• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.375-385
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• 2020

Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.

• Journal of the Korean Institute of Navigation
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• v.13 no.1
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• pp.1-10
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• 1989

Nowadays Hyperbolic Navigation System-LORAN, DECCA, OMEGA, OMEGA-is available on the ocean, and Spherical Navigation System, GPS (Global Positioning System) is operated partially. Hyperbolic Navigation System has the blind area near the base line extention because divergence rate of hyperbola is infinite theoretically. The Position Accuracy is differ from the cross angle of LOP although each LOP has the same error of quantity. GDOP(Geometric Dilution of Precisoin) is used to estimate the position accuracy according to the cross angle of LOP and LOP error. Hyperbola and ellipse are crossed at right angle everywhere. Hyperbola and ellipse are used to LOP in Rectangular Navigation System. The equation calculating the GDOP of rectangular Navigation System is induced and GDOP diagram is completed in this paper. A scheme that can improve the position accuracy in the blind area of Hyperboic Navigation System using the Rectangular Navigation System is proposed through the computer simulation.

• Journal of Korean Association for Spatial Structures
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• v.11 no.1
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• pp.87-95
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• 2011

This study presents the comparisons between the analysis results based on membrane theory and finite element analysis for the inverted umbrella-type hyperbolic paraboloid shell structure. The effects of the roof angle on the roof deflections, member forces of edge beams and ribs, and shell stress are also investigated with various roof angles. Results show that the membrane theory overestimates the member forces of edge beams and ribs. On the contrary, the shell stresses are underestimated in the membrane theory when compared to the results from the finite element analysis. The deflections of roof slabs by finite element analysis show drastic increasement as the roof angle decreases.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.133-138
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• 2014

We show that a compact immersed annular Bryant surface in $\mathbb{H}^3$ meeting two parallel horospheres in constant contact an gles is rotational.

• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.797-816
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• 2014

Cooling tower is analyzed as an assembly of layered nonlinear shell elements. Geometric representation of the shell is enabled through layered nonlinear shell elements to define the different layers of reinforcements and concrete by considering the material nonlinearity of each layer for the cooling tower shell. Modal analysis using Ritz vector analysis and nonlinear time history analysis by direct integration method have been carried out to study the effects of the inclination of the supporting columns of the cooling tower shell on its dynamic characteristics. The cooling tower is supported by I-type columns and ${\Lambda}$-type columns supports having the different inclination angles. Relevant comparisons of the dynamic response of the structural system at the base level (at the junction of the column and shell), throat level and at the top of the tower have been made. Dynamic response of the cooling tower is found to be significantly sensitive to the change of the inclination of the supporting columns. It is also found that the stiffness of the structure system increases with increase in inclination angle of the supporting columns, resulting in decrease of the period of the structural system. The participation of the stiffness of the tower in structural response of the cooling tower is fund to be dependent of the change in the inclination angle and even in the types of the supporting columns.

• Advances in nano research
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• v.7 no.5
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• pp.337-349
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• 2019

The size-dependent vibration analysis of a cross-/angle-ply laminated composite plate when embedded on the Pasternak elastic foundation and exposed to an in-plane magnetic field are investigated by adopting an analytical eigenvalue approach. The formulation, which is based on refined-hyperbolic-shear-deformation-plate theory in conjunction with the Eringen Nonlocal Differential Model (ENDM), is tested against considering problems for which numerical/analytical solutions available in the literature. The findings of this study demonstrated the role of magnetic field, size effect, elastic foundation coefficients, geometry, moduli ratio, lay-up numbers and fiber orientations on the nonlocal frequency of cross-/angle-ply laminated composite plates.

• Geomechanics and Engineering
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• v.9 no.3
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• pp.313-328
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• 2015

In the present study, a CPT-based p-y analysis method was proposed for offshore mono-piles embedded in sands. Static and cyclic loading conditions were both taken into account for the proposed method. The continuous soil profiling capability of CPT was an important consideration for the proposed method, where detailed soil profile condition with depth can be readily incorporated into the analysis. The hyperbolic function was adopted to describe the non-linear p-y curves. For the proposed hyperbolic p-y relationship, the ultimate lateral soil resistance $p_u$ was given as a function of the cone resistance, which is directly introduced into the analysis as an input data. For cyclic loading condition, two different cyclic modification factors were considered and compared. Case examples were selected to check the validity of the proposed CPT-based method. Calculated lateral displacements and bending moments from the proposed method were in good agreement with measured results for lateral displacement and bending moment profiles. It was observed the accuracy of calculated results for the conventional approach was largely dependent on the selection of friction angle that is to be adopted into the analysis.

• Journal of Korean Association for Spatial Structures
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• v.17 no.1
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• pp.49-58
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• 2017

The result of the previous work leads to the idea that the inner area of the hyperbolic shell generator should be minimized for the cooling tower with higher first natural frequency. In this study the inner area of the hyperbolic shell generator was graphically established under varying height of the throat and angle of the base lintel. From the graph, several shell geometries were selected and analysed in the aspect of the natural frequency. Three representative towers reinforced differently due to different first natural frequencies were analysed non-linearly and evaluated using a damage indicator based on the change of natural frequencies. The results demonstrated that the damage behaviour of the tower reinforced higher due to a lower first natural frequency was not necessarily advantageous than the others.

• KSTLE International Journal
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• v.1 no.2
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• pp.101-106
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• 2000

Variable displacement axial piston pumps are widely used for raising the energy level of the fluid in hydraulic systems. And the regulator is the device which regulates the discharge flow of the piston pump by controlling the swivel angle. The regulator receives the hydraulic pilot pressure and controls the pump output flow depending on the machine load and engine speed. This work deals with constant power control (horsepower control) in the design of a regulator by using a bent-axis type piston pump. In order to effectively use engine power, we must keep the horsepower from the engine to the pump constant. Therefore the regulator operates the constant power control. As a result, optimum power usage is obtained by accurately following the power hyperbola. This study focused on developing a simulation model of a regulator. First, the governing equations of the regulator are derived, and analysis is performed by computer simulation, which can identify significant parameters of regulator. As a result, the variation of the swivel angle, flow rate, hyperbolic curve, inner leakage and responsibility are simulated, and significant parameters of a regulator are identified.

• Geomechanics and Engineering
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• v.11 no.5
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• pp.639-655
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• 2016

The effect of particle breakage and intermediate principal stress ratio on the behaviour of crushable granular assemblies under true triaxial stress conditions is studied using the discrete element method. Numerical results show that the increase of intermediate principal stress ratio $b(b=({\sigma}_2-{\sigma}_3)/({\sigma}_1-{\sigma}_3))$ results in the increase of dilatancy at low confining pressures but the decrease of dilatancy at high confining pressures, which stems from the distinct increasing compaction caused by breakage with b. The influence of b on the evolution of the peak apparent friction angle is also weakened by particle breakage. For low relative breakage, the relationship between the peak apparent friction angle and b is close to the Lade-Duncan failure model, whereas it conforms to the Matsuoka-Nakai failure model for high relative breakage. In addition, the increasing tendency of relative breakage, calculated based on a fractal particle size distribution with the fractal dimension being 2.5, declines with the increasing confining pressure and axial strain, which implies the existence of an ultimate graduation. Finally, the relationship between particle breakage and plastic work is found to conform to a unique hyperbolic correlation regardless of the test conditions.