• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.689-694
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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 pipe conveying fluid subject to the moving mass. The equation of motion is derived by using Lagrange's equation. The influences of the velocity of moving mass and the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The presence of crack results in higher deflections of pipe. 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. Totally, as the velocity of fluid flow and the crack severity are increased, the mid-span deflection of simply supported pipe conveying fluid is increased. The time which produce the maximum dynamic deflection of the simply supported pipe is delayed according to the increment of the crack severity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.534-537
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• 2004

In this paper, a dynamic behavior of spring supported cantilever beam with a crack and a moving mass is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's eauation. 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 the first mode of fracture. As the depth of the crack is increased the tip displacement of the cantilever beam is increased.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.22 no.6
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• pp.950-956
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• 2013

This paper describes a sensitivity-coefficient-based iterative method for detecting cracks in a structure. The sensitivity coefficients of a cracked structure are obtained by changing its eigenvectors. The proposed method is applied to a cracked cantilever. The crack is modeled as a rotational stiffness. The predicted cracks are in good agreement with those from a structural reanalysis of the cracked structure.

• Smart Structures and Systems
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• v.33 no.2
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• pp.165-175
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• 2024

Rotating beams play a crucial role in representing complex mechanical components that are prevalent in vital sectors like energy and transportation industries. These components are susceptible to the initiation and propagation of cracks, posing a substantial risk to their structural integrity. This study presents a two-stage methodology for detecting the location and estimating the size of an open-edge transverse crack in a rotating Euler-Bernoulli beam with a uniform cross-section. Understanding the dynamic behavior of beams is vital for the effective design and evaluation of their operational performance. In this regard, modal parameters such as natural frequencies and eigenmodes are frequently employed to detect and identify damages in mechanical components. In this instance, the Frobenius method has been employed to determine the first two natural frequencies and corresponding eigenmodes associated with flapwise bending vibration. These calculations have been performed by solving the governing differential equation that describes the motion of the beam. Various parameters have been considered, such as rotational speed, beam slenderness, hub radius, and crack size and location. The effect of the crack has been replaced by a rotational spring whose stiffness represents the increase in local flexibility as a result of the damage presence. In the initial phase of the proposed methodology, a damage index utilizing the slope of the beam's eigenmode has been employed to estimate the location of the crack. After detecting the presence of damage, the size of the crack is determined using a Genetic Algorithm optimization technique. The ultimate goal of the proposed methodology is to enable the development of more suitable and reliable maintenance plans.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.826-831
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• 2005

In this paper the effect of moving mass on dynamic behavior of cracked cantilever beam on elastic foundations is presented. Based on the Euler-Bernoulli 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. That is, 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. The crack is assumed to be in the first mode of fracture. As the depth of the crack is increased, the tip displacement of the cantilever beam is increased. When the crack depth is constant the frequency of a cracked beam is proportional to the spring stiffness.

• Journal of Ocean Engineering and Technology
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• v.17 no.6
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• pp.47-52
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• 2003

To determine the effect of transverse open crack on the dynamic behavior of simply-supported Euler-Bernoulli beam with the moving masses, an iterative modal analysis approach is developed. The influence of depth and position of the crack in the beam, on the dynamic behavior of the simply supported beam system, have been studied by numerical method. The cracked section is represented by a local flexibility matrix, connecting two undamaged beam segments that is, the crack is modeled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section, and is derived by applying a fundamental fracture mechanics theory. As the depth of the crack is increased, the mid-span deflection of the simply-supported beam, with the moving mass, is increased. The crack is positioned in the middle point of the pipe, and the mid-span defection of the simply-supported pipe represents maximum deflection.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.10 s.103
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• pp.1195-1201
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• 2005

In this paper, the effect of a moving mass on dynamic behavior of the cracked cantilever beam on elastic foundations is presented. Based on the Euler-Bernoulli 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. That is, 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 The crack is assumed to be in the first mode of fracture. As the depth of crack is increased, the tip displacement of the cantilever beam is Increased. When the depth of crack is constant, the frequency of a cracked beam is proportional to the spring stiffness.

• Journal of Mechanical Science and Technology
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• v.18 no.12
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• pp.2216-2224
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• 2004

In this paper we studied about the effect of the open crack and the moving mass on the dynamic behavior of simply supported pipe conveying fluid. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments i.e. the crack is modeled as a rotational spring. The influences of the crack severity, the position of the crack, the moving mass and its velocity, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the mid-span displacement of the simply supported pipe are depicted.

• 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.

• 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.