• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.9
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• pp.720-729
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported Euler-Bernoulli beam with the moving mass. The influences of the depth and the position of the crack in the beam have been studied on the dynamic behavior of the simply supported beam system by numerical method. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. As the depth of the crack is increased the frequency of the simply supported beam with the moving mass is increased.

• Steel and Composite Structures
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• v.44 no.1
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• pp.17-31
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• 2022

This investigation studies the characteristics of wave dispersion in sigmoid functionally graded (SFG) curved beams lying on an elastic substrate for the first time. Homogenization process was performed with the help of sigmoid function and two power laws. Moreover, various materials such as Zirconia, Alumina, Monel and Nickel steel were explored as curved beams materials. In addition, curved beams were rested on an elastic substrate which was modelled based on Winkler-Pasternak foundation. The SFG curved beams' governing equations were derived according to Euler-Bernoulli curved beam theory which is known as classic beam theory and Hamilton's principle. The resulted governing equations were solved via an analytical method. In order to validate the utilized method, the obtained outcomes were compared with other researches. Finally, the influences of various parameters, including wave number, opening angle, gradient index, Winkler coefficient and Pasternak coefficient were evaluated and indicated in the form of diagrams.

• Structural Engineering and Mechanics
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• v.61 no.6
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• pp.765-773
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• 2017

The quadratic B-spline finite element method yields mass and stiffness matrices which are half the size of matrices obtained by the conventional finite element method. We solve the free vibration problem of a rotating Rayleigh beam using the quadratic B-spline finite element method. Rayleigh beam theory includes the rotary inertia effects in addition to the Euler-Bernoulli theory assumptions and presents a good mathematical model for rotating beams. Galerkin's approach is used to obtain the weak form which yields a system of symmetric matrices. Results obtained for the natural frequencies at different rotating speeds show an accurate match with the published results. A comparison with Euler-Bernoulli beam is done to decipher the variations in higher modes of the Rayleigh beam due to the slenderness ratio. The results are obtained for different values of non-uniform parameter ($\bar{n}$).

• Interaction and multiscale mechanics
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• v.3 no.4
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• pp.343-363
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• 2010

The present paper is concerned with vibrations of an elastic bridge loaded by a moving elastic beam of a finite length, which is an extension of the authors' previous study where the second beam was modeled as a semi-infinite beam. The second beam, which represents a train, moves with a constant speed along the bridge and is assumed to be connected to the bridge by the limiting case of a rigid interface such that the deflections of the bridge and the train are forced to be equal. The elastic stiffness and the mass of the train are taken into account. The differential equations are developed according to the Bernoulli-Euler theory and formulated in a non-dimensional form. A solution strategy is developed for the flexural vibrations, bending moments and shear forces in the bridge by means of symbolic computation. When the train travels across the bridge, concentrated forces and moments are found to take place at the front and back side of the train.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.201-208
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• 2000

This paper explores the non-linear behavior of tapered beam subjected to a floating concentrated load. For applying the Bernoulli-Euler beam theory to this beam, the bending moment at any point of elastica is obtained from the final equilibrium state. By using the bending moment equation and the Bernoulli-Euler beam theory, the differential equations governing the elastica of clamped-roller beam are derived, and solved numerically. Three kinds of tapered beam types are considered. The numerical results of the non-linear behavior obtained in this study are agreed quite well to the results obtained from the laboratory-scale experiments.

• 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.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.455-470
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• 2016

In this paper, we investigate the free vibration of axially loaded non-uniform Rayleigh cantilever beams. The Rayleigh beams account for the rotary inertia effect which is ignored in Euler-Bernoulli beam theory. Using an inverse problem approach we show, that for certain polynomial variations of the mass per unit length and the flexural stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation for Rayleigh beams. The derived property variation can serve as test functions for numerical methods. For the rotating beam case, the results have been compared with those derived using the Euler-Bernoulli beam theory.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.528-532
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• 2013

In this study, an analytical model of micro-beam structure including thermoelastic damping with irregularly distributed masses is investigated. The significance of thermoelastic damping for micro-scale mechanical resonators is evaluated to design -with high quality factor(Q-factor). The beam model of this work is based on Euler-Bernoulli beam theory. In order to determine the natural frequency of the model, energy method is applied. Also, the thermoelatic damping effects are considered by using heat conduction equations, and the Q-factor can be determined. To derive the equation of motion, non-dimensionalization is employed for systematic analysis. Results of the model are verified, and present mode shapes and Q-factors for the micro-beam with thermoelastic damping including random point masses.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.6
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• pp.384-390
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• 2015

The vibration analysis of rotating inward beams considering the pre-twisted is presented based on Euler-Bernoulli beam theory. The frequency equations, are calculated using hybrid deformation variable modeling along with the Rayleigh-Ritz assumed mode methods. In this study, resulting system of ordinary differential equations shows the effects of angular speed, and Young's modulus ratio. It is believed that the results will be a reference with which other researchers and commercial FE analysis program, ANSYS can compare their result.