• Structural Engineering and Mechanics
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• v.82 no.1
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• pp.1-16
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• 2022

This work elaborately investigates the influences of the guideway geometry parameters and track irregularity on the dynamic performances of the suspended monorail vehicle-guideway system (SMVGS). Firstly, a spatial dynamic analysis model of the SMVGS is established by adopting ANSYS parameter design language. Then, the dynamic interaction between a vehicle with maximum design load and guideway is investigated by numerical simulation and field tests, revealing the vehicle-guideway dynamic features. Subsequently, the influences of the guideway geometry parameters and track irregularity on the dynamic performances of the SMVGS are analyzed and discussed in detail, and the reasonable ranges of several key geometry parameters of the guideway are also obtained. Results show that the vehicle-guideway dynamic responses change nonlinearly with an increase of the guideway span, and especially the guideway dynamic performances can be effectively improved by reducing the guideway span; based on a comprehensive consideration of all performance indices of the SMVGS, the deflection-span ratio of the suspended monorail guideway is finally recommended to be 1/1054~1/868. The train load could cause a large bending deformation of the pier, which would intensify the car-body lateral displacement and decrease the vehicle riding comfort; to well limit the bending deformation of the pier, its cross-section dimension is suggested to be more than 0.8 m×0.8 m. The addition of the track irregularity amplitude has small influences on the displacements and stress of the guideway; however, it would significantly increase the vehicle-guideway vibrations and rate of load reduction of the driving tyre.

• Research in Mathematical Education
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• v.11 no.3
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• pp.209-218
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• 2007

The purpose of this study is to create an interactive tool Geometry Player for geometric explorations. In designing this software, we referred to van Hiele's geometric learning theory of and Duval's cognitive comprehension theory of geometric figures. With Geometry Player, it is easy to construct and manipulate dynamic geometric figures. Teachers can easily present the dynamic process of geometric figures in class, and students can use it as a leaning tool to construct geometric concepts by themselves. It is hoped that Geometry Player can be a useful assistant for teachers and a nice partner for students. A brief introduction to Geometry Player and some application examples are included in this paper.

• The Mathematical Education
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• v.43 no.2
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• pp.177-186
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• 2004

In this paper, we introduce new functional definitions for school geometry based on DGS (dynamic geometry system) teaching-learning environment. For the vertices forming a geometric figure, we first consider the relationship between the independent vertices and dependent vertices, and using this relationship and educational considerations in DGS, we introduce functional definitions for the geometric figures in terms of its independent vertices. For this purpose, we design a new DGS called JavaMAL MicroWorld. Based on the needs of new definitions in DGS environment for the student's construction activities in learning geometry, we also design a new DGS based geometry curriculum in which the definitions of the school geometry are newly defined and reconnected in a new way. Using these funct onal definitions, we have taught the new geometry contents emphasizing the sequential expressions for the student's geometric activities.

• Journal of the Korean Society of Safety
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• v.11 no.3
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• pp.3-9
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• 1996

Dynamic fracture characteristics of Polycarbonate WL-RDCB specimen were investigated. The dynamic crack propagation velocities in these specimens were measured by using both high speed camera system and silver paint grid method developed and justified in the INHA Fracture Mechanics Laboratory. The measured crack propagation velocities were fed into the INSAMCR code(a dynamic finite element code which has been developed in the INBA Fracture Mechanics Laboratory) to extract the dynamic stress intensity factors. It has been confirmed that both dynamic crack arrest toughness and the static crack arrest toughness depend on both the geometry and the dynamic crack propagation velocity of specimens. The maximum dynamic crack propagation velocity of Polycarbonate WL-RDCB specimen was found to be dependent on the material property, geometry and the type of loading. The dynamic cracks in these Polycarbonate WL-RDCB specimens seemed to propagate in a successive manner, involving distinguished 'propagation-arrest-propagation-arrest' steps on the microsecond time scale. It was also found that the relat-ionship between dynamic stress intensity factor and dynamic crack propagation velocities might be represented by the typical '$\Gamma$'shape.

• Journal of the Korean School Mathematics Society
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• v.9 no.4
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• pp.459-479
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• 2006

The purpose of this study is to investigate the applicability of DGS(dynamic geometry software) for the assessment of reasoning ability and the influence of DGS on the process of assessing students' reasoning ability in middle school geometry. We developed items for assessing students' reasoning ability by using DGS in the connected form of 'construction - inductive reasoning - deductive reasoning'. And then, a case study was carried out with 5 students. We analyzed the results from 3 perspectives, that is, the assessment of students' construction ability, inductive reasoning ability, and justification types. Items can help students more precisely display reasoning ability Moreover, using of DGS will help teachers easily construct the assessment items of inductive reasoning, and widen range of constructing items.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.245-261
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• 1999

Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. But, teaching proof in school mathematics have been unsuccessful for many students. The traditional approach to proofs stresses formal logic and rigorous proof. Thus, most students have difficulties of the concept of proof and students' experiences with proof do not seem meaningful to them. However, different views of proof were asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth. These different views of justification need to be reflected in demonstrative geometry classes. The purpose of this study is to characterize the types of students' justification in demonstrative geometry classes taught using dynamic software. The types of justification can be organized into three categories : empirical justification, deductive justification, and authoritarian justification. Empirical justification are based on evidence from examples, whereas deductive justification are based logical reasoning. If we assume that a strong understanding of demonstrative geometry is shown when empirical justification and deductive justification coexist and benefit from each other, then students' justification should not only some empirical basis but also use chains of deductive reasoning. Thus, interaction between empirical and deductive justification is important. Dynamic geometry software can be used to design the approach to justification that can be successful in moving students toward meaningful justification of ideas. Interactive geometry software can connect visual and empirical justification to higher levels of geometric justification with logical arguments in formal proof.

• Journal of the Korean Institute of Gas
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• v.15 no.5
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• pp.31-36
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• 2011

In this paper, an analytical model of a cantilever beam having a midpoint load is considered for structural optimization and design. This involves creation of the geometry through a parametric study of all design variables. For this purpose, the optimization of the cantilever beam was elaborated in order to find the optimum geometry which minimizes its volume eventually for minimum weight by FEM (finite element method) analysis. Such geometry can be obtained by different combinations of width and height, so that the beam may have the same cross-sectional area, yet different dynamic behavior. So for optimum safe design, besides minimum volume it should have minimum vibration as well. In order to predict vibration, different dynamic analyses were performed simultaneously to identify the resonant frequencies and mode shapes belonging to the lowest three modes of vibration. Next, by introducing damping effects, the tip displacement and bending stress at the fixed end was evaluated under dynamic loads of varying frequency. Investigation of the results clearly shows that only structural analysis is not enough to predict the optimum values of dimension for safe design it must be aided by dynamic analysis as well.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.906-909
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• 2005

In this study, the dynamic flying characteristics of the worn head sliders are investigated theoretically due to the change in head geometry caused by head and disk contact. The film shapes can be approximated as taper- truncated cycloidal-flat film. Two-dimensional time dependent modified Reynolds equation included molecular slip effect are formulated with neglected the roughness effect. The motion of head slider was assumed to have two degree of freedom in this work. Finite difference approximation with Newton Raphson iterative technique and the fourth order Runge-Kutta method were implemented to obtain the transient response of the slider head with various change in head geometry numerically and compared with the transient response of the IBM3380 type head slider. The simulation results show the film shape has affects significantly on the static and dynamic characteristic of slider head in magnetic storage systems.

• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.375-384
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• 2007

As teachings that use the ICT are more popular, many studies on the dynamic geometry environment(DGE) are under way. An important factor emphasized in the studies is to practical use learning activities of learners. In this study, we first define the learning history data in DGE. Second we develop a prototype of the DGE that is able to collect and analyze the learning history data automatically. The environment enables not only to grasp leaning history but also to create and manage new learning objects.

• East Asian mathematical journal
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• v.37 no.4
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• pp.499-521
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• 2021

This research is devoted to investigate Omar Khayyām's geometric solution for the cubic equation using conic sections in the Medieval Islam as a useful alternative connecting logic geometry with analytic geometry at a secondary school. We also introduce Omar Khayyām's 25 cases classification of the cubic equation with all positive coefficients. Moreover we study 6 cases with 4 terms of 25 cubic equations and in particular we reinterpret geometric methods of solving in 2015 secondary Mathematics curriculum and visualize them by means of dynamic geometry software.