• Structural Engineering and Mechanics
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• v.48 no.5
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• pp.697-709
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• 2013

A simulation method called modified differential transform is studied to solve the free vibration problems of uniform Euler-Bernoulli beam. First of all, the modified differential transform method is derived. Secondly, the modified differential transformation is applied to uniform Euler-Bernoulli beam free-free vibration. And then a set of differential equations are established. Through algebraic operations on these equations, we can get any natural frequency and normalized mode shape. Thirdly, the FEM is applied to obtain the numerical solutions. Finally, mode experimental method (MEM) is conducted to obtain experimental data for analysis by signal processing with LMS Test.lab Vibration testing and analysis system. Experimental data and simulation results are illustrated to be in comparison with the analytical solutions. The results show that the modified differential transform method can achieve good results in predicting the solution of such problems.

• Structural Engineering and Mechanics
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• v.5 no.3
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• pp.297-306
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• 1997

The bouncing of a cantilever with the free end pressed against a stop can create high-frequency vibration that the Bernoulli-Euler beam theory is inadequate to solve. An analytic procedure is presented using Timoshenko beam theory to obtain the non-linear response of a cantilever supported by an elastic stop with clearance at the free end. Through a numerical example, the bouncing behavior of the Timoshenko and Bernoulli-Euler beam models are compared and discussed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.623-630
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• 1995

The impulse response functions (force-strain relations) for Euler-Bernoulli and Timoshenko beams are considered. The response of a beam to a transverse impact force is numerically obtained with the convolution approach using the impulse response function obtained by Laplace transform. Using this relation, the impact force history is determined in the time domain and results are compared with those from Hertz's contact law. The parameters of timpact force model are identified using the recovered force and compared with the Hertz's contact model. In order to verify the proposed algorithm, measurements were done using an impact hammer and a steel ball drop test and these results are also compared with the simulated values.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.3 s.246
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• pp.279-286
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• 2006

The main purpose of this paper is to apply differential transformation method(DTM) and generalized differential quadrature method(GDQM) to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. In this paper the concepts of DTM and GDQM were briefly introduced. The governing equation of motion of the beam with open cracks on elastic foundation is derived. The cracks are modeled by massless substitute spring. The effects of the crack location, size and the foundation constants, on the natural frequencies of the beam, are investigated. Numerical calculations are carried out and compared with previous published results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.402.1-402
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• 2002

A linearly tapered beam immersed partially in other material is considered and is modelled as a linearly tapered Bernoulli-Euler beam fixed at the bottom with a concentrated mass at the top. Its governing equations is derived and its free vibration analysis is performed for various boundary conditions. And the rotatory inertia of the eccentric lumped tip mass is considered. (omitted)

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.2
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• pp.129-138
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• 2012

This paper deals with geometrical non-linear analyses of the tapered variable-arc-length beam, subjected to the combined load with an end moment and a point load. The beam is supported by a hinged end and a frictionless sliding support so that the axial length of the deformed beam can be increased by its load. Cross sections of the beam whose flexural rigidities are functionally varied with the axial coordinate. The simultaneous differential equations governing the elastica of such beam are derived on the basis of the Bernoulli-Euler beam theory. These differential equations are numerically solved by the iteration technique for obtaining the elastica of the deformed beam. For validating theories developed herein, laboratory scaled experiments are conducted.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.1
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• pp.13-22
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• 2013

This paper deals with a novel method for numerical analyses of the tapered geometrical non-linear beam with three unknown parameters, subjected a floating point load. The beams with hinged-movable end constraint are chosen as the objective beam. Cross sections of the beam whose flexural rigidities are functionally varied with the axial coordinate. The first order simultaneous differential equations governing the elastica of such beam are derived on the basis of the Bernoulli-Euler beam theory. A novel numerical method for solving these equations is developed by using the iteration technique. The processes of the solution method are extensively discussed through a typical numerical example. For validating theories developed herein, laboratory scaled experiments are conducted.

• The Journal of the Korea institute of electronic communication sciences
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• v.4 no.3
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• pp.236-242
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• 2009

When two-link flexible arm is rotated about an joint axis, transverse vibration may occur. In this paper, vibration dynamics of flexible robot arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Using the fact that matrix $\dot{D}$-2C is skew symmetric, new controllers which have a simplified structure with less computational burden is proposed. Lyapunov stability theory is applied to achieve a stable deterministic nonlinear controller for the regulation of joint angle.

• The Journal of the Korea institute of electronic communication sciences
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• v.5 no.5
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• pp.541-546
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• 2010

When a flexible arm is rotated by a motor about an joint axis, transverse vibration may occur. The motor torque should be controlled in such a way that the moter rotates by a specified angle, while simultaneously stabilizing vibration of the flexible arm so that it is arrested at the end of rotation. In this paper, the dynamic model of flexible robot arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Nonlinear control with hysteresis deadzone using the sliding sector theory with continued input function in the sector is proposed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.690-695
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• 2003

The main purpose of this paper is to apply differential transformation method to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. The governing equation of motion of beam with open cracks on elastic foundation is derived. The concept of differential transformation is briefly introduced. The cracks are modeled by massless substitute spring. The effects of the crack location, size and the foundation constants, on the natural frequencies of the beam, are investigated.