In this paper, the physical model and governing equations of a shallow arch with a moving boundary were studied. A model with a moving boundary can be easily found in a long span retractable roof, and it corresponds to a problem of a non-cylindrical domain in which the boundary moves with time. In particular, a motion equation of a shallow arch having a moving boundary is expressed in the form of an integral-differential equation. This is expressed by the time-varying integration interval of the integral coefficient term in the arch equation with an un-movable boundary. Also, the change in internal force due to the moving boundary is also considered. Therefore, in this study, the governing equation was derived by transforming the equation of the non-cylindrical domain into the cylindrical domain to solve this problem. A governing equation for vertical vibration was derived from the transformed equation, where a sinusoidal function was used as the orthonormal basis. Terms that consider the effect of the moving boundary over time in the original equation were added in the equation of the transformed cylindrical problem. In addition, a solution was obtained using a numerical analysis technique in a symmetric mode arch system, and the result effectively reflected the effect of the moving boundary.

Abstract
1. 서론
2. 이동 경계를 갖는 얕은 아치
    2.1 이동 경계를 갖는 아치의 운동 방정식
    2.2 운동 방정식의 영역 변환
3. 정규직교기저와 지배방정식
4. 결론
References

• 손수덕(한국기술교육대학교 건축공학과 대우교수) | Shon Sudeok (Dept. of Architectural Eng., Koreatech University)
• 하준홍(한국기술교육대학교 교양학부 교수) | Ha Junhong (School of Liberal Arts, Koreatech University) Corresponding author
• 이승재(한국기술교육대학교 건축공학과, 교수) | Lee Seungjae (Dept. of Architectural Eng., Koreatech University)