• Smart Structures and Systems
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• v.9 no.4
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• pp.355-371
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• 2012

A composite element method (CEM) is presented to analyze the free and forced vibrations of a cracked Euler-Bernoulli beam with axial force. The cracks are introduced by using Christides and Barr crack model with an adjustment on one crack parameter. The effects of the cracks and axial force on the reduction of natural frequencies and the dynamic responses of the beam are investigated. The time response sensitivities with respect to the crack parameters (i.e., crack location, crack depth) and the axial force are calculated. The natural frequencies obtained from the proposed method are compared with the analytical results in the literature, and good agreement is found. This study shows that the cracks in the beam may have significant effects on the dynamic responses of the beam. In the inverse problem, a response sensitivity-based model updating method is proposed to identify both a single crack and multiple cracks from measured dynamic responses. The cracks can be identified successfully even using simulated noisy acceleration responses.

• Journal of Korean Association for Spatial Structures
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• v.24 no.1
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• pp.65-72
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• 2024

This paper aims to advance our understanding of extensible beams with multiple cracks by presenting a crack energy and motion equation, and mathematically justifying the energy functions of axial and bending deformations caused by cracks. Utilizing an extended form of Hamilton's principle, we derive a normalized governing equation for the motion of the extensible beam, taking into account crack energy. To achieve a closed-form solution of the beam equation, we employ a simple approach that incorporates the crack's patching condition into the eigenvalue problem associated with the linear part of the governing equation. This methodology not only yields a valuable eigenmode function but also significantly enhances our understanding of the dynamics of cracked extensible beams. Furthermore, we derive a governing equation that is an ordinary differential equation concerning time, based on orthogonal eigenmodes. This research lays the foundation for further studies, including experimental validations, applications, and the study of damage estimation and detection in the presence of cracks.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.372.2-372
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• 2002

This paper presents an efficient modeling method fur open cracked beam structures. An equivalent bending spring model is introduced to represent the structural weakening effect in the presence of open cracks. The proposed method adopts the exact dynamic element method (EDEM) to avoid the difficulty and numerical errors in association with re-meshing the structure. The proposed method is rigorously compared with a commercial finite element code. (omitted)

• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.2
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• pp.49-59
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• 1992

In our researches we made mix-design, with the mixing ratio and pre-cracked ratio of steel fibrous different from each other, building the steel fibrous concrete beam which had pre-cracks. To obtain the fracture characteristics of steel fibrous reinforced concrete, series of experiment were conducted on pre-cracked beam subjected to 3-point bending. Thus, we carried out experiments on the destructive characteristics of its pre-crack and post-crack and the result is as follows. 1. The compressive strength of steel fibrous concrete beam increased more slightly than plane beam, and the tensile strength increased 37%, 59%, 94% and 121% respectively when the amount of fibrous was 0.5%, 0.1% 1.5%, and 1.75% respectively. 2. As the amount of steel fibrous mixing increased ant the steel fibrous inhibited the crack growth, the crack condition of steel fibrous concrete beam was retarded irregularly, and this increased fracture load. 3. The defiance of destruction was reduced in the ratio of 1.35 times and 1.22 times respectively when the length of pre-crack was each 2cm and 4cm in comparison with the case of being without the length, and was similar to that of plane beam when the amount of steel fibrous mixing was below 1.0%, and increased linearly when it as above 1.0%. 4. The experimental formula seeking fracture energy was follows and thus we found that the value of fracture energy depended upon tensile strength and the size of speciment. $G_f=K\;{\cdot}\;f_f^'{\cdot}$da/Ec 5. We observed that in the load-strain curve of steel fibrous concrete beam the progress of the crack became slow, compared with plane beam because the crack condition became long to the extent of about 10 times. Concrete was faultiest brittleness fracture through the study, it was known ductile.

• International Journal of Concrete Structures and Materials
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• v.11 no.1
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• pp.171-183
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• 2017

Strengthening reinforced concrete (RC) beams with openings by using aramid fiber reinforcement polymers (AFRP) on the beams' surfaces offers a useful solution for upgrading concrete structures to carry heavy loads. This paper presents a repairing technique of the AFRP sheets that effectively strengthens RC beams, controls both the failure modes and the stress distribution around the beam chords and enhances the serviceability (deflection produced under working loads be sufficiently small and cracking be controlled) of pre-cracked RC beams with openings. To investigate the possible damage that was caused by the service load and to simulate the structure behavior in the site, a comprehensive experimental study was performed. Two unstrengthened control beams, four beams that were pre-cracked before the application of the AFRP sheets and one beam that was strengthened without pre-cracking were tested. Cracking was first induced, followed by repair using various orientations of AFRP sheets, and then the beams were tested to failure. This load was kept constant during the strengthening process. The results show that both the preexisting damage level and the FRP orientation have a significant effect on strengthening effectiveness and failure mode. All of the strengthened specimens exhibited higher capacities with capacity enhancements ranging from 21.8 to 66.4%, and the crack width reduced by 25.6-82.7% at failure load compared to the control beam. Finally, the authors present a comparison between the experimental results and the predictions using the ACI 440.2R-08 guidelines.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.9 no.3
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• pp.49-55
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• 2010

In this paper, the stability of cracked cantilever T-beams subjected to subtangential follower force is investigated. Also, the effect of subtangential coefficient and crack on the natural frequency of T-beams is presented. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by the energy expressions using extended Hamilton's Principle. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The values of critical follower force and the stability maps of cantilever T-beams are obtained according to the subtangential coefficient and crack severity. The results of this study will contribute to the safety testing and the stability estimation of cracked T-beams subjected to follower force.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.703-708
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• 2006

In this paper a dynamic behavior(natural frequency) of a cracked simply supported pipe conveying fluid is presented. In addition, an analysis of the buckling instability of a cracked pipe conveying fluid subjected to a follower compressive load is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. TI1e crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.4
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• pp.8-15
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• 2011

In this paper, the influence of a crack on the natural frequency of cracked cantilever L-shaped beam with coupled bending and torsional vibrations by analytically and experimentally is analyzed. The L-shaped beam with a crack is modeled by Hamilton's principle with consideration of bending and torsional energy. The two coupled governing differential equations are reduced to one sixth-order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first, second and third mode of fracture and to be always opened during the vibrations. The theoretical results are validated by a comparison with experimental measurements. The maximal difference between the theoretical results and experimental measurements of the natural frequency is less than 7.5% in the second vibration mode.

• International Journal of Precision Engineering and Manufacturing
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• v.9 no.3
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• pp.33-39
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• 2008

The effects of a double crack and tip masses on the dynamic behavior of cantilever beams with a moving mass are studied using numerical methods. The cantilever beams are modeled by applying Euler-Bernoulli beam theory. The cracked sections are represented by a local flexibility matrix connecting three undamaged beam segments. The influences of the crack, moving mass, and tip mass, and the coupling of these factors on the vibration mode and the frequencies of the double-cracked cantilever beams are determined analytically. The methodology provides a basis for analyzing the dynamic behavior of a beam with an arbitrary number of cracks and a moving mass.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.958-963
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• 2003

In this paper a dynamic behavior of simply supported cracked pipe conveying fluid with the moving mass is presented. Based on the Timoshenko beam theory, the equation of motion can be constructed by using the Lagrange's equation. 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. And the crack is assumed to be in th first mode of fracture. As the depth of the crack and velocity of fluid are increased the mid-span deflection of the pipe conveying fluid with the moving mass is increased. As depth of the crack is increased, the effect that the velocity of the fluid on the mid-span deflection appears more greatly.