• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.347-354
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• 2000

The seismic behaviors of a bridge system with several simple spans are examined to see the effects of the longitudinal stiffness degradation due to abutment-soil interaction. The abutment-backfill system is modeled as one degree-of-freedom-system with nonlinear spring and linear damper. various soil-conditions surrounding the abutment such as loose sand, medium dense sand, and dense sand are considered in the bridge seismic analysis. The idealized mechanical model for the whole bridge system is modeled by adopting the multiple-degree-of-freedom system, which can consider components such as pounding phenomena, friction at the movable supports, rotational and translational motions of foundations, and the nonlinear pier motions. The stiffness of the abutment is found to be rapidly reduced at the beginning of the earthquakes, and to be converged to constant values shortly after the displacement approaches to the Predefined critical values. It is observed that the maximum relative distanced an maximum relative displacements are generally Increased as the relative density of a soil decreases As the peak ground acceleration increases, the response ratio of the case considering stiffness degradation to the case considering constant stiffness decreases.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.2
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• pp.179-186
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• 2016

This paper presents a numerical method that can evaluate the effect of crack for the in-plane bending vibration of Timoshenko beam. The method is a transfer matrix method that the element transfer matrix is deduced from the element dynamic stiffness matrix. An edge crack is expressed as a rotational spring, and then is formulated as an independent transfer matrix. To demonstrate the accuracy of this theory, the results computed from the present are compared with those obtained from the commercial finite element analysis program. Based on these comparison results, a parametric study is performed to analyze the effects for the size and locations of crack.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.767-780
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• 2015

Delaminations and cracks are common failures in structures. They may significantly reduce the stiffness of the structure and affect their vibration characteristics. In the present study, an analytical solution is developed to study the effect of an edge crack on the vibration characteristics of delaminated beams. The rotational spring model, the 'free mode' and 'constrained mode' assumptions in delamination vibration are adopted. This is the first study on how an edge crack affects the vibration characteristic of delaminated beams and new nondimensional parameters are developed accordingly. The crack may occur inside or outside the delaminated area and both cases are studied. Results show that the effect of delamination length and thickness-wise location on reducing the natural frequencies is aggravated by an increasing crack depth. The location of the crack also influences the effect of delamination, but such influence is different between crack occurring inside and outside the delaminated area. The difference of natural frequencies between 'free mode' and 'constrained mode' increases then decreases as the crack moves from one side of the delaminated region to the other side, peaking at the middle. The analytical results of this study can serve as the benchmark for FEM and other numerical solutions.

• Advances in nano research
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• v.6 no.1
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• pp.57-80
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• 2018

In this study, the thermal loading effect on free vibration characteristics of carbon nanotubes (CNTs) with multiple cracks is studied. Various boundary conditions for nanotube are taken in to account. In order to take the small scale effect, the nonlocal elasticity of Eringen is employed in the framework of Euler-Bernoulli beam theory. This theory states that the stress at a reference point is a function of strains at all points in the continuum. A cracked nanotube is assumed to be consisted of two segments that are connected by a rotational spring which is located in the position of the cracked section. Hamilton's principle is used to achieve the governing equations. Influences of the nonlocal parameter, crack severity, temperature change and the number of cracks on the system frequencies are investigated. Also, it is found that at room or lower temperature the natural frequency for CNT decreases as the value of temperature change increases, while at temperature higher than room temperature the natural frequency of CNT increases as the value of temperature change increases. Various boundary conditions have been applied to the nanotube.

• Structural Engineering and Mechanics
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• v.67 no.5
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• pp.439-455
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• 2018

Within a probabilistic framework, this paper addresses the determination of the static structural response of beams and frames with partially restrained (semi-rigid) connections. The flexibility of the nodal connections is incorporated via an idealized linear-elastic behavior of the beam constraints through the use of rotational springs, which are here considered uncertain for taking into account the largely scattered results observed in experimental findings. The analysis is conducted via the Probabilistic Transformation Method, by modelling the spring stiffness terms (or equivalently, the fixity factors of the beam) as uniformly distributed random variables. The limit values of the Eurocode 3 fixity factors for steel semi-rigid connections are assumed. The exact probability density function of a few indicators of the structural response is derived and discussed in order to identify to what extent the uncertainty of the beam constraints affects the resulting beam response. Some design considerations arise which point out the paramount importance of probability-based approaches whenever a comprehensive experimental background regarding the stiffness of the beam connection is lacking, for example in steel frames with semi-rigid connections or in precast reinforced concrete framed structures. Indeed, it is demonstrated that resorting to deterministic approaches may lead to misleading (and in some cases non-conservative) outcomes from a design viewpoint.

• Journal of the Korean Institute of Intelligent Systems
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• v.5 no.2
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• pp.86-96
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• 1995

In this paper the fuzzy extension for the classical engineering mechanics problems is studied. The governing differential equation is derived for the buckling loads of the columns with uncertain mediums: the their own weight and the flexural rigidity. The columns with one typical end constraint(hinged1 clarnped/free) and the other finite rotational spring with fuzzy constant are considered in numerical examples. The vertex method is used to evaluate the fuzzy functions. The Runge-Kutta method and Determinant Search method are used to solve the differential equation and determine the buckling loads, respectively. The membership functions of the buckling load are calculated. The index of fuzziness to quantitatively describe the propagation of fuzziness is defined. According to the fuzziness of governing factors, the varlation of index of fuzziness for buckling load is investigated, and the sensitivity for the end constraints is analyzed.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.5
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• pp.16-25
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• 1996

In the present work a rigid-plastic finite element formulation using dynamic explicit time integration scheme is proposed for numerical analysis of auto-body panel stamping processes. The rigid-plastic finite element method based on membrane elements has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. A damping scheme is proposed in order to achieve a stable solution procedure in dynamic sheet forming problems. In order to improve the drawbacks of the conventional membrane elements, BEAM(abbreviated from Bending Energy Augmented Membrane) elements are employed. Rotational damping and spring about the drilling direction are introduced to prevent a zero energy mode. The lumping scheme is employed for the diagonal mass matrix and linearizing dynamic formulation. A contact scheme is developed by combining the skew boundary condition and the direct trial-and-error method. Computations are carried out for analysis of complicated auto-body panel stamping processes such as forming of an oilpan, a fuel tank and a front fender. The numerical results of explicit analysis are compared with the implicit results with good agreements and it is shown that the explicit scheme requires much shorter computational time, especially when the problem becomes more complicated. It is thus shown that the proposed dynamic explicit rigid-plastic finite element method enables an effective computation for complicated autobody panel stamping processes.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.4
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• pp.352-357
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• 2012

The ground resonance instability of a helicopter with bearingless main rotor hub were investigated. The ground resonance instability is caused by an interaction between the blade lag motion and hub inplane motion. This instability occurs when the helicopter is on the ground and is important for soft-inplane rotors where the rotating lag mode frequency is less than the rotor rotational speed. For the analysis, the bearingless rotor was composed of blades, flexbeam, torque tube, damper, shear restrainer, and pitch links. The fuselage was modeled as a mass-damper-spring system having natural frequencies in roll and pitch motions. The rotor-fuselage coupling equations are derived in non-rotating frame to consider the rotor and fuselage equations in the same frame. The ground resonance instabilities for three cases where are without lead-lag damper and fuselage damping, with lead-lag damper and without fuselage damping, and finally with lead-lag damper and fuselage damping. There is no ground resonance instability in the only rotor-fuselage configuration with lead-lag damper and fuselage damping.

• Journal of the Earthquake Engineering Society of Korea
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• v.13 no.2
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• pp.29-36
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• 2009

The present study emphasizes a nonlinear model to predict the shear behaviour of reinforced concrete interior beam-column joints. To model the shear behaviour of a panel zone in the beam-column joint, a modified softened truss model theory for in-plane shear prediction was introduced. This relationship was changed to define the characteristics for the rotational spring to represent the shear deformation in the joint by an equivalent moment-rotation relationship from the joint equilibrium. The analysis model was compared with experiments on reinforced concrete interior beam-column joints that were subjected to axial and shear forces, and the current model was found to accurately predict not only the shear force but also the shear deformation in the joint.

• 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.