• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.21 no.1
• /
• pp.66-73
• /
• 2011

This paper deals with free vibrations of the tapered beams with the constant surface area. The surface area of the objective beams are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear and parabolic ones. Ordinary differential equations governing free vibrations of such beams 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 beam parameters such as section ratio, surface area ratio, end constraint and taper type are reported in tables and figures. Especially, section ratios of the strongest beam are calculated, under which the maximum frequencies are achieved.

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

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.21 no.6
• /
• pp.570-579
• /
• 2011

This paper deals with free vibrations of the circular curved beams with constant volume, whose cross sectional shapes are the circular solid cross-sections. Volumes of the objective beam are always held in constant regardless shape functions of the cross-sectional radius. The shape functions are chosen as the linear, parabolic and sinusoidal ones. Ordinary differential equations governing free vibrations of such beam are derived and solved numerically for determining the natural frequencies. In numerical examples, the hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, relationships between frequency parameters and various beam parameters such as rise ratio, section ratio, elasticity ratio, volume ratio, slenderness ratio and taper type are reported in tables and figures.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.16 no.10 s.115
• /
• pp.1074-1081
• /
• 2006

This paper deals with the dynamic stability analysis of clamped-hinged columns with constant volume. Numerical methods are developed for solving natural frequencies and buckling loads of such columns, subjected to an axial compressive load. The parabolic taper with the regular polygon cross-section is considered, whose material volume and column length are always held constant. Differential equations governing both free vibrations and buckled shapes of such columns are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine natural frequencies and buckling loads, respectively. The numerical methods developed herein for computing natural frequencies and buckling loads are found to be efficient and robust. From the numerical results, dynamic stability regions, dynamic optimal shapes and configurations of strongest columns are reported in figures and tables.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2005.04a
• /
• pp.79-86
• /
• 2005

This paper deals with the static optimal shapes of simple beams which are subjected to a vertical point load. The area and second moment of inertia of the regular polygon cross-section of the tapered beams are determined, which have always same volume and same length for the parabolic taper. The differential equation governing the elastic curve is derived using the small deflection theory and solved numerically. By using the numerical results of deflections, rotations and bending stresses of such beams, the optimal shapes, namely, optimal section ratios, of the beams subjected to a single point load according to variation of load position parameters are determined and presented in the figures. Examples of the static optimal shapes for beams with a single load and multiple loads are reported. The design process of this study can be used directly for the minimum weight design of simple beams.

• Journal of Korean Society of Steel Construction
• /
• v.19 no.1
• /
• pp.99-106
• /
• 2007

This paper deals with the static and dynamic optimal shapes of both clamped columns with constant volume. The parabolic taper with the regular polygon cross-section is considered, whose material volume and column length are held constant. Numerical methods are developed for solving natural frequencies and buckling loads of columns subjected to an axial compressive load. Differential equations governing the free vibrations of such column are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine natural frequencies and buckling loads, respectively. From the numerical results, dynamic stability regions, dynamic optimal shapes and configurations of strongest columns are presented in figures and tables.

• Journal of electromagnetic engineering and science
• /
• v.1 no.1
• /
• pp.67-72
• /
• 2001

In this paper, the plano-convex lens antenna fed by a single patch is studied for a microwave remote-traffic monitoring sensor with constraints of small size and low cost. Measurement of an AUT (Antenna Under Test) involves the considerations of a triangular groove for matched layer and metallic shielding effects. A formulation for extracting the parameters of a piano-convex lens antenna, based on geometrical optics, is introduced using Fermat`s principle of the equi-phased ray condition. Teflon ($\varepsilon_{{\gamma}}$/ =2.0) is chosen as a material of a plano-convex lens antenna for adjustment of aberrations on the lens surfaces automatically. A fabricated plano-convex lens shows 3-dB beamwidth of 7.5 degree and side-lobe level of -29 dB with an aperture distribution of the parabolic-squared taper on pedestal. This lens supports easier integration with the planar microwave circuits by using a microstrip single patch as a primary feeder of the lens antenna.feeder of the lens antenna.

• Steel and Composite Structures
• /
• v.11 no.6
• /
• pp.435-454
• /
• 2011

Bonding composite materials to structural members for strengthening purpose has received a considerable attention in recent years. The major problem when using bonded FRP or steel plates to strengthen existing structures is the high interfacial stresses that may be built up near the plate ends which lead to premature failure of the structure. As a result, many researchers have developed several analytical methods to predict the interface performance of bonded repairs. In this paper, a numerical solution using finite - difference method is used to calculate the interfacial stress distribution in beams strengthened with FRP plate having a tapered ends with different thinning profiles. These latter, can significantly reduce the stress concentration. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both beam and bonded plate. Numerical results from the present analysis are presented to demonstrate the advantages of use the tapers in design of strengthened beams.

• Journal of the korean Society of Automotive Engineers
• /
• v.4 no.3
• /
• pp.18-23
• /
• 1982

최근 자동차의 고속경향화 추세는 많은 진전을 보고 있으며 또 앞으로도 많은 연구와 노력이 경주되어야 하리라고 본다. 그 가운데 하나로 스프링의 경량화는 대략 다음과 같은 3방향에서 연구되고 있다. 1) 복합재료, 즉 GFRP(carbon fiber reinforced plastics), 나아가서는 BFRP(born fiber reinforced plastics)의 탄선과 경량성을 이용한 스프링. 2) 형상, 즉 구조적인 면에서 스프링소재를 후판으로 사용함으로서, 다매물에서 단매 또는 소수 매의 거물곡선 스피링(parabolic taper spring)으로의 변진. 3) 고응력 사용, 즉 종래의 스프링량보다 높은 탄성을 가진 재료로써 스프링 응력을 톺게 사용할 수 있는 강종의 개발 등이다. 특히 3)의 탄성한을 \ulcorner이는 문제는 2)의 후재화와 더불어 열처리성, 가공성 등이 문제가 되어 이에 따라 신강종으로서의 변천을 강요하게 된다. 그러므로 국제경쟁력을 강화하기 위하여 각국 들이 활발하게 연구 및 개발을 추진하고 있는 현상이다. 우리나라의 경우 현재 제작기술은 어느 정동 많이 축적되고 있으나, 아직 R&D면에서는 점진적으로 추진되고 있다. 이와 같은 실정에서 자동차산업의 국제화와 더불어 종래 사용된 스프링강재의 재검토가 우리나라에서도 긴급히 필 요하게 되었따. 그 예로서 KS SPS5(JIS SUP9)의 강종이 종래 일본에서 자동차용스프링의 대 종을 이루고 있던것이 최근에는 SUP9A로 전환되고 있다. 이것은 SUP9A는 SUP9보다 기계적 성질이 우수하며, 또한 자동차분야의 세계제일위인 미국의 SAE5160재와 일지되고 있다. 그러므로 국제화 경향과 더불어 SUP9종은 SUP9A로 전환되고 있으므로서 우리 나라의 경우에도 자동차 스프링의 수출용은물론이고, 국내용에도 SUP9A에 해당하는 규격이 제정되고, 또한 빠른 전환이 필요하다고 본다. 이와 같은 국제적인 추세는 SUP6을 SUP7H종으로 더욱 향상된 것이 실용 화되고 있다. 아래에서 이에 대한 기계적 특성을 중심으로 검토키로 한다.

• Steel and Composite Structures
• /
• v.17 no.5
• /
• pp.601-621
• /
• 2014

Repairing and strengthening structural members by bonding composite materials have received a considerable attention in recent years. The major problem when using bonded FRP or steel plates to strengthen existing structures is the high interfacial stresses that may be built up near the plate ends which lead to premature failure of the structure. As a result, many researchers have developed several analytical methods to predict the interface performance of bonded repairs under various types of loading. In this paper, a numerical solution using finite - difference method (FDM) is used to calculate the interfacial stress distribution in beams strengthened with FRP plate having a tapered ends under thermal loading. Different thinning profiles are investigated since the later can significantly reduce the stress concentration. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both beam and bonded plate. The shear correction factor for I-section beams is also included in the solution. Numerical results from the present analysis are presented to demonstrate the advantages of use the tapers in design of strengthened beams.