• Smart Structures and Systems
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• v.15 no.5
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• pp.1233-1252
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• 2015

This study investigates the problem of crack detection in post-buckled beam-type structures. The beam under the axial compressive force has a crack, assumed to be open and through the width. The crack, which is modeled by a massless rotational spring, divides the beam into two segments. The crack detection is considered as an optimization problem, and the weighted sum of the squared errors between the measured and computed natural frequencies is minimized by the bees algorithm. To find the natural frequencies, the governing nonlinear equations of motion for the post-buckled state are first derived. The solution of the nonlinear differential equations of the two segments consists of static and dynamic parts. The differential quadrature method along with an arc length strategy is used to solve the static part, while the same method is utilized for the solution of the linearized dynamic part and the extraction of the natural frequencies of the cracked beam. The investigation includes several numerical as well as experimental case studies on the post-buckled simply supported and clamped-clamped beams having open cracks. The results show that several parameters such as the amount of applied compressive force and boundary conditions influences the outcome of the crack detection scheme. The identification results also show that the crack position and depth can be predicted well by the presented method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.1085-1090
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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 beams with the moving masses. The influences of the velocities of moving masses, the distance between the moving masses and a crack have been studied on the dynamic behavior or a simply supported beam system by numerical method. no presence or crack results in large deflection of beam. 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. Totally, as the velocity of the moving masses and the distance between the moving masses are increased, the mid-span deflection of simply supported beam with the crack is decreased.

• 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.

• Structural Engineering and Mechanics
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• v.42 no.3
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• pp.409-424
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• 2012

Since relatively low elasticity modulus of the FRP materials results in lower natural frequencies, it is necessary to study the free vibration of FRP transmission poles. In this paper, the free vibration of tapered FRP transmission poles with thin-walled circular cross-section is investigated by a tapered beam element. To model the flexible joints of the modular poles, a rotational spring model is used. Modal analysis is performed for typical FRP poles with/without joint and they are also modeled by ANSYS commercial finite element software. There is a good correlation between the results of the tapered beam finite element model and those obtained from ANSYS as well as the existing experimental results. The effects of different geometries, material lay-ups, concentrated masses at the pole tip, and joint flexibilities are evaluated. Moreover, it is concluded that using tougher fibres at the inner and outer layers of the cross-section, results in higher natural frequencies, significantly.

• 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.

• Earthquakes and Structures
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• v.14 no.6
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• pp.525-535
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• 2018

This study presents a new beam-column model comprising material nonlinearity and joint flexibility to predict the nonlinear response of reinforced concrete structures. The nonlinear behavior of connections has an outstanding role on the nonlinear response of reinforced concrete structures. In presented research, the joint flexibility is considered applying a rotational spring at each end of the member. To derive the moment-rotation behavior of beam-column connections, the relative rotations produced by the relative slip of flexural reinforcement in the joint and the flexural cracking of the beam end are taken into consideration. Furthermore, the considered spread plasticity model, unlike the previous models that have been developed based on the linear moment distribution subjected to lateral loads includes both lateral and gravity load effects, simultaneously. To confirm the accuracy of the proposed methodology, a simply-supported test beam and three reinforced concrete frames are considered. Pushover and nonlinear dynamic analysis of three numerical examples are performed. In these examples the nonlinear behavior of connections and the material nonlinearity using the proposed methodology and also linear flexibility model with different number of elements for each member and fiber based distributed plasticity model with different number of integration points are simulated. Comparing the results of the proposed methodology with those of the aforementioned models describes that suggested model that only uses one element for each member can appropriately estimate the nonlinear behavior of reinforced concrete structures.

• 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.

• Aerospace Engineering and Technology
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• v.12 no.1
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• pp.105-110
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• 2013

The gimbal expansion joint for the pipe line of a liquid rocket engine undergoes high pressure and cyclic rotational displacement loadings. In present study, the moment analyses and tests of the internal-type gimbal expansion joint for the engine were performed. The moment components due to spring stiffness, friction and lateral force were obtained using a analytic method and their sums at low and high pressures were compared with the test results. Also, applying a $MoS_2$ dry film lubricant to the pin of a external hinge expansion joint, it is tested that the galling of the pin was removed and the friction coefficient was decreased for low pressures.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.1
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• pp.11-19
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• 2008

This paper proposes small VCM(voice coil motor) type, auto-focusing and zoom actuators for mobile information devices. In order to meet the large output displacement within small height restriction, the proposed auto-focusing actuator adopts curved suspensions, which are similar to a leaf-spring type suspension of optical disk drives. The sensitivity of design parameters on output displacement and dynamic performance is implemented using ANSYS (3D FEM tool) to determine the optimal geometry and stiffness of the curved suspensions. This paper also investigates a new zoom actuator without a suspension supporting a bobbin. The zoom actuator uses a moving rail and a stoper mechanism by generating rotational force at lens holder. Magnetic flux density of the zoom actuator are calculated by both the FEM and permeance method. Experiments using prototypes of the proposed focusing and zoom models show that both actuators meet the required displacement and performance.

• Earthquakes and Structures
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• v.7 no.3
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• pp.349-365
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• 2014

The dynamic response of structures under extremely short duration dynamic loads is of great concern nowadays. This paper investigates structures' response as well as the associated structural damage to explosive loads considering and ignoring the supporting soil flexibility effect. In the analysis, buildings are modeled by two alternate approaches namely, (1) building with fixed supports, (2) building with supports accounting for soil-flexibility. A lumped parameter model with spring-dashpot elements is incorporated at the base of the building model to simulate the horizontal and rotational movements of supporting soil. The soil flexibility for various shear wave velocities has been considered in the investigation. In addition, the influence of variation of lateral natural periods of building models on the obtained response and peak response time-histories besides damage indices has also been investigated under blast loads with different peak over static pressures. The Dynamic response is obtained by solving the governing equations of motion of the considered building model using a developed Matlab code based on the finite element toolbox CALFEM. The predicted results expressed in time-domain by the building model incorporating SSI effect are compared with the corresponding model results ignoring soil flexibility effect. The results show that the effect of surrounding soil medium leads to significant changes in the obtained dynamic response of the considered systems and hence cannot be simply ignored in damage assessment and response time-histories of structures where it increases response and amplifies damage of structures subjected to blast loads. Moreover, the numerical results provide an understanding of level of damage of structure through the computed damage indices.