KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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In-plane Free Vibrations of Horseshoe Circular Arch

마제형 원호 아치의 면내 자유진동

  • 이병구 (원광대학교 토목환경공학과) ;
  • 오상진 (전남도립대학교 토목환경과) ;
  • 이태은 (원광대학교 토목환경공학과)
  • Received : 2013.12.30
  • Accepted : 2014.04.26
  • Published : 2014.08.01
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Abstract

This paper deals with in-plane free vibrations of the horseshoe circular arch. Simultaneous ordinary differential equations governing free vibration of the arch are derived with respect to the radial and tangential deformations. Particularly, differential equations are obtained under the arc length coordinate rather than the angular one in order to extend the horseshoe arch whose subtended angle is greater than ${\pi}$ radians. The differential equations are numerically solved for calculating the natural frequencies accompanying with the corresponding mode shapes. In parametric studies, effects of the rotatory inertia, slenderness ratio and circumferential arc length ratio on frequency parameters are extensively discussed.

이 연구는 마제형 원호 아치의 면내 저유진동에 관한 연구이다. 마제형 아치의 면내 자유진동을 지배하는 연립 상미분방정식을 곡률중심 및 접선 방향의 변위에 대하여 유도하였다. 특히 지배미분방정식은 반원보다 큰 중심각을 갖는 마제형 아치에 적용하기 위하여 각좌표보다는 곡선거리 좌표에 관한 미분방정식으로 유도하였다. 미분방정식을 수치해석하여 고유진동수와 진동형을 산출하였다. 변수연구를 통하여 회전관성, 세장비, 곡선길이비가 무차원 고유진동수에 미치는 영향을 분석하였다.

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References

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