engineering
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• v.28 no.8
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• pp.951-958
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• 2011

In this paper, the purpose is to investigate the vibration characteristics and the design of resonance avoidance of the unmanned helicopter master. Based on the Euler-Bernoulli beam theory for helicopter master, the equation of motion is derived by using extended Hamilton's principle. It was studied about the natural frequency of helicopter master as the design variances(tip mass, length and diameter of master). Also, it was compared the theoretical results for natural frequency with the results of FE analysis. The results of this study showed the vibration characteristics of helicopter master for the design of resonance avoidance.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.1
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• pp.104-109
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• 2016

The noncontact vibration exciter system using the electro-magnet for a thin plate is studied in this paper. Based on the Euler-Bernoulli beam theory, the equation of motion of thin plate is derived. The main purpose of this experiment is to match the input-frequency and response frequency of thin plate. The test equipment is configured to vibrate on both sides of the thin plate using the electro-magnet. Two frequencies(input frequency and response frequency) in our experiments show very good agreement. This study results will contribute to basic investigate of an alternative air-knife system for the steel industry.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1521-1526
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• 2008

IPMC(Ionic Polymer-Metal Comosite) exhibits large deformation, having great attention in many application fields. It generates bending moment by ion exchange polymer film. It can be quickly bended by the applied voltage across the plated electrode of the polymer film. In the present paper, we derive the theoretical modeling and dynamic analysis of bending motions of IPMC actuators using the Euler-Bernoulli beam theory. The theoretical model of a cantilever IPMC actuator estimates the moment produced by the applied voltage. The dynamic characteristics, including natural frequencies and frequency response, are calculated by the theoretical model, and they are compared with the experimental results and finite element analysis. It is shown that the mathematical modeling allows precise estimation to the voltage-driven motion of the cantilever IPMC in air.