• Structural Engineering and Mechanics
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• v.20 no.2
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• pp.143-160
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• 2005

Modal analysis of cracked cantilever composite beams, made of graphite-fibre reinforced polyamide, is studied. By using the finite element and component mode synthesis methods, a numeric model applicable to investigate the vibration of cracked composite beams is developed. In this new approach, from the crack section, the composite beam separated into two parts coupled by a flexibility matrix taking into account the interaction forces. These forces are derived from the fracture mechanics theory as the inverse of the compliance matrix calculated with the proper stress intensity factors and strain energy release rate expressions. Numerical results are obtained for modal analysis of composite beams with a transverse non-propagating open crack, addressing the effects of the location and depth of the crack, and the volume fraction and orientation of the fibre on the natural frequencies and mode shapes. By means of modal data, the position and dimension of the defect can be found. The results of the study confirmed that presented method is suitable for the vibration analysis of cracked cantilever composite beams. Present technique can be easily extended to composite plates and shells.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.1 s.118
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• pp.10-16
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• 2007

In this paper, the dynamic stability of a cracked simply supported pipe conveying fluid is investigated. In addition, an analysis of the flutter and buckling instability of a cracked pipe conveying fluid due to the coupled mode(modes combined) is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Galerkin method. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The stiffness of the spring depends on the crack severity and the geometry of the cracked section. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. This results of study will contribute to the safety test and a stability estimation of the structures of a cracked pipe conveying fluid.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.747-756
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• 2022

This study presents the nonlinear free and forced vibrations of a cracked atomic force microscopy (AFM) cantilever by using the modified couple stress. The cracked section of the AFM cantilever is considered and modeled as rotational spring. In the frame work of Euler-Bernoulli beam theory, Von-Karman type of geometric nonlinear equation and the modified couple stress theory, the nonlinear equation of motion for the cracked AFM is derived by Hamilton's principle and then discretized by using the Galerkin's method. The semi-inverse method is utilized for analysis nonlinear free oscillation of the system. Then the method of multiple scale is employed to investigate primary resonance of the system. Some numerical examples are presented to illustrate the effects of some parameters such as depth of the crack, length scale parameter, Tip-Mass, the magnitude and the location of the external excitation force on the nonlinear free and forced vibration behavior of the system.

• Steel and Composite Structures
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• v.46 no.4
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• pp.539-551
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• 2023

In order to study the fire resistance of castellated composite beams with ortho-hexagonal holes and different beam-end restraints, temperature rise tests with constant load were conducted on full-scale castellated composite beams with ortho-hexagonal holes and hinge or rigid joint constraints to investigate the temperature distribution, displacement changes and failure patterns of castellated composite beams with two different beam-end constraints during the whole course of fire. The results show that (1) During the fire, the axial pressure and horizontal expansion deformation generated in the rigid joint constrained composite beam were larger than those in the hinge joint constrained castellated composite beam, and their maximum horizontal expansion displacements were 30.2 mm and 17.8 mm, respectively. (2) After the fire, the cracks on the slab surface of the castellated composite beam with rigid joint constraint were more complicated than hinge restraint, and the failure more serious; the lower flange and web at the ends of the castellated steal beams with hinge and rigid joint constraint produced serious local buckling, and the angles of the ortho-hexagonal holes at the support cracked; the welds at both ends of the castellated composite beam with rigid joint constraint cracked. (3) Based on the simplified calculation method of solid-web composite beam, considering the effect of holes on the web, this paper calculated the axial force and displacement of the beam-end constrained castellated composite beams under fire. The calculation results agreed well with the test results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.3
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• pp.236-243
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• 2004

In this paper a dynamic behavior of a 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 of the velocity of the fluid on the mid-span deflection appears more greatly.

• Computers and Concrete
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• v.17 no.1
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• pp.29-51
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• 2016

Tension-stiffening is the contribution of concrete between the cracks to carry tensile stresses after cracking in Reinforced Concrete (RC) members. In this paper, a tension-stiffening model has been proposed for computationally efficient nonlinear analysis of RC flexural members subjected to service load. The proposed model has been embedded in a typical cracked span length beam element. The element is visualized to consist of at the most five zones (cracked or uncracked). Closed form expressions for flexibility and stiffness coefficients and end displacements have been obtained for the cracked span length beam element. Further, for use in everyday design, a hybrid analytical-numerical procedure has been developed for nonlinear analysis of RC flexural members using the proposed tension-stiffening model. The procedure yields deflections as well as redistributed bending moments. The proposed model (and developed procedure) has been validated by the comparison with experimental results reported elsewhere and also by comparison with the Finite Element Method (FEM) results. The procedure would lead to drastic reduction in computational time in case of large RC structures.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.12
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• pp.1295-1303
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• 2004

In this Paper a dynamic behavior of a cracked cantilever pipe conveying fluid with the moving mass is presented. It has the results focused on the response characteristics. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The cracked section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. When the fluid velocity is constant, the influences of the crack severity, the position of the crack, the moving mass and its velocity, and the coupling of these factors on the tip-displacement of the cantilever pipe are depicted.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.632-637
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• 2003

In this study, the effect of surface treatment of CFRP and aluminum on the fracture toughness of CFRP/aluminum composites was investigated. CFRP was surface-treated by Ar$^{+}$ ion beam under oxygen environment, and the aluminum was surface-treated by DC plasma. CFRP was adhesively bonded to aluminum using the secondary bonding procedure. Cracked lap shear specimens were used to determine fracture toughness. Three cases of cracked lap shear specimens were made depending on the surface treatment. The values of fracture toughness of three cases were compared to each other It was found that the fracture toughness of ion beam-treated CFRP/aluminum composites was almost 72 % higher than that of unrented CFRP/aluminum composites. The fracture toughness of CFRP/plasma-treated aluminum composites was 50 % higher than that of untreated CFRP/aluminum composites.s.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.254-257
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• 2006

In this paper a dynamic behavior(natural frequency) of a cracked cantilever and simply supported pipe conveying fluid is presented. In addition, an analysis of the flutter and 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. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.773-789
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• 2010

It is well known that the analytical vibration characteristic of a cracked beam depends largely on the crack model. In the forward analysis, an improved and simplified approach in modeling discrete open cracks in beams is presented. The effective length of the crack zone on both sides of a crack with stiffness reduction is formulated in terms of the crack depth. Both free and forced vibrations of cracked beams are studied in this paper and the results from the proposed modified crack model and other existing models are compared. The modified crack model gives very accurate predictions in the modal frequencies and time responses of the beams particularly with overlaps in the effective lengths with reduced stiffness. In the inverse analysis, the response sensitivity with respect to damage parameters (the location and depth of crack, etc.) is derived. And the dynamic response sensitivity is used to update the damage parameters. The identified results from both numerical simulations and experiment work illustrate the effectiveness of the proposed method.