• 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 The effect of the crack has been replaced by a rotational spring whose stiffness represents the increase in local flexibility as a result of the damage presence.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 Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.271-276
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• 2004

In this paper. dynamic behavior of the cracked beam under a moving mass is presented using the finite element method (FEM). Model accuracy is improved with the following consideration: (1) FE model with Timoshenko beam element (2) Additional flexibility matrix due to crack presence (3) Interaction forces between the moving mass and supported beam. The Timoshenko bean model with a two-node finite element is constructed based on Guyan condensation that leads to the results of classical formulations. but in a simple and systematic manner. The cracked section is represented by local flexibility matrix connecting two unchanged beam segments and the crack as modeled a massless rotational spring. The inertia force due to the moving mass is also involved with gravity force equivalent to a moving load. The numerical tests for various mass levels. crack sizes. locations and boundary conditions were performed.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.197.2-197.2
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• 2005

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.54-58
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• 2008

The structural intensities have been applied to understand a source point and the path of vibrational energy flows in interested structures by many researchers. In this paper, a feasibility study was carried out to investigate the characteristics of a damaged beam with a inflicted open crack using the structural intensities. The damaged beam was taken as a continuous system with equivalent bending stiffness and the flexural vibrations were only considered in numerical simulation and experiments. A four(4)-transducer array was used to measure the flexural vibrations of the beam and the structural intensities were estimated by means of cross spectral density method. As a result, the magnitude changes of the structural intensities could be observed in the vicinity of the damage location and a damage index was newly proposed to identify the damage zone. It has been confirmed that the measurement of the structural intensities was simple and effective method to find out the damage zone.

• Proceedings of the KWS Conference
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• 2010.05a
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• pp.71-71
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• 2010

SBD (Strain-based design) of pipe lines have gained world-wide attention in recent years. The present research aims to evaluate the fracture characteristics of API (America Petroleum Institute) SBD X100 girth weldment that typically applied for cold climate and deep water offshore, with the focus on the influence of heat input changing with 6kJ/cm and 10kJ/cm from GMAW (Gas Metal Arc Welding). At a low heat input at 6kJ/cm, the weld metal had Multi-phase matrix (Acicular ferrite + Banite + Martensite) that could fill up both fracture toughness and strength as reported previously. Also, the weld metal exhibited 859MPa YS (Yield strength), 108J impact toughness at $-40^{\circ}C$ and 0.52mm CTOD (Crack Tip Open Displacement) at $-10^{\circ}C$. These results can be satisfied with the requirement of API SBD X100 girth weldment and Alaska pipe line project.

• Journal of Welding and Joining
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• v.27 no.6
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• pp.25-30
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• 2009

SBD (Strain-based design) of pipe lines have gained world-wide attention in recent years. The present research aims to evaluate the fracture characteristics of API (America Petroleum Institute) SBD X100 girth weldment that typically applied for cold climate and deep water offshore, with the focus on the influence of heat input changing with 6kJ/cm and 10kJ/cm from GMAW (Gas Metal Arc Welding). At a low heat input at 6kJ/cm, the weld metal had Multi-phase matrix (Acicular ferrite + Banite + Martensite) that could fill up both fracture toughness and strength as reported previously. Also, the weld metal exhibited 859MPa YS (Yield strength), 108J impact toughness at $-40^{\circ}C$ and 0.52mm CTOD (Crack Tip Open Displacement) at $-10^{\circ}C$. These results can be satisfied with the requirement of API SBD X100 girth weldment and Alaska pipe line project.

• Journal of the Microelectronics and Packaging Society
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• v.15 no.2
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• pp.55-61
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• 2008

This paper shows quantitative reliability evaluations of a Bluetooth module through extending previous qualitative methods limited to structure reliability tests and solder joint reliability tests for Bluetooth modules. Accelerated Life Testing (ALT) of the modules using temperature difference in temperature cycling as an accelerated stress was conducted for quantitative reliability evaluation under field environment conditions. Lifetime distribution parameters were estimated using the failure times obtained through the ALT, and then Coffin-Manson model was implemented. Results of the ALT showed that the failure mode of the modules was open and the failure mechanisms are both crack and delamination. The ALT reproduced the failure mode and mechanisms of failed Bluetooth modules collected from the field. Further, a quantitative reliability evaluation method with respect to various temperature differences in temperature cycling was proposed in this paper. $B_{10}$ lifetime of the module for the temperature difference $70^{\circ}C$ using the proposed method would be estimated as about 4 years.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.3 s.246
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• pp.279-286
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• 2006

The main purpose of this paper is to apply differential transformation method(DTM) and generalized differential quadrature method(GDQM) to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. In this paper the concepts of DTM and GDQM were briefly introduced. The governing equation of motion of the beam with open cracks on elastic foundation is derived. The cracks are modeled by massless substitute spring. The effects of the crack location, size and the foundation constants, on the natural frequencies of the beam, are investigated. Numerical calculations are carried out and compared with previous published results.

• Structural Engineering and Mechanics
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• v.15 no.4
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• pp.437-449
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• 2003

The aim of this study is to develop an analytical model of a beam with open cracks and external strengthening which is able to predict its modal scheme components (natural frequencies and mode shapes). The model is valid as far as the excitation level is low enough not to activate non linear effects. The application field of the model are either the prediction of the efficiency of the reinforcement or the non destructive assessment of the structural properties. The degrees of freedom associated to the fault lips must be taken into account in order to introduce the effect of the external strengthening. In a first step, an analytical formulation of a beam with thin notches is proposed according to the references. The model is then extended to incorporate the strengthening consisting in a longitudinal stiffness applied in the vicinity of the cracks. In a second step, the analytical results are compared with these obtained from a finite element simulation.

• 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.