• Journal of KSNVE
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• v.10 no.2
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• pp.353-360
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• 2000

Numerical methods are developed for calculating the natural frequencies and mode shapes of the tapered cantilever arches with variable curvature. The differential equations governing the free vibrations of such arches are derived and solved numerically, in which the effect of rotatory inertia is included. The parabolic shape is chosen as the arch with variable curvature while both the prime and quadratic arched members are considered as the tapered arch with variable curvature while both the prime and quadratic arched members are considered as the tapered arch. Comparisons the natural jfrequencies between this study and finite element method SAP 90 seve to validate the numerical method developed herein. The lowest four natural frequencies are reported as a function of four non-dimensional system parameters. The effects of both the rotatory inertia and cross-sectional shape are reported. Also, the typical mode shapes of stress resultants as well as the displacements are reported.

• Magazine of the Korean Society of Agricultural Engineers
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• v.19 no.3
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• pp.4462-4471
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• 1977

The governing differential equations for the tapered circular arch with fixed ends have been derived, and a numerical procedure for the solution of these equations have been developed. The governing differential equations were solved numerically by an initial value integration procedure and Shooting Methods for boundary value problems. The Rungekutta fourth order integration technique was used. The methods was programmed for a Cyber 73-18 computer System, and all esults were obtained on this computer. A detailed study has been made for a fixed arch with an angle of opening equal to 0.7 radian, and the results are presented in detail in tables and curves. It is hoped that the results presented herein is applied to the deformations of gives point from the tri-axial direction of tapered circular arch with fixed ends, bending moment, and torsional moment, and that at the same time results to be used for archwise structures in steel structure.

• The korean journal of orthodontics
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• v.35 no.1 s.108
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• pp.15-22
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• 2005

The Purpose of this study was to clarity morphological differences among mandibular dental arch forms in Korean malocclusion patients. The sample in this study consisted of 114 Class I. 119 Class II, and 135 Class III malocclusion cases. The most facial portions of 13 proximal contact areas were digitized from photocopied images of the mandibular dental arches. Clinical bracket points were calculated for each tooth based on the data on the mandibular tooth thickness. Four linear and two proportional measurements were undertaken The dental arches were classified into square. ovoid, and tapered forms to compare the frequency distributions. Our results suggested that there was no single arch form specific to any particular Angle classification or sex. It appeared to be the frequency of a particular arch form that varies among the Angle classifications. In comparison of arch measurements between male and female. there was no statistical difference except in the intermolar width. In comparison of arch size measurements among the different Angle classifications, there were statistically significant differences between Class I and Class III malocclusion groups and between Class II and Class III malocclusion groups. In comparison oi frequency distribution of arch forms in Class I and III malocclusion groups, the square form demonstrated the highest distribution followed by the ovoid and tapered forms in that order. In the Class II malocclusion group, the square form showed the highest distribution. followed by the tapered and ovoid forms in that order There was no statistical difference in the frequency distribution of arch forms between male and female groups.

• The korean journal of orthodontics
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• v.34 no.6 s.107
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• pp.481-487
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• 2004

The purpose of this study was to clarify morphologic characteristics between mandibular clinical arch forms in Koreans with normal occlusions. The study included data from 102 Koreans. The most facial portion of 13 proximal contact areas was digitized from photocopied images of the mandibular dental arches. Clinical bracket points were calculated for each tooth based on mandibular tooth thickness data. Four linear and two proportional measurements were taken. The dental arches were classified into ovoid, square and tapered forms. The frequency distributions of the three mandibular arch form classifications were determined and compared between male and female subjects. No significant differences in arch form size were found between the sexes. However, there were a few differences in molar width. It was useful to classify mandibular clinical arch forms present in normal occlusion samples into ovoid, square and tapered categories. The frequency of the ovoid form was the highest, and that of the square form was the second highest. The tapered arch form was found in less than 10 percent of subjects. No significant differences in their frequency distributions and dimensions were shown between males and females.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.2
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• pp.144-152
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• 2010

This paper deals with free vibrations of the tapered circular arches with constant volume, whose cross sectional shape is the solid regular polygon. Volumes of the objective arches are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear, parabolic and sinusoidal ones. Ordinary differential equations governing free vibrations of such arches are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various arch parameters such as rise ratio, section ratio, side number, volume ratio and taper type are reported in tables and figures.

• The korean journal of orthodontics
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• v.41 no.4
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• pp.288-296
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• 2011

Objective: The purposes of this study were to evaluate the relationship between the dental and basal arch forms; to analyze their differences in the tapered, ovoid, and square arch forms in normal occlusion by using three-dimensional (3D) virtual models; and to test the hypothesis that the overjet and maxillomandibular basal arch width difference have a significantly positive correlation. Methods: Seventy-seven normal occlusion plaster casts were examined by 3D scanning. Facial axis (FA) and WALA points were digitized using the Rapidform 2006 software. The dimensions of the dental and basal arches and the overjet were measured. The samples were classified into 3 groups according to arch forms: tapered (n = 20), ovoid (n = 20), and square (n = 37). Analysis of variance (ANOVA) was used to compare the dental and basal arch dimensions. The Pearson correlation coefficients between the intercanine as well as the intermolar widths at the FA and WALA points were calculated. Results: With regard to the basal arch dimensions, the tapered arch form showed a larger mandibular intermolar depth than the ovoid. Strong correlations were noted between the basal and dental intermolar widths in both the upper and lower arches (r = 0.83 and 0.85, respectively). Moderate correlation was found between the upper and lower intercanine widths (r = 0.65 and 0.48, respectively). Conclusions: The 3 dental arch form groups differed only in some dimensions of the skeletal arch. Moderate correlations were found between the basal and dental intercanine widths. These findings suggest that the basal arch may not be a principle factor in determining the dental arch form.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.223-226
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• 2007

In current specification, modification factor(B) for web-tapered beam is used to account for the stress gradient and the restraining effect for adjacent spans. However, because these effects are considered together in modification factor, this paper revaluate the accuracy of the modification factor used in current specification. Also this paper investigate the flexural torsional buckling strength of laterally fixed thin-walled arch with doubly symmetric section using the analytical and numerical method. From this investigate the concept of effective length to consider the out-of-plane boundary condition for straight column or beam is not applicate for the flexural-torsional buckling of laterally fixed arches.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.846-851
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• 2003

The differential equations governing free, in-plane vibrations of non-circular arches with non-uniform cross-section, including the effects of rotatory inertia, shear deformation and axial deformation, are derived and solved numerically to obtain frequencies. The lowest four natural frequencies are calculated for the prime parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. Three general taper types for rectangular section are considered. A wide range of arch rise to span length ratios, slenderness ratios, and section ratios are considered. The agreement with results determined by means of a finite element method is good from an engineering viewpoint.

• The korean journal of orthodontics
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• v.40 no.5
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• pp.334-341
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• 2010

Objective: The purpose of this study was to evaluate morphologic differences in the mandibular arch between Egyptian and Korean subjects. Methods: The Egyptian sample consisted of 94 mandibular casts (35 Class I, 32 Class II and 27 Class III). The Korean sample consisted of 462 mandibular casts (114 Class I, 119 Class II, and 135 Class III). The most facial portion of 13 proximal contact areas was digitized from photocopied images of the mandibular dental arches. Clinical bracket points were calculated for each tooth. The subjects were grouped according to arch form to compare the frequency distribution of the 3 arch forms between the ethnic groups in each Angle classification. Results: Egyptians had significantly narrower intermolar and intercanine widths ($p$ < 0.001), and shallower intermolar and intercanine depths ($p$ < 0.001) than Koreans. There was an even frequency distribution of the 3 arch forms within the Egyptian group ($p$ = 0.46). However, in the Korean group, the most frequent arch form was the square arch form (46.7%), while the frequency of the tapered arch form was significantly lower (18.8%). Conclusions: These results might provide helpful information in evaluating morphologic differences between ethnic groups in selection of preformed superelastic archwires.

• Structural Engineering and Mechanics
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• v.45 no.4
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• pp.569-594
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• 2013

The free vibration of axially functionally graded tapered arches including shear deformation and rotatory inertia are studied through solving the governing differential equation of motion. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal arches with hinged-hinged, hinged-clamped and clamped-clamped end restraints. In this study Differential Quadrature element of lowest order (DQEL) or Lagrangian Interpolation technique is applied to solve the problems. Three general taper types for rectangular section are considered. The lowest four natural frequencies are calculated and compared with the published results.