• Structural Engineering and Mechanics
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• v.31 no.4
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• pp.453-475
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• 2009

The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko beams on elastic soil is plenty, but the free vibration analysis of Reddy-Bickford beams on elastic soil with/without axial force effect using the Differential Transform Method (DTM) has not been investigated by any of the studies in open literature so far. In this study, the free vibration analysis of axially loaded Reddy-Bickford beam on elastic soil is carried out by using DTM. The model has six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments in this study. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton's principle and considering rotatory inertia. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. At first, the terms are found directly from the analytical solutions of the differential equations that describe the deformations of the cross-section according to the high-order theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The calculated natural frequencies of one end fixed and the other end simply supported Reddy-Bickford beam on elastic soil using DTM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed and the mode shapes are presented in graphs.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.297-302
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• 2007

Vibrating test of vehicle component can be possible in lab-based simulators instead of field testing owing to the development of technology in control algorithm as well as computational process. Currently, Multi-Axial Simulation Table(MAST) is recommended as a vibrating equipment, which excites a target component for 3-directional translation and rotation motion simultaneously and hence, vibrational condition can be fully approximated to that of real road test. But, the vibration-free performance of target component is not guaranteed with MAST system, which is only simulator subjective to the operator. Rather, the reliability of multi-axial vibration test is dependent on the quality of input profile which should cover the required severity of vibrating condition on target component. In this paper, multi-axial vibration testing methodology of vehicle component is presented here, from data acquisition of vehicle accelerations to the obtaining the input profile of MAST using severe data at proving ground. To compare the severity of vibration condition, between real road test and proving ground one, energy principle of equivalent damage is proposed to calculate energy matrices of acceleration data and then, it is determined the optimal combination of special events on proving ground which is equivalent to real road test at the aspects of vibration fatigue using sequential searching optimal algorithm. To explain the vibration methodology clearly, seat and door component of vehicle are selected as a example.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.764-769
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• 2006

Vibration test on MAST(multi axial simulation table) system has several advantage over one-axial vibration test that could simulate 6-DOF, 3-axial translation and 3-axial moment, at the same time. Since field vibration motion can be fully represented with 6-DOF, multi-axial vibration test on vehicle component is widely conducted in technical leading companies to make sure its fatigue performance in vibration environment. On the way to fulfill the process, editing technique of obtained field data is key issue to success a reliable vibration testing with MAST system. Since the original signals are not only too large to fulfill it directly, but all of the measured data is not guarantee its convergency on generating its driving files, editing technique of the original signals are highly required to make some events that should meet the equal fatigue damage on the target component In this paper, key technique on editing a field data feasible for MAST system is described based on energy method in vibration fatigue. To explain its technique explicitly, author first introduced a process on field data acquisition of two vehicle component and then, representing events are produced to keep up with the editing strategy about a energy method. In the final chapter, a time information regarding a vibration test on MAST system is derived from the energy data which is critical information to perform a vibration test.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.4
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• pp.64-69
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• 2002

Dynamic analysis of laminated beams with a embedded damping layer under tension or compression axial load is investigated. Improved Layer-Wise Zig-Zag Beam Theory and Interdependent Kinematic Relation using the governing equations of motion are incorporated to model the laminated beams with a damping layer and a corresponding beam zig-zag finite element is developed. Flexural frequencies and modal loss factors under tension or compression axial load are calculated based on Complex Eigenvalue Method. The effects of the axial tension and compression load on the frequencies and loss factors are discussed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.11
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• pp.1371-1378
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• 1999

Flow through turbomachinery has a very complex structure and Is Intrinsically unsteady. In addition, trend to highly loaded turbomachinery makes the flow extremely complex due to the interaction between rotor and stator. In this study, flows through UTRC LSRR turbine are numerically analyzed using 2 dimensional Navier-Stokes equations. The convective terms of the governing equations are discretized using the Van-Leer's FVS(Flux vector splitting) with an upwind TVD scheme. The conventional central differencing is used to discretize the diffusion terms on the finite volume. The accurate unsteady motion is achieved by using a 2nd order accurate, 3-point Euler implicit scheme. The quasi-conservative zonal scheme is used for calculating the flow variables on the zonal interface between the rotor and stator. The axial gap between stator and rotor has been configured in two variations, 15% and 65% of average chord length. The analysis program is validated using experimental results and the effect of axial gap is examined. The numerical analysis results are presented by time averaged pressure coefficient and pressure magnitude coefficient and compared with experimental results.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.759-769
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• 2017

The effect of central axial load on natural frequencies of various thin-walled beams, are investigated by some researchers using different methods such as finite element, transfer matrix and dynamic stiffness matrix methods. However, there are situations that the load will be off centre. This type of loading is called eccentric load. The effect of the eccentricity of axial load on the natural frequencies of asymmetric thin-walled beams is a subject that has not been investigated so far. In this paper, the mentioned effect is studied using exact dynamic stiffness matrix method. Flexure and torsion of the aforesaid thin-walled beam is based on the Bernoulli-Euler and Vlasov theories, respectively. Therefore, the intended thin-walled beam has flexural rigidity, saint-venant torsional rigidity and warping rigidity. In this paper, the Hamilton‟s principle is used for deriving governing partial differential equations of motion and force boundary conditions. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using ABAQUS software.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1008-1013
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• 2003

This paper concerns the structural characteristic analysis and evaluation on the hydrostatic guide way and feeding system of a high precision centerless grinder for machining ferrules. In order to realize the required accuracy of ferrules with sub-micron order, the axial stiffness and motion accuracy of feeding system have to become higher level than those of existing centerless grinders. Under these points of view, the physical prototype of feeding system consisted of steel bed, hydrostatic guide way and ballscrew feeding mechanism is designed and manufactured for trial. Experimental results show that the axial and vertical stiffnesses of the physical prototype are very low as compared with those design values. In this paper, to reveal the cause of these stiffness difference, the structural deformations on the virtual prototype of feeding system are analyzed based on the finite element method under experimental conditions. The simulated results illustrate that the deformation of front ballscrew support-bearing bracket is the main cause of reduction in the axial stiffness of feeding system, and the deflection of bed structure and the bending deformation of hydrostatic guide rails are the main causes of reduction in the vertical stiffness of feeding system.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.7
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• pp.896-903
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• 2004

This paper proposes the structural characteristic analysis and evaluation on the hydrostatic guide way and feeding system of a high-precision centerless grinder for machining ferrules. In order to realize the required accuracy of ferrules with sub-micron order, the axial stiffness and motion accuracy of feeding system have to become higher level than those of existing centerless grinders. Under these points of view, the physical prototype of feeding system composed of steel bed, hydrostatic guide way and ballscrew feeding mechanism is designed and manufactured for trial. Experimental results show that the axial and vertical stiffnesses of the physical prototype are very low as compared with those design values. In this paper, to reveal the cause of these stiffness difference, the structural deformations on the virtual prototype of feeding system are analyzed based on the finite element method under experimental conditions. The simulated results illustrate that the deformation of front ballscrew support-bearing bracket is the main cause of reduction in the axial stiffness of feeding system, and the deflection of bed structure and the bending deformation of hydrostatic guide rails are the main causes of reduction in the vertical stiffness of feeding system.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.111-120
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• 2018

This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

• Journal of the korean academy of Pediatric Dentistry
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• v.11 no.1
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• pp.13-24
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• 1984

To Study the eruption pattern of the maxillary first permanent molar, the author took 266 cases of true lateral cephalogram (Male; 137 cases, Female; 129 cases) from 3 to 7 years old children and observed the vertical change and axial change. The following results were obtained: 1. The angle of axial inclination of the maxillary first permanent molar to the F-H plane increased gradually from age 3 to 7, except for age 6 in both sexes. There was a slight reversal of this motion at age 6. 2. The distance from the cusp of the maxillary first permanent molar to the occlusal plane slightly decreased from age 3 to 5, and rapidly decreased from age 5 in both sexes. 3. The change of angle of the axial inclination resulted in the distance from the distobuccal cusp of the maxillary first permanent molar to the occlusal plane decreasing more than that from the mesiobuccal cusp of the maxillary first permanent molar to the occlusal plane in both sexes. 4. The eruption of the maxillary first permanent molar generally was found to be earlier in girls than boys.