• Advances in nano research
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• v.6 no.3
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• pp.219-242
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• 2018

In this study, static bending of an edge cracked cantilever nanobeam composed of functionally graded material (FGM) subjected to transversal point load at the free end of the beam is investigated based on modified couple stress theory. Material properties of the beam change in the height direction according to exponential distributions. The cracked nanobeam is modelled using a proper modification of the classical cracked-beam theory consisting of two sub-nanobeams connected through a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The considered problem is investigated within the Euler-Bernoulli beam theory by using finite element method. In order to establish the accuracy of the present formulation and results, the deflections are obtained, and compared with the published results available in the literature. Good agreement is observed. In the numerical study, the static deflections of the edge cracked FGM nanobeams are calculated and discussed for different crack positions, different lengths of the beam, different length scale parameter, different crack depths, and different material distributions. Also, the difference between the classical beam theory and modified couple stress theory is investigated for static bending of edge cracked FGM nanobeams. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• Structural Engineering and Mechanics
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• v.74 no.1
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• pp.33-54
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• 2020

The aim of this study is to calculate natural frequencies and harmonic responses of cracked frames with general boundary conditions by using transfer matrix method (TMM). The TMM is a straightforward technique to obtain harmonic responses and natural frequencies of frame structures as the method is based on constructing a relationship between state vectors of two ends of structure by a chain multiplication procedure. A single variable shear deformation theory (SVSDT) is applied, as well as, Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT) for comparison purposes. Firstly, free vibration analysis of intact and cracked frames are performed for different crack ratios using TMM. The crack is modelled by means of a linear rotational spring that divides frame members into segments. The results are verified by experimental data and finite element method (FEM) solutions. The harmonic response curves that represent resonant and anti-resonant frequencies directly are plotted for various crack lengths. It is seen that the TMM can be used effectively for harmonic response analysis of cracked frames as well as natural frequencies calculation. The results imply that the SVSDT is an efficient alternative for investigation of cracked frame vibrations especially with thick frame members. Moreover, EBT results can easily be obtained by ignoring shear deformation related terms from governing equation of motion of SVSDT.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.953-962
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• 1987

Domestic dissimilar structural steels, SM 45 C and SUS304 were friction welded under optimal welding condition and the micro-artificial holes were drilled at SM 45 C base metal, SM 45 C HAZ, welded zone, SUS 304 HAZ, and SUS 304 base metal for fatigue behavior tests. In this study, the fatigue limit and the behavior of micro-crack propagation, crack propagation rate, and its dependency on stress intensity factor under the low stress level and high stress level of bending stress have been investigated. The results obtained are as follows. (1) The fatgiue strength of the portion of SM45C B.M., SM45C HAZ, welded zune, SUS304 HAZ and SUS304 B.M. on notched friction welded specimens are 20 kgf/mm$^{2}$, 32 kgf/mm$^{2}$, 27kgf/mm$^{2}$, 29kgf/mm$^{2}$, and 29kgf/mm$^{2}$, respectively. (2) The fatigue strength of welded zone of unnotched and notched specimens are 32.5kgf/mm$^{2}$, and 27kgf/mm$^{2}$, respectively. (3) Micro-crack initiation in the welded zone, HAZ, and each base metals occurrs simultaneously in front and rear of micro-hole tips in the view of the rotational directions. (4) Fatigue crack propagates more slowly in the welded zone than in another protions of specimen, regardless of the magnitude of the stress level. (5) Fatigue crack propagation rates were plotted as a function of stress intensity range. The value of m in the equation da/dN=C(.DELTA.K)$^{m}$ was found to range from 2.09-2.55 in this study.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.2
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• pp.150-157
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• 1985

In terms of behavior of fatigue cracks propagated after build-up around the artificial drilled miro-hole, this study has been made of the build-up process of slips and micro cracks, behavior of micro-crack propagation and the definition of fatigue limit under the rotating bending stress with low carbon steel. The results of this study are as follows: (1) The fatigue limit is the repropagating critical stress for the nonpropagating cracks which have grown to some limit around the micro-hole in regard of the magnitude of micro-hole. (2) Behavior of the slips and micro-cracks initiation are occurring simultaneously in front and in rear of micro-hole tips in the view of the rotational direction, regardless of the magnitude of micro-hole. (3) Behavior of fatigue crack propagation is different from magnitude of micro-hole, its behavior is propagation of single crack about respectively large hole, but about respectively small hole, fatigue crack propagated joining phenomena of micro-cracks. (4) The behavior of fatigue fracture is affected by the factor of its defects in the view of magnitude of micro-hole when the diameter of the micro-holes are smaller than 50.mu.m, and this is also affected with the size effect of micro-hole diameter.

• Composites Research
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• v.13 no.3
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• pp.9-20
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• 2000

Free vibration characteristics of a cantilevered laminated composite beam with multiple non-propagating transverse open cracks are investigated. In the present analysis a special ply-angle distribution referred to as asymmetric stiffness configuration inducing the elastic coupling between chord-wise bending and extension is considered. The multiple open cracks are modelled as equivalent rotational springs whose spring constants are calculated based on the fracture mechanics of composite material structures. Governing equations of a composite beam with open cracks are derived via Hamilton's Principle and Timoshenko beam theory encompassing transverse shear and rotary inertia effect is adopted. The effects of various parameters such as the ply angle, fiber volume fraction, crack numbers, crack positions and crack depthes on the free vibration characteristics of the beam with multiple cracks are highlighted. The numerical results show that the existence of the multiple cracks in an anisotropic composite beam affects the free vibration characteristics in a more complex fashion compared with the beam with a single crack.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.05a
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• pp.370-375
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• 2004

Fatigue tests were carried out to find the fatigue characteristics in the super-long life range by using a cantilever type rotational bending fatigue test machine. Three kinds of specimen in bearing steels with the quenched and tempered in air (A and B, B: shot peened after heal treatment) and under vacuum conditions(C:non-shot peened)were tested in this study. S-N curves obtained from fatigue tests of C specimen tend to come dawn again in the super-long life range due to fish-eye type cracking, while most of A and B specimens fractured by surface defects such as scratches and slip lines. This duplex S-N behavior for the high strength steels have to be reviewed by the change of fracture modes.

• 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.63 no.4
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• pp.551-565
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• 2017

In this paper, an analytical approach is proposed for determining vibration characteristics of cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems. This method is based on the Timoshenko beam theory, transfer matrix method and numerical assembly method to obtain natural frequencies and mode shapes. Firstly, the beam is considered to be divided into several segments by spring-mass systems and support points, and four undetermined coefficients of vibration modal function are contained in each sub-segment. The undetermined coefficient matrices at spring-mass systems and pinned supports are obtained by using equilibrium and continuity conditions. Then, the overall matrix of undetermined coefficients for the whole vibration system is obtained by the numerical assembly technique. The natural frequencies and mode shapes of a cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems are obtained from the overall matrix combined with half-interval method and Runge-Kutta method. Finally, two numerical examples are used to verify the validity and reliability of this method, and the effects of cracks on the transverse vibration mode shapes and the rotational mode shapes are compared. The influences of the crack location, depth, position of spring-mass system and other parameters on natural frequencies of non-uniform continuous Timoshenko beam are discussed.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.125-138
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• 2018

This paper proposes a transfer matrix method for the bending vibration of two types of tapered beams subjected to axial force, and it is applied to analyze tapered beams with an edge or multiple edge open cracks. One beam type is assumed to be reduced linearly in the cross-section height along the beam length. The other type is a tapered beam in which the cross-section height and width with the same taper ratio is linearly reduced simultaneously. Each crack is modeled as two sub-elements connected by a rotational spring, and the method can evaluate the effect of cracking on the desired number of eigenfrequencies using a minimum number of subdivisions. Among the power series available for the solutions, the roots of the differential equation are computed using the Frobenius method. The computed results confirm the accuracy of the method and are compared with previously reported results. The effectiveness of the proposed methods is demonstrated by examining specific examples, and the effects of cracking and axial loading are carefully examined by a comparison of the single and double tapered beam results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.2
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• pp.131-143
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• 2013

Vibration condition monitoring of low-speed rotational slewing bearings is essential ever since it became necessary for a proper maintenance schedule that replaces the slewing bearings installed in massive machinery in the steel industry, among other applications. So far, acoustic emission(AE) is still the primary technique used for dealing with low-speed bearing cases. Few studies employed vibration analysis because the signal generated as a result of the impact between the rolling element and the natural defect spots at low rotational speeds is generally weak and sometimes buried in noise and other interference frequencies. In order to increase the impact energy, some researchers generate artificial defects with a predetermined length, width, and depth of crack on the inner or outer race surfaces. Consequently, the fault frequency of a particular fault is easy to identify. This paper presents the applications of empirical mode decomposition(EMD) and ensemble empirical mode decomposition(EEMD) for measuring vibration signals slewing bearings running at a low rotational speed of 15 rpm. The natural vibration damage data used in this paper are obtained from a Korean industrial company. In this study, EEMD is used to support and clarify the results of the fast Fourier transform(FFT) in identifying bearing fault frequencies.