• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.12
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• pp.979-985
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• 2002

The paper presents the dynamic stability of a vertical cantilevered pipe conveying fluid and haying translational linear spring supports. Real pipe systems may have some elastic hanger supports or other mechanical attached parts. which can be regarded as attached spring supports. Governing equations are derived by energy expressions, and numerical technique using Galerkin's method is applied to the equations of small motion of the pipe. Effects of spring supports on the dynamic stability of a vortical cantilevered pipe conveying fluid are fully investigated for various locations and spring constants of elastic supports.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.606-612
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• 1985

On the stability of the Beck's column with a tip mass, the influence of the characteristics of the springs at the fixed end of the column are studied. The equations of motion and boundary conditions of this system are established by using the Hamiton's principle. On the evaluation of the stability of the column, t he effect of the shear deformation and rotatory inertial is considered in calculation. For the maintenance of the stability of the column, it is proved that the constant of the translational spring at the fixed end must be very large while th magnitude of the constant of the rotational spring at the fixed end has no effect. When the constants of the springs at the fixed end are small, it is also proved that the influence of the moment of inertial of the tip mass on the stability of the column are decreased and for the translational spring the degree of the decrease is more and more. Therefore it is found that the characteristics of the springs at the fixed end are very effective elements for the stability of the column when the columns subjected to a compressive follower force are designed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.697-702
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• 2006

This paper deals with the free vibrations of immersed columns with soft base. The support condition of the column is represented by using a translational spring and a rotational spring. The eccentricity and rotatory inertia of the concentrated mass at the top are taken into account. In the governing equation for the free vibration of column, the density of immersed part was modified to account for the added fluid mass. The governing differential equations are solved numerically using the corresponding boundary conditions. Numerical results are presented to show the effects on the natural frequencies of non-dimensional system parameters: the mass density ratio of fluid to column, the ratio of fluid depth to span length, the ratio of tip mass to total column mass, the dimensionless mass moment of inertia, the eccentricity, the translation spring parameter, and the rotational spring parameter.

• 한국방재학회:학술대회논문집
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• 2007.02a
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• pp.307-311
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• 2007

In the case of the railway bridges, uplift forces were occurred at the edge of the segments when vehicular loads were applied. These forces made the compressive and tensile forces occur in the fastening system. Therefore, the structural analysis was performed to investigate the safety of fastening system which was modeled as one directional spring element. In this case, the stiffness of the spring element was obtained from experimental study which was conducted by compressive load. For that reason, to perform rational and exact structural analysis, the translational stiffness of the fastening system obtained from the experimental study applied the tensile load and the rotational stiffness should be considered because it was occurred the tensile force as well as the compressive force in fastening system. In this study, an elastic and inelastic experimental study was performed for six specimens. The translational stiffness along the vertical axis of rail and the rotational stiffness along the strong axis of rail were investigated. Also structural behavior of the fastening system was analyzed.

• Smart Structures and Systems
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• v.30 no.2
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• pp.173-181
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• 2022

The current paper presents a technique to detect crack in non-uniform cantilever-type pipe beams, that have step changes in the properties of their cross sections, restrained by a translational and rotational spring with a tip mass at the free end. An equation for estimating the natural frequencies for the non-uniform beams is derived using the boundary and continuity conditions, and an equivalent bending stiffness for cracked beam is applied to calculate the natural frequencies of the cracked beam. An experimental study for a step-changed non-uniform cantilever-type pipe beam restrained by bolts with a tip mass is carried out to verify the proposed method. The translational and rotational spring constants are updated using the neural network technique to the results of the experiment for intact case in order to establish a baseline model for the subsequent crack detection. Then, several numerical simulations for the specimen are carried out using the derived equation for estimating the natural frequencies of the cracked beam to construct a set of training patterns of a neural network. The crack locations and sizes are identified using the trained neural network for the 5 damage cases. It is found that the crack locations and sizes are reasonably well estimated from a practical point of view. And it is considered that the usefulness of the proposed method for structural health monitoring of the step-changed non-uniform cantilever-type pipe beam-like structures elastically restrained in the ground and have a tip mass at the free end could be verified.

• Structural Engineering and Mechanics
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• v.21 no.6
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• pp.713-735
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• 2005

Due to the complexity of mathematical expressions, the literature concerning the free vibration analysis of plates carrying multiple three-degree-of-freedom (dof) spring-mass systems is rare. In this paper, the three degrees of freedom (dof's) for a spring-mass system refer to the translational motion of its lumped mass in the vertical ($\bar{z}$) direction and the two pitching motions of its lumped mass about the two horizontal ($\bar{x}$ and $\bar{y}$) axes. The basic concept of this paper is to replace each three-dof spring-mass system by a set of equivalent springs, so that the free vibration characteristics of a rectangular plate carrying any number of three-dof spring-mass systems can be obtained from those of the same plate supported by the same number of sets of equivalent springs. Since the three dof's of the lumped mass for each three-dof spring-mass system are eliminated to yield a set of equivalent springs, the total dof of the entire vibrating system is not affected by the total number of the spring-mass systems attached to the rectangular plate. However, this is not true in the conventional finite element method (FEM), where the total dof of the entire vibrating system increases three if one more three-dof spring-mass system is attached to the rectangular plate. Hence, the computer storage memory required by using the presented equivalent spring method (ESM) is less than that required by the conventional FEM, and the more the total number of the three-dof spring-mass systems attached to the plate, the more the advantage of the ESM. In addition, since manufacturing a spring with the specified stiffness is much easier than making a three-dof spring-mass system with the specified spring constants and mass magnitude, the presented theory of replacing a three-dof spring-mass system by a set of equivalent springs will be also significant from this viewpoint.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.3
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• pp.495-501
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• 2001

In this paper, a new technique which models the joints characteristics through reduction of DOFs of structures with joints using component mode synthesis (CMS) method is proposed. Bolt joints are modeled by mass-spring systems. Also generalized mass and stiffness matrices for this models are introduced. Because bolt joints have influence on eigenvalues of structures, exact eigenvalues from modal test are used. The results show that the behaviors of structures with bolt joints depend to a large extent on the translational DOFs and not on rotational DOFs of mass and stiffness matrices of bolts. Furthermore it is confirmed that lumped mass-spring systems as models of bolt joints are effective models considering the facts that joint characteristics converged to constant values in some iterations and eignevalues from proposed method are in good agreement with ones from modal test.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.822-826
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• 2008

A linkage mechanism is a device to convert an input motion into a desired output motion. Traditional linkage mechanism designs are based on trial and error approaches so that size or shape changes of an original mechanism often result in improper results. In order to resolve these problems, an improved automatic mechanism synthesis method that determines the linkage type and dimensions by using an optimization method during the synthesis process has been proposed. For the synthesis, a planar linkage is modeled as a set of rigid blocks connected by zero-length translational springs with variable stiffness. In this study, the sizes of rigid blocks were also treated as design variables for more general linkage synthesis. The values of spring stiffness and the size of rigid block yielding a desired output motion at the end-effecter are found by using an optimization method.

• Journal of Korean Association for Spatial Structures
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• v.3 no.3 s.9
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• pp.95-103
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• 2003

Frame is one of the most commonly used structural systems for the resistance of applied loads. Many researchers have recently conducted their studies to investigate the effect of several parameters such as the connection flexibility, boundary condition of each support, beam-to-column stiffness ratio. These parameters play important roles on the characteristic behavior of frames. A simplified spring model is proposed to obtain the story drifts of frames with various beam-to-column connection stiffnesses in this research. A point bracing system with adequate spring stiffness is also suggested to establish the relationship between the applied load and the resisting translational spring stiffness within the limit state of story drift.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.3
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• pp.244-252
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• 2004

The theoretical method is developed to investigate the vibration characteristics for the partially fluid-filled continuous cylindrical shells with the intermediate supports. The intermediate supports are simulated by two types of artificial springs : the translational spring for the translation for each direction and the rotational spring for a rotation. The springs are continuously distributed along the circumferential direction. By allowing the spring stiffness to become very high compared to the stiffness of the structure, the rigid intermediate supports are approximated. In the theoretical procedure, the Love's thin shell theory is adopted to formulate the theoretical model. The frequency equation of the continuous cylindrical shell is derived by the Rayleigh-Ritz approach based on the energy method. Comparison and convergence studies are carried out to verify and establish the appropriate number of series term and the artificial spring stiffness to produce results with an acceptable order of accuracy. The effect of intermediate supports, their positions and fluid level on the natural frequencies and mode shapes are studied.